leetcode.cpp

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#include "leetcode.h"
#include "templates.h"
#include <algorithm>
#include <bit>
#include <bitset>
#include <climits>
#include <cmath>
#include <cstring>
#include <numeric>
#include <queue>
#include <regex>
#include <sstream>
#include <stack>
#include <unordered_set>
 
using namespace std;
 
namespace leetcode {
    bool TreeNode::operator==(const TreeNode &node) const {
        if(this->left != nullptr && node.left == nullptr) {
            return false;
        }
        if(this->left == nullptr && node.left != nullptr) {
            return false;
        }
        if(this->right != nullptr && node.right == nullptr) {
            return false;
        }
        if(this->right == nullptr && node.right != nullptr) {
            return false;
        }
        if(this->left != nullptr && node.left != nullptr && *this->left != *node.left) {
            return false;
        }
        if(this->right != nullptr && node.right != nullptr && *this->right != *node.right) {
            return false;
        }
        return this->val == node.val;
    }
 
    bool TreeNode::operator!=(const TreeNode &node) const { return !(*this == node); }
 
    namespace concatenated_words {
        vector<string> Solution::findAllConcatenatedWordsInADict(vector<string> &words) {
            sort(words.begin(), words.end(), [&](const string &a, const string &b) { return a.size() < b.size(); });
            auto ans  = vector<string>();
            auto node = TrieNode(0);
            for(const string &word: words) {
                if(word.length() == 0) {
                    continue;
                }
                if(node.dfs(&node, word, 0, false)) {
                    ans.push_back(word);
                } else {
                    node.insert(word);
                }
            }
            return ans;
        }
 
        TrieNode::TrieNode(char ch) {
            this->ch     = ch;
            this->is_end = false;
        }
 
        void TrieNode::insert(const string &str) {
            auto *node = this->nexts[str[0] - 'a'];
            if(node == nullptr) {
                node                      = new TrieNode(str[0]);
                this->nexts[str[0] - 'a'] = node;
            }
            if(str.length() == 1) {
                node->is_end = true;
                return;
            }
            return node->insert(str.substr(1));
        }
 
        bool TrieNode::dfs(TrieNode *root, const string &str, int start, bool flag) const {
            if(this->ch == 0) {
                //根节点
                const auto *const node = this->nexts[str[start] - 'a'];
                if(node == nullptr) {
                    return false;
                }
                return node->dfs(root, str, start, flag);
            }
            //非根节点
            //到一个单词结束处
            if(this->is_end) {
                if(start == str.length() - 1) {
                    return flag;
                }
                const auto res = root->dfs(root, str, start + 1, true);
                if(res) {
                    return true;
                }
            }
            const TrieNode *node = nullptr;
            if(str[start + 1] - 'a' >= 0) {
                node = this->nexts[str[start + 1] - 'a'];
            }
            return node != nullptr && node->dfs(root, str, start + 1, flag);
        }
    }// namespace concatenated_words
 
    namespace excel_sheet_column_number {
        int Solution::titleToNumber(const std::string &columnTitle) {
            int sum    = 0;
            int length = static_cast<int>(columnTitle.length());
            for(const char c: columnTitle) {
                sum += static_cast<int>(static_cast<double>(c - 'A' + 1) * pow(26, length-- - 1));
            }
            return sum;
        }
    }// namespace excel_sheet_column_number
 
    namespace excel_sheet_column_title {
        string Solution::convertToTitle(int columnNumber) {
            auto ans   = string();
            bool round = false;
            while(columnNumber != 0) {
                char ch = 0;
                if(round) {
                    ch    = static_cast<char>(columnNumber % 26 + 63);
                    round = false;
                } else {
                    ch = static_cast<char>(columnNumber % 26 + 64);
                }
                if(ch == '@' && columnNumber >= 26) {
                    ch    = 'Z';
                    round = true;
                } else if(ch == '?' && columnNumber >= 26) {
                    ch    = 'Y';
                    round = true;
                }
                if('A' <= ch && ch <= 'Z') {
                    ans.insert(0, 1, ch);
                }
                columnNumber /= 26;
            }
            return ans;
        }
    }// namespace excel_sheet_column_title
 
    namespace majority_element {
        Solution::Solution() { this->m = std::map<int, int>(); }
 
        int Solution::majorityElement(vector<int> &nums) {
            for(int i: nums) {
                if(m.contains(i)) {
                    m[i] = m[i] + 1;
                    if(m[i] > nums.size() / 2) {
                        return i;
                    }
                } else {
                    m[i] = 1;
                }
            }
            return 0;
        }
    }// namespace majority_element
 
    namespace count_special_quadruplets {
        int Solution::countQuadruplets(vector<int> &nums) {
            int sum = 0;
            for(int i = 3; i < nums.size(); i++) {
                for(int j = 0; j < i - 2; j++) {
                    if(j == i) {
                        continue;
                    }
                    for(int k = j + 1; k < i - 1; k++) {
                        if(k == i) {
                            continue;
                        }
                        for(int l = k + 1; l < i; l++) {
                            if(l == i) {
                                continue;
                            }
                            if(nums[k] + nums[j] + nums[l] == nums[i]) {
                                sum++;
                            }
                        }
                    }
                }
            }
            return sum;
        }
    }// namespace count_special_quadruplets
 
    namespace hand_of_straights {
        bool Solution::isNStraightHand(vector<int> &hand, int groupSize) {
            if(hand.size() % groupSize != 0) {
                return false;
            }
            if(groupSize == 1) {
                return true;
            }
            sort(hand.begin(), hand.end());
            const auto len = hand.size() / groupSize;
            for(int i = 0; i < len; i++) {
                int current = *hand.begin();
                hand.erase(hand.begin());
                for(int j = 1; j < groupSize; j++) {
                    auto next = find(hand.begin(), hand.end(), current + 1);
                    if(next == hand.end()) {
                        return false;
                    }
                    current = *next;
                    hand.erase(next);
                }
            }
            return true;
        }
    }// namespace hand_of_straights
 
    namespace perfect_number {
        bool Solution::checkPerfectNumber(int num) {
            int sum = 0;
            int max = num;
            for(int i = 1; i < max; i++) {
                if(num % i == 0) {
                    sum += i;
                    if(i != 1) {
                        sum += num / i;
                    }
                    max = num / i;
                }
            }
            return sum == num;
        }
    }// namespace perfect_number
 
    namespace convert_bst_to_greater_tree {
        TreeNode *Solution::convertBST(TreeNode *root) {
            if(root == nullptr) {
                return nullptr;
            }
            FriendTreeNode *sum = copy(root);
            get_sum(sum);
            sum->val = sum->sum - (sum->left == nullptr ? 0 : sum->left->sum);
            convert(sum);
            return root;
        }
 
        FriendTreeNode *Solution::copy(TreeNode *node) {
            auto *ret = new FriendTreeNode(node->val, node);
            if(node->left != nullptr) {
                ret->left = copy(node->left);
            }
            if(node->right != nullptr) {
                ret->right = copy(node->right);
            }
            return ret;
        }
 
        void Solution::get_sum(FriendTreeNode *node) {
            if(node->left != nullptr) {
                get_sum(node->left);
                node->sum += node->left->sum;
            }
            if(node->right != nullptr) {
                get_sum(node->right);
                node->sum += node->right->sum;
            }
        }
 
        void Solution::convert(FriendTreeNode *sum_node) {
            if(sum_node->right != nullptr) {
                sum_node->right->val = sum_node->val - sum_node->friend_node->val -
                                       (sum_node->right->left == nullptr ? 0 : sum_node->right->left->sum);
                convert(sum_node->right);
            }
            if(sum_node->left != nullptr) {
                sum_node->left->val = sum_node->val + sum_node->left->friend_node->val +
                                      (sum_node->left->right == nullptr ? 0 : sum_node->left->right->sum);
                convert(sum_node->left);
            }
            sum_node->friend_node->val = sum_node->val;
        }
    }// namespace convert_bst_to_greater_tree
 
    namespace convert_1d_array_into_2d_array {
        vector<vector<int>> Solution::construct2DArray(vector<int> &original, int m, int n) {
            if(original.size() != static_cast<unsigned long long>(m) * static_cast<unsigned long long>(n)) {
                return {};
            }
            auto ans  = vector<vector<int>>();
            int count = 0;
            for(int i = 0; i < m; i++) {
                auto row = vector<int>();
                for(int j = 0; j < n; j++) {
                    row.push_back(original[count++]);
                }
                ans.push_back(row);
            }
            return ans;
        }
    }// namespace convert_1d_array_into_2d_array
 
    namespace elimination_game {
        int Solution::lastRemaining(int n) {
            int num_amount = n;
            int loop_cnt   = 0;
            int a0         = 1;//初项
            int d          = 1;//差
            while(num_amount != 1) {
                //剩下的数目不为1时
                if(num_amount % 2 == 1) {
                    // 奇数个数字
                    a0 = a0 + d;
                } else if(num_amount % 2 == 0) {
                    // 偶数个数字
                    const bool left_to_right = loop_cnt % 2 == 0;
                    if(left_to_right) {
                        a0 = a0 + d;
                    } else {
                        a0 = a0;
                    }
                }
                loop_cnt++;
                d *= 2;
                num_amount /= 2;
            }
            return a0;
        }
    }// namespace elimination_game
 
    namespace check_if_all_as_appears_before_all_bs {
        bool Solution::checkString(const string &s) {
            bool flag = true;
            for(const char ch: s) {
                if(ch == 'a') {
                    if(!flag) {
                        return false;
                    }
                } else if(ch == 'b') {
                    flag = false;
                }
            }
            return true;
        }
    }// namespace check_if_all_as_appears_before_all_bs
 
    namespace number_of_laser_beams_in_a_bank {
        int Solution::numberOfBeams(vector<string> &bank) {
            if(bank.size() == 1) {
                return 0;
            }
            int count   = 0;
            int i       = 0;
            int count_i = deviceCount(bank[i]);
            int j       = 1;
            while(i < j && i < bank.size() && j < bank.size()) {
                if(deviceCount(bank[j]) == 0) {
                    j++;
                    continue;
                }
                const int count_j = deviceCount(bank[j]);
                count += count_i * count_j;
                count_i = count_j;
                i       = j;
                j++;
            }
            return count;
        }
 
        int Solution::deviceCount(const string &str) {
            int count = 0;
            for(const char c: str) {
                if(c == '1') {
                    count++;
                }
            }
            return count;
        }
    }// namespace number_of_laser_beams_in_a_bank
 
    namespace destroying_asteroids {
        bool Solution::asteroidsDestroyed(int mass, vector<int> &asteroids) {
            long long m = mass;
            sort(asteroids.begin(), asteroids.end());
            for(const int i: asteroids) {
                if(m < i) {
                    return false;
                }
                m += i;
            }
            return true;
        }
    }// namespace destroying_asteroids
 
    /*namespace maximum_employees_to_be_invited_to_a_meeting {
        int Solution::maximumInvitations(vector<int>& favorite) {
            int n = static_cast<int>(favorite.size());
            vector<vector<int >> g(n), rg(n); // rg 为图 g 的反图
            vector<int> deg(n); // 图 g 上每个节点的入度
            for (int v = 0; v < n; ++v) {
                int w = favorite[v];
                g[v].emplace_back(w);
                rg[w].emplace_back(v);
                ++deg[w];
            }
 
            // 拓扑排序，剪掉图 g 上的所有树枝
            queue<int> q;
            for (int i = 0; i < n; ++i) {
                if (deg[i] == 0) {
                    q.emplace(i);
                }
            }
            while (!q.empty()) {
                int v = q.front();
                q.pop();
                for (int w : g[v]) {
                    if (--deg[w] == 0) {
                        q.emplace(w);
                    }
                }
            }
 
            // 寻找图 g 上的基环
            vector<int> ring;
            vector<int> vis(n);
 
            function<void(int)> dfs = [&](int v) {
                vis[v] = true;
                ring.emplace_back(v);
                for (int w : g[v]) {
                    if (!vis[w]) {
                        dfs(w);
                    }
                }
            };
 
            // 通过反图 rg 寻找树枝上最深的链
            int max_depth = 0;
 
            function<void(int, int, int)> rdfs = [&](int v, int fa, int depth) {
                max_depth = max(max_depth, depth);
                for (int w : rg[v]) {
                    if (w != fa) {
                        rdfs(w, v, depth + 1);
                    }
                }
            };
 
            int max_ring_size = 0, sum_chian_size = 0;
            for (int i = 0; i < n; ++i) {
                if (!vis[i] && deg[i]) { // 遍历基环上的点（拓扑排序后入度不为 0）
                    ring.resize(0);
                    dfs(i);
                    int sz = static_cast<int>(ring.size());
                    if (sz == 2) { // 基环大小为 2
                        int v = ring[0], w = ring[1];
                        max_depth = 0;
                        rdfs(v, w, 1);
                        sum_chian_size += max_depth; // 累加 v 这一侧的最长链的长度
                        max_depth = 0;
                        rdfs(w, v, 1);
                        sum_chian_size += max_depth; // 累加 w 这一侧的最长链的长度
                    }
                    else {
                        max_ring_size = max(max_ring_size, sz); // 取所有基环的最大值
                    }
                }
            }
            return max(max_ring_size, sum_chian_size);
        }
    }*/
    namespace day_of_the_week {
        string Solution::dayOfTheWeek(int day, int month, int year) {
            const string output[]   = {"Sunday", "Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday"};
            const int dayofmonths[] = {31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};
            int count               = 5;
            count += (year - 1971) * 365;
            count += (year - 1) / 4 - 1970 / 4;
            for(int m = 0; m < month - 1; m++) {
                count += dayofmonths[m];
            }
            if(month > 2 && year % 4 == 0 && year % 100 != 0) {
                count++;
            }
            count += day - 1;
            count %= 7;
            return output[count];
        }
    }// namespace day_of_the_week
 
    namespace cat_and_mouse {
        int Solution::catMouseGame(vector<vector<int>> &graph) {
            this->n     = graph.size();
            this->graph = graph;
            memset(dp, -1, sizeof dp);
            return getResult(1, 2, 0);
        }
 
        int Solution::getResult(int mouse, int cat, int turns) {
            if(turns == n * 2) {
                return DRAW;
            }
            if(dp[mouse][cat][turns] < 0) {
                if(mouse == 0) {
                    dp[mouse][cat][turns] = MOUSE_WIN;
                } else if(cat == mouse) {
                    dp[mouse][cat][turns] = CAT_WIN;
                } else {
                    getNextResult(mouse, cat, turns);
                }
            }
            return dp[mouse][cat][turns];
        }
 
        void Solution::getNextResult(int mouse, int cat, int turns) {
            const int curMove       = turns % 2 == 0 ? mouse : cat;
            const int defaultResult = curMove == mouse ? CAT_WIN : MOUSE_WIN;
            int result              = defaultResult;
            for(int next: graph[curMove]) {
                if(curMove == cat && next == 0) {
                    continue;
                }
                const int nextMouse  = curMove == mouse ? next : mouse;
                const int nextCat    = curMove == cat ? next : cat;
                const int nextResult = getResult(nextMouse, nextCat, turns + 1);
                if(nextResult != defaultResult) {
                    result = nextResult;
                    if(result != DRAW) {
                        break;
                    }
                }
            }
            dp[mouse][cat][turns] = result;
        }
    }// namespace cat_and_mouse
 
    namespace replace_all_s_to_avoid_consecutive_repeating_characters {
        string Solution::modifyString(string s) {
            for(int i = 0; i < s.size(); i++) {
                if(s[i] == '?') {
                    for(char ch = 'a'; ch < 'z' + 1; ch++) {
                        if(0 <= i - 1 && s[i - 1] == ch) {
                            continue;
                        }
                        if(i + 1 < s.size() && s[i + 1] == ch) {
                            continue;
                        }
                        s[i] = ch;
                        break;
                    }
                }
            }
            return s;
        }
    }// namespace replace_all_s_to_avoid_consecutive_repeating_characters
 
    namespace simplify_path {
        string Solution::simplifyPath(const string &path) {
            auto *const str_cpy = new char[path.size() + 1];
            memcpy(str_cpy, path.c_str(), path.size() + 1);
            auto *next = strtok(str_cpy, "/");
            auto stck  = deque<string>();
            while(next != nullptr) {
                auto nextstr = string(next);
                if(nextstr == "..") {
                    if(!stck.empty()) {
                        stck.pop_back();
                    }
                    next = strtok(nullptr, "/");
                    continue;
                }
                if(nextstr == ".") {
                    next = strtok(nullptr, "/");
                    continue;
                }
                stck.emplace_back(next);
                next = strtok(nullptr, "/");
            }
            auto oss = ostringstream();
            if(stck.empty()) {
                oss << '/';
            } else {
                while(!stck.empty()) {
                    auto pname = stck.front();
                    oss << '/' << pname;
                    stck.pop_front();
                }
            }
            delete[] str_cpy;
            return oss.str();
        }
    }// namespace simplify_path
 
    namespace maximum_nesting_depth_of_the_parentheses {
        int Solution::maxDepth(const string &s) {
            int max     = 0;
            int current = 0;
            for(const char ch: s) {
                if(ch == '(') {
                    current++;
                } else if(ch == ')') {
                    current--;
                }
                if(max < current) {
                    max = current;
                }
            }
            return max;
        }
    }// namespace maximum_nesting_depth_of_the_parentheses
 
    namespace gray_code {
        vector<int> Solution::grayCode(int n) {
            vector<int> ret(1 << n);
            for(int i = 0; i < ret.size(); i++) {
                ret[i] = i >> 1 ^ i;
            }
            return ret;
        }
    }// namespace gray_code
 
    namespace check_if_every_row_and_column_contains_all_numbers {
        bool Solution::checkValid(vector<vector<int>> &matrix) {
            const unsigned int n = matrix.size();
            for(int i = 0; i < n; i++) {
                auto *const row = new bool[n + 1];
                memset(row, 1, (n + 1) * sizeof(bool));
                for(int j = 0; j < n; j++) {
                    if(!row[matrix[i][j]]) {
                        delete[] row;
                        return false;
                    }
                    row[matrix[i][j]] = false;
                }
                delete[] row;
            }
 
            for(int j = 0; j < n; j++) {
                auto *const column = new bool[n + 1];
                memset(column, 1, (n + 1) * sizeof(bool));
                for(int i = 0; i < n; i++) {
                    if(!column[matrix[i][j]]) {
                        delete[] column;
                        return false;
                    }
                    column[matrix[i][j]] = false;
                }
                delete[] column;
            }
            return true;
        }
    }// namespace check_if_every_row_and_column_contains_all_numbers
 
    namespace minimum_swaps_to_group_all_1s_together_ii {
        int Solution::minSwaps(vector<int> &nums) {
            int onecount = 0;
            for(const int num: nums) {
                if(num == 1) {
                    onecount++;
                }
            }
            if(onecount == 0) {
                return 0;
            }
 
            int zerocount = 0;
            for(int i = 0; i < onecount; i++) {
                if(nums[i] == 0) {
                    zerocount++;
                }
            }
            int min = zerocount;
 
            for(int i = 0; i < nums.size(); i++) {
                if(nums[i] == 0) {
                    zerocount--;
                }
                if(nums[(onecount + i) % nums.size()] == 0) {
                    zerocount++;
                }
                if(zerocount < min) {
                    min = zerocount;
                }
            }
            return min;
        }
    }// namespace minimum_swaps_to_group_all_1s_together_ii
 
    namespace count_words_obtained_after_adding_a_letter {
        int Solution::wordCount(vector<string> &startWords,
                                vector<string> &targetWords) {
            int count  = 0;
            auto start = unordered_set<unsigned int>();
            for(const string &word: startWords) {
                auto bin = str2bin(word);
                start.insert(bin);
            }
            for(const string &word: targetWords) {
                const auto bin = str2bin(word);
                for(int i = 0; i < 26; i++) {
                    if((bin & 1 << i) != 0 && start.contains(bin - (1 << i))) {
                        //bin有第i个字母且bin去掉第i个字母在start中仍然存在
                        count++;
                        break;
                    }
                }
            }
            return count;
        }
 
        unsigned int Solution::str2bin(const string &str) {
            unsigned int ret = 0;
            for(const char ch: str) {
                ret |= 1 << ch - 'a';
            }
            return ret;
        }
    }// namespace count_words_obtained_after_adding_a_letter
 
    namespace slowest_key {
        char Solution::slowestKey(vector<int> &releaseTimes, string keysPressed) {
            int max  = releaseTimes[0];
            int maxi = 0;
            for(int i = 1; i < releaseTimes.size(); i++) {
                const int time = releaseTimes[i] - releaseTimes[i - 1];
                if(max < time) {
                    max  = time;
                    maxi = i;
                } else if(max == time) {
                    if(keysPressed[i] > keysPressed[maxi]) {
                        maxi = i;
                    }
                }
            }
            return keysPressed[maxi];
        }
    }// namespace slowest_key
 
    namespace additive_number {
        bool Solution::isAdditiveNumber(string num) {
            if(num.length() < 3) {
                return false;
            }
            auto *const nums = new char[num.length()];
            for(int i = 0; i < num.length(); i++) {
                nums[i] = num[i];
            }
            for(int i = 1; i <= num.length() - i; i++) {
                const auto n1 = str2ui(nums, 0, i);
                for(int j = i + 1; j - i <= num.length() - j; j++) {
                    const auto n2 = str2ui(nums, i, j - i);
                    if(dfs(n1, n2, nums, num.length(), j)) {
                        return true;
                    }
                    if(n2 == 0) {
                        break;
                    }
                }
                if(n1 == 0) {
                    break;
                }
            }
            delete[] nums;
            return false;
        }
 
        bool Solution::dfs(unsigned long long n1, unsigned long long n2, const char *nums, unsigned short length, unsigned short current) {
            const auto sum = to_string(n1 + n2);
            if(sum.length() > length - current) {
                //前两位和的位数超过剩余的位数
                return false;
            }
            if(!equal(sum, nums, current, length)) {
                //不包含下一个数字
                return false;
            }
            if(current + sum.length() == length) {
                //终止条件
                return true;
            }
            const auto n3 = str2ui(nums, current, sum.length());
            return dfs(n2, n3, nums, length, current + sum.length());
        }
 
        unsigned long long Solution::str2ui(const char *str, unsigned short start, unsigned short length) {
            unsigned long long ans = 0;
            for(int i = start; i < start + length; i++) {
                ans *= 10;
                ans += str[i] - '0';
            }
            return ans;
        }
 
        bool Solution::equal(string sum, const char *nums, unsigned short start, unsigned short length) {
            int j = 0;
            for(int i = start; j < sum.length() && i < length; i++, j++) {
                if(sum[j] != nums[i]) {
                    return false;
                }
            }
            return j == sum.length();
        }
    }// namespace additive_number
 
    namespace decode_the_slanted_ciphertext {
        string Solution::decodeCiphertext(string encodedText, int rows) {
            if(encodedText.empty()) {
                return "";
            }
            const int columns = encodedText.length() / rows;
            auto *const table = new char *[rows];
            for(int i = 0; i < rows; i++) {
                table[i] = new char[columns - rows + 2];
                for(int j = i; j - i < columns - rows + 2; j++) {
                    if(i * columns + j < encodedText.length()) {
                        table[i][j - i] = encodedText[i * columns + j];
                    } else {
                        table[i][j - i] = ' ';
                    }
                }
            }
            auto oss = ostringstream();
            for(int j = 0; j < columns - rows + 2; j++) {
                for(int i = 0; i < rows; i++) {
                    oss << table[i][j];
                }
            }
            string ans = oss.str();
            for(int i = 0; i < rows; i++) {
                delete[] table[i];
            }
            delete[] table;
            return rtrim(ans);
        }
 
        string Solution::rtrim(string &s) {
            for(int i = s.length() - 1; i >= 0; i--) {
                if(s[i] != ' ') {
                    string ans = s.substr(0, i + 1);
                    return ans;
                }
            }
            return s;
        }
    }// namespace decode_the_slanted_ciphertext
 
    namespace escape_a_large_maze {
        bool Solution::isEscapePossible(vector<vector<int>> &blocked, vector<int> &source, vector<int> &target) {
            const int limit = blocked.size() * (blocked.size() - 1) / 2;
            if(blocked.empty()) {
                return true;
            }
            auto *p_source          = new point(source[0], source[1], 0, nullptr);
            auto *p_target          = new point(target[0], target[1], 0, nullptr);
            auto blocked_set_source = unordered_set<point, point_hash>();
            auto blocked_set_target = unordered_set<point, point_hash>();
            for(auto block: blocked) {
                blocked_set_source.insert(point(block[0], block[1], 0, nullptr));
                blocked_set_target.insert(point(block[0], block[1], 0, nullptr));
            }
            const unsigned int source_status = search(blocked_set_source, p_source, p_target, limit);
            if(source_status == 0) {
                return false;
            }
            if(source_status == 1) {
                return true;
            }
            const unsigned int target_status = search(blocked_set_target, p_target, p_source, limit);
            delete p_source;
            delete p_target;
            return target_status != 0;
        }
 
        unsigned int Solution::search(unordered_set<point, point_hash> &block_set, point *source, point *target, unsigned int limit) {
            auto pq = priority_queue<point>();
            pq.push(point(source->x, source->y, 0, target));
            int count = 0;
            while(!pq.empty()) {
                if(count > limit || pq.size() > limit) {
                    return 2;//不包围
                }
                count++;
                const auto p = pq.top();
                pq.pop();
                point nexts[] = {point(p.x + 1, p.y, p.distance + 1, target), point(p.x - 1, p.y, p.distance + 1, target), point(p.x, p.y + 1, p.distance + 1, target), point(p.x, p.y - 1, p.distance + 1, target)};
                for(auto next: nexts) {
                    if(0 <= next.x && next.x < 1000000 && 0 <= next.y && next.y < 1000000 && !block_set.contains(next)) {
                        if(next.x == target->x && next.y == target->y) {
                            return 1;//连通
                        }
                        pq.push(next);
                        block_set.insert(next);
                    }
                }
            }
            return 0;//不连通
        }
 
        bool point::operator<(const point &p) const { return this->distance + (abs(static_cast<int>(this->x - target->x)) + abs(static_cast<int>(this->y - target->y))) < p.distance + (abs(static_cast<int>(p.x - target->x)) + abs(static_cast<int>(p.y - target->y))); }
        bool point::operator==(const point &p) const { return this->x == p.x && this->y == p.y; }
 
        size_t point_hash::operator()(const point &p) const { return p.x * 1000000 + p.y; }
    }// namespace escape_a_large_maze
 
    namespace increasing_triplet_subsequence {
        bool Solution::increasingTriplet(vector<int> &nums) {
            if(nums.size() < 3) {
                return false;
            }
            auto *min            = new int[nums.size()];
            auto *max            = new int[nums.size()];
            min[0]               = nums[0];
            max[nums.size() - 1] = nums[nums.size() - 1];
            for(int i = 1, j = nums.size() - 2; i < nums.size() && j >= 0; i++, j--) {
                if(min[i - 1] > nums[i]) {
                    min[i] = nums[i];
                } else {
                    min[i] = min[i - 1];
                }
 
                if(max[j + 1] < nums[j]) {
                    max[j] = nums[j];
                } else {
                    max[j] = max[j + 1];
                }
            }
            for(int i = 0; i < nums.size(); i++) {
                if(nums[i] > min[i] && nums[i] < max[i]) {
                    delete[] min;
                    delete[] max;
                    return true;
                }
            }
            delete[] min;
            delete[] max;
            return false;
        }
    }// namespace increasing_triplet_subsequence
 
    namespace largest_number_at_least_twice_of_others {
        int Solution::dominantIndex(vector<int> &nums) {
            if(nums.size() < 2) {
                return 0;
            }
            unsigned int max;
            unsigned int index;
            unsigned int second;
            if(nums[0] < nums[1]) {
                max    = nums[1];
                index  = 1;
                second = nums[0];
            } else {
                max    = nums[0];
                index  = 0;
                second = nums[1];
            }
            for(int i = 2; i < nums.size(); i++) {
                if(nums[i] > max) {
                    second = max;
                    index  = i;
                    max    = nums[i];
                } else if(nums[i] > second) {
                    second = nums[i];
                }
            }
            if(max >= 2 * second) {
                return index;
            }
            return -1;
        }
    }// namespace largest_number_at_least_twice_of_others
 
    namespace find_k_pairs_with_smallest_sums {
        vector<vector<int>> Solution::kSmallestPairs(vector<int> &nums1, vector<int> &nums2, int k) {
            auto ans = vector<vector<int>>();
            auto pq  = priority_queue<pair>();
            for(int i = 0; i < k && i < nums1.size(); i++) {
                for(int j = 0; j < k && j < nums2.size(); j++) {
                    pq.push(pair(nums1[i], nums2[j]));
                }
            }
            for(int i = 0; i < k && i < nums1.size() * nums2.size(); i++) {
                const pair p = pq.top();
                pq.pop();
                auto to_add = vector<int>();
                to_add.resize(2);
                to_add[0] = p.u;
                to_add[1] = p.v;
                ans.push_back(to_add);
            }
            return ans;
        }
 
        bool pair::operator<(const pair &p) const { return this->u + this->v > p.u + p.v; }
    }// namespace find_k_pairs_with_smallest_sums
 
    namespace permutations {
        vector<vector<int>> Solution::permute(vector<int> &nums) {
            auto ans = vector<vector<int>>();
            if(nums.size() == 1) {
                auto next_ans = vector<int>();
                next_ans.push_back(nums[0]);
                ans.push_back(next_ans);
                return ans;
            }
            for(auto num: nums) {
                auto next = vector(nums);
                next.erase(find(next.begin(), next.end(), num));
                auto next_permutations = permute(next);
                auto new_ans           = vector<int>();
                new_ans.push_back(num);
                for(auto next_permutation: next_permutations) {
                    auto next_ans = vector(new_ans);
                    next_ans.insert(next_ans.end(), next_permutation.begin(), next_permutation.end());
                    ans.push_back(next_ans);
                }
            }
            return ans;
        }
    }// namespace permutations
 
    namespace calculate_money_in_leetcode_bank {
        int Solution::totalMoney(int n) {
            int sum = n / 7 * (28 + 7 * (n / 7 + 3)) / 2;
            for(int i = 0; i < n % 7; i++) {
                sum += n / 7 + 1 + i;
            }
            return sum;
        }
    }// namespace calculate_money_in_leetcode_bank
 
    namespace linked_list_random_node {
        int Solution::getRandom() const {
            int i   = 1;
            int ans = 0;
            for(const auto *node = head; node != nullptr; node = node->next, i++) {
                if(rand() % i == 0) {
                    // 1/i 的概率选中（替换为答案）
                    ans = node->val;
                }
            }
            return ans;
        }
    }// namespace linked_list_random_node
 
    namespace divide_a_string_into_groups_of_size_k {
        vector<string> Solution::divideString(const string &s, int k, char fill) {
            auto ans = vector<string>();
            int i    = 0;
            for(; i * k + k < s.length(); i++) {
                ans.push_back(s.substr(i * k, k));
            }
            if(i * k != s.length()) {
                string last = s.substr(i * k);
                for(int j = last.length(); j < k; j++) {
                    last += fill;
                }
                ans.push_back(last);
            }
            return ans;
        }
    }// namespace divide_a_string_into_groups_of_size_k
 
    namespace minimum_moves_to_reach_target_score {
        int Solution::minMoves(int target, int maxDoubles) {
            int count = 0;
            while(target != 1) {
                if(maxDoubles == 0) {
                    return count + target - 1;
                }
                if(target % 2 == 0 && maxDoubles != 0) {
                    target /= 2;
                    maxDoubles--;
                } else {
                    target--;
                }
                count++;
            }
            return count;
        }
    }// namespace minimum_moves_to_reach_target_score
 
    namespace solving_questions_with_brainpower {
        long long Solution::mostPoints(vector<vector<int>> &questions) {
            vector<long long> f(questions.size() + 1);
            for(int i = questions.size() - 1; i >= 0; --i) {
                auto &q     = questions[i];
                const int j = i + q[1] + 1;
                f[i]        = max(f[i + 1], q[0] + (j < questions.size() ? f[j] : 0));
            }
            return f[0];
        }
    }// namespace solving_questions_with_brainpower
 
    namespace maximum_running_time_of_n_computers {
        long long Solution::maxRunTime(int n, vector<int> &batteries) {
            auto check = [&](long long t) {
                long long sum = 0;
                for(const int i: batteries) {
                    sum += min(t, static_cast<long long>(i));
                }
                return sum / t >= n;
            };
 
            long long l = 1;
            long long r = 1e16;
            while(l < r) {
                const long long m = (l + r) / 2;
                if(check(m)) {
                    l = m + 1;
                } else {
                    r = m;
                }
            }
            return l - 1;
        }
    }// namespace maximum_running_time_of_n_computers
 
    namespace coun_vowels_permutation {
        int Solution::countVowelPermutation(int n) {
            unsigned long long end[5] = {1, 1, 1, 1, 1};
            for(int _i = 1; _i < n; _i++) {
                const unsigned long long a = (end[1] + end[2] + end[4]) % 1000000007;
                const unsigned long long e = (end[0] + end[2]) % 1000000007;
                const unsigned long long i = (end[1] + end[3]) % 1000000007;
                const unsigned long long o = end[2] % 1000000007;
                const unsigned long long u = (end[2] + end[3]) % 1000000007;
                end[0]                     = a;
                end[1]                     = e;
                end[2]                     = i;
                end[3]                     = o;
                end[4]                     = u;
            }
            return (end[0] + end[1] + end[2] + end[3] + end[4]) % 1000000007;
        }
    }// namespace coun_vowels_permutation
 
    namespace minimum_time_difference {
        int Solution::findMinDifference(vector<string> &timePoints) {
            auto vec = vector<int>();
            for(string timePoint: timePoints) {
                vec.push_back(((timePoint[0] - '0') * 10 + (timePoint[1] - '0')) * 60 + (timePoint[3] - '0') * 10 + (timePoint[4] - '0'));
            }
            sort(vec.begin(), vec.end());
            int minimum = INT_MAX;
            for(int i = 0; i + 1 < vec.size(); i++) {
                minimum = min(minimum, vec[i + 1] - vec[i]);
            }
            minimum = min(minimum, vec[0] + 24 * 60 - vec[vec.size() - 1]);
            return minimum;
        }
    }// namespace minimum_time_difference
 
    namespace contains_duplicate_ii {
        bool Solution::containsNearbyDuplicate(vector<int> &nums, int k) {
            auto um = unordered_map<int, vector<int>>();
            for(int i = 0; i < nums.size(); i++) {
                if(!um.contains(nums[i])) {
                    um.insert(pair(nums[i], vector<int>()));
                }
                auto pos = lower_bound(um[nums[i]].begin(), um[nums[i]].end(), i);
                if(pos != um[nums[i]].end() && abs(*pos - i) <= k || pos != um[nums[i]].begin() && abs(*(pos - 1) - i) <= k) {
                    return true;
                }
                um[nums[i]].insert(pos, i);
            }
            for(auto i: um) {
                sort(i.second.begin(), i.second.end());
            }
            return false;
        }
    }// namespace contains_duplicate_ii
 
    namespace stone_game_ix {
        bool Solution::stoneGameIX(vector<int> &stones) {
            unsigned int remove    = 0;
            unsigned int counts[3] = {0, 0, 0};
            for(auto stone: stones) {
                stone %= 3;
                counts[stone]++;
            }
            if(stones.size() == 1) {
                return false;
            }
            if(counts[1] + counts[2] == 2) {
                if(counts[1] == 2 || counts[2] == 2) {
                    return false;
                }
            }
            if(counts[1] == 0 && counts[2] == 0) {
                return false;
            }
            if(abs(static_cast<int>(counts[1]) - static_cast<int>(counts[2])) <= 2) {
                return counts[0] % 2 == 0;
            }
            return true;
        }
    }// namespace stone_game_ix
 
    namespace jump_game_iv {
        int Solution::minJumps(vector<int> &arr) {
            if(arr.size() == 1) {
                return 0;
            }
            auto pq    = queue<pair<int, int>>();//<下标,step>
            auto *flag = new bool[arr.size()];
            memset(flag, 0, arr.size() * sizeof(bool));
            auto um = unordered_map<int, vector<int>>();//<值,下标>
            for(int i = 0; i < arr.size(); i++) {
                if(!um.contains(arr[i])) {
                    auto vec = vector<int>();
                    vec.push_back(i);
                    um.insert(pair(arr[i], vec));
                } else {
                    um[arr[i]].push_back(i);
                }
            }
            pq.push(pair(0, 0));
            flag[0] = true;
            while(!pq.empty()) {
                auto [current_i, current_count] = pq.front();
                pq.pop();
                if(current_i == arr.size() - 1) {
                    return current_count;
                }
                if(um.contains(arr[current_i])) {
                    for(auto i: um[arr[current_i]]) {
                        if(i != current_i && !flag[i]) {
                            pq.push(pair(i, current_count + 1));
                            flag[i] = true;
                        }
                    }
                }
                um.erase(arr[current_i]);
                if(current_i - 1 >= 0 && !flag[current_i - 1]) {
                    pq.push(pair(current_i - 1, current_count + 1));
                    flag[current_i - 1] = true;
                }
                if(current_i + 1 < arr.size() && !flag[current_i + 1]) {
                    pq.push(pair(current_i + 1, current_count + 1));
                    flag[current_i + 1] = true;
                }
            }
            delete[] flag;
            return 0;
        }
    }// namespace jump_game_iv
 
    namespace remove_palindromic_subsequences {
        int Solution::removePalindromeSub(string s) {
            for(int i = 0, j = s.length() - 1; i < j; i++, j--) {
                if(s[i] != s[j]) {
                    return 2;
                }
            }
            return 1;
        }
    }// namespace remove_palindromic_subsequences
 
    namespace UhWRSj {
        string Solution::replaceWords(vector<string> &dictionary, const string &sentence) {
            auto oss         = ostringstream();
            auto *const nstr = new char[sentence.length() + 1];
            auto tn          = TrieNode();
            for(const auto &root: dictionary) {
                tn.insert(root);
            }
            strcpy(nstr, sentence.c_str());
            char *word = strtok(nstr, " ");
            while(word != nullptr) {
                oss << tn.get_prefix("", string(word)) << " ";
                word = strtok(nullptr, " ");
            }
            const string ans = oss.str();
            delete[] nstr;
            return ans.substr(0, ans.length() - 1);
        }
 
        void TrieNode::insert(const string &str) {
            if(str.empty()) {
                this->endroot = true;
                return;
            }
            if(this->next[str[0] - 'a'] == nullptr) {
                this->next[str[0] - 'a'] = new TrieNode(str[0]);
            }
            this->next[str[0] - 'a']->insert(str.substr(1));
        }
 
        string TrieNode::get_prefix(string root, const string &str) const {
            if(this->endroot || str.empty()) {
                return root;
            }
            if(this->next[str[0] - 'a'] == nullptr) {
                return root + str;
            }
            return this->next[str[0] - 'a']->get_prefix(root + str[0], str.substr(1));
        }
    }// namespace UhWRSj
 
    namespace minimum_cost_of_buying_candies_with_discount {
        int Solution::minimumCost(vector<int> &cost) {
            if(cost.size() == 1) {
                return cost[0];
            }
            if(cost.size() == 2) {
                return cost[0] + cost[1];
            }
            int count = 0;
            sort(cost.rbegin(), cost.rend());
            for(int i = 0; i < cost.size(); i++) {
                if(i % 3 != 2) {
                    count += cost[i];
                }
            }
            return count;
        }
    }// namespace minimum_cost_of_buying_candies_with_discount
 
    namespace count_the_hidden_sequences {
        int Solution::numberOfArrays(vector<int> &differences, int lower, int upper) {
            long long current = 0;
            long long maximum = 0;
            long long minimum = 0;
            for(const auto difference: differences) {
                current += difference;
                maximum = max(maximum, current);
                minimum = min(minimum, current);
            }
            return max(static_cast<long long>(0), upper - lower - (maximum - minimum) + 1);
        }
    }// namespace count_the_hidden_sequences
 
    namespace k_highest_ranked_items_within_a_price_range {
        vector<vector<int>> Solution::highestRankedKItems(vector<vector<int>> &grid, vector<int> &pricing, vector<int> &start, int k) {
            const auto m    = grid.size();
            const auto n    = grid[0].size();
            auto ans        = vector<vector<int>>();
            const auto low  = pricing[0];
            const auto high = pricing[1];
            const auto row  = start[0];
            const auto col  = start[1];
            auto pq         = priority_queue<item>();
            pq.push(item(0, grid[row][col], row, col));
            grid[row][col] = 0;
            while(pq.empty() && k != 0) {
                auto current = pq.top();
                pq.pop();
                if(current.price != 1 && current.price >= low && current.price <= high) {
                    k--;
                    auto vec = vector<int>();
                    vec.push_back(current.row);
                    vec.push_back(current.col);
                    ans.push_back(vec);
                }
                pair<int, int> nexts[4] = {pair(current.row + 1, current.col),
                                           pair(current.row - 1, current.col),
                                           pair(current.row, current.col + 1),
                                           pair(current.row, current.col - 1)};
                for(const pair<int, int> next: nexts) {
                    if(0 <= next.first && next.first < m && 0 <= next.second && next.second < n && grid[next.first][next.second] != 0) {
                        pq.push(item(current.distance + 1, grid[next.first][next.second], next.first, next.second));
                        grid[next.first][next.second] = 0;
                    }
                }
            }
            return ans;
        }
 
        bool item::operator<(const item &i) const {
            if(this->distance != i.distance) {
                return this->distance > i.distance;
            }
            if(this->price != i.price) {
                return this->price > i.price;
            }
            if(this->row != i.row) {
                return this->row > i.row;
            }
            return this->col > i.col;
        }
    }// namespace k_highest_ranked_items_within_a_price_range
 
    namespace number_of_ways_to_divide_a_long_corridor {
        int Solution::numberOfWays(string corridor) {
            unsigned int s_count = 0;
            auto p               = vector<unsigned int>();
            for(const char ch: corridor) {
                if(ch == 'S') {
                    s_count++;
                }
            }
            if(s_count == 0 || s_count % 2 != 0) {
                return 0;
            }
            if(s_count == 2) {
                return 1;
            }
            unsigned int start = 0;
            unsigned int end   = corridor.length() - 1;
            for(; start < end; start++) {
                if(corridor[start] == 'S') {
                    break;
                }
            }
            for(; end > start; end--) {
                if(corridor[end] == 'S') {
                    break;
                }
            }
            s_count              = 1;
            unsigned int p_count = 0;
            bool flag            = false;//是否在边界
            for(unsigned int i = start + 1; i <= end; i++) {
                if(corridor[i] == 'S') {
                    s_count++;
                } else {
                    if(s_count == 0) {
                        p_count++;
                    }
                }
                s_count %= 2;
                if(s_count == 0) {
                    flag = true;
                } else if(s_count == 1) {
                    if(flag) {
                        p.push_back(p_count + 1);
                        p_count = 0;
                    }
                    flag = false;
                }
            }
            unsigned long long ans = 1;
            for(const auto i: p) {
                ans *= i;
                ans %= 1000000007;
            }
            return ans;
        }
    }// namespace number_of_ways_to_divide_a_long_corridor
 
    namespace count_elements_with_strictly_smaller_and_greater_elements {
        int Solution::countElements(vector<int> &nums) {
            int maximum = nums[0];
            int minimum = nums[0];
            for(auto num: nums) {
                maximum = max(maximum, num);
                minimum = min(minimum, num);
            }
            unsigned int count = 0;
            for(const auto num: nums) {
                if(maximum != num && minimum != num) {
                    count++;
                }
            }
            return count;
        }
    }// namespace count_elements_with_strictly_smaller_and_greater_elements
 
    namespace rearrange_array_elements_by_sign {
        vector<int> Solution::rearrangeArray(vector<int> &nums) {
            const auto size = nums.size();
            auto ans        = vector<int>();
            auto positive   = vector<int>();
            auto negative   = vector<int>();
            for(auto num: nums) {
                if(num > 0) {
                    positive.push_back(num);
                } else {
                    negative.push_back(num);
                }
            }
            for(int i = 0; i < size / 2; i++) {
                ans.push_back(positive[i]);
                ans.push_back(negative[i]);
            }
            return ans;
        }
    }// namespace rearrange_array_elements_by_sign
 
    namespace find_all_lonely_numbers_in_the_array {
        vector<int> Solution::findLonely(vector<int> &nums) {
            if(nums.size() == 1) {
                return nums;
            }
            sort(nums.begin(), nums.end());
            auto ans = vector<int>();
            if(nums[1] - nums[0] > 1) {
                ans.push_back(nums[0]);
            }
            if(nums[nums.size() - 1] - nums[nums.size() - 2] > 1) {
                ans.push_back(nums[nums.size() - 1]);
            }
            for(int i = 1; i < nums.size() - 1; i++) {
                if(nums[i] - nums[i - 1] > 1 && nums[i + 1] - nums[i] > 1) {
                    ans.push_back(nums[i]);
                }
            }
            return ans;
        }
    }// namespace find_all_lonely_numbers_in_the_array
 
    namespace maximum_good_people_based_on_statements {
        int Solution::maximumGood(vector<vector<int>> &statements) {
            int maximum = 0;
            auto dup    = unordered_map<int, bool>();
            for(int i = 0; i < statements.size(); i++) {
                if(dup[i]) {
                    continue;
                }
                const auto um = unordered_map<int, bool>();
                auto que      = queue<msg>();
                que.push(msg(i, true));
                auto ans = dfs(statements, um, que);
                maximum  = max(maximum, ans.first);
                for(auto it: ans.second) {
                    if(it.second) {
                        dup.insert(it);
                    }
                }
            }
            return maximum;
        }
 
        pair<int, unordered_map<int, bool>> Solution::dfs(vector<vector<int>> &statements, unordered_map<int, bool> um, queue<msg> que) {
            int maximum     = 0;
            bool contradict = false;
            while(!que.empty()) {
                auto current = que.front();
                que.pop();
                if(um.contains(current.person)) {
                    //已经存在
                    if(um[current.person] != current.good) {
                        //矛盾
                        return pair<int, unordered_map<int, bool>>(0, {});
                    }
                } else {
                    um.insert(pair(current.person, current.good));
                }
                if(current.good) {
                    //是好人
                    for(int j = 0; j < statements.size(); j++) {
                        if(statements[current.person][j] != 2 && j != current.person) {
                            auto nmsg = msg(j, statements[current.person][j] == 1);
                            if(um.contains(nmsg.person)) {
                                //已经有了
                                if(um[nmsg.person] != nmsg.good) {
                                    //矛盾
                                    contradict = true;
                                    return pair<int, unordered_map<int, bool>>(0, {});
                                }
                            } else {
                                //还没有
                                que.push(nmsg);
                            }
                        }
                    }
                }
            }
            if(!contradict) {
                //不矛盾
                auto dup = unordered_map<int, bool>();
                for(int i = 0; i < statements.size(); i++) {
                    if(dup[i]) {
                        continue;
                    }
                    if(!um.contains(i)) {
                        bool all2 = true;
                        for(auto v: statements[i]) {
                            if(v != 2) {
                                all2 = false;
                            }
                        }
                        if(all2) {
                            um.insert(pair(i, true));
                            continue;
                        }
                        auto nque = queue<msg>();
                        nque.push(msg(i, true));
                        auto ans = dfs(statements, um, nque);
                        maximum  = max(maximum, ans.first);
                        for(auto it: ans.second) {
                            if(it.second) {
                                dup.insert(it);
                            }
                        }
                    }
                }
 
                int good_count = 0;
                for(auto i: um) {
                    if(i.second) {
                        good_count++;
                    }
                }
                maximum = max(maximum, good_count);
            }
            return pair(maximum, um);
        }
    }// namespace maximum_good_people_based_on_statements
 
    namespace stock_price_fluctuation {
        StockPrice::StockPrice() {
            ms = multiset<int>();
            m  = map<int, int>();
        }
 
        void StockPrice::update(int timestamp, int price) {
            if(!m.contains(timestamp)) {
                m.insert(pair(timestamp, price));
            } else {
                ms.erase(ms.find(m[timestamp]));
                m[timestamp] = price;
            }
            ms.insert(price);
        }
 
        int StockPrice::current() const { return (*m.rbegin()).second; }
 
        int StockPrice::maximum() const { return *ms.rbegin(); }
 
        int StockPrice::minimum() const { return *ms.begin(); }
    }// namespace stock_price_fluctuation
 
    namespace second_minimum_time_to_reach_destination {
        int Solution::secondMinimum(int n, vector<vector<int>> &edges, int time, int change) {
            auto record = unordered_map<int, vector<int>>();
            for(int i = 1; i <= n; i++) {
                record.insert(pair(i, vector<int>()));
            }
            auto um = unordered_map<int, unordered_set<int>>();
            for(auto edge: edges) {
                if(!um.contains(edge[0])) {
                    auto us = unordered_set<int>();
                    us.insert(edge[1]);
                    um.insert(pair(edge[0], us));
                } else {
                    um[edge[0]].insert(edge[1]);
                }
                if(!um.contains(edge[1])) {
                    auto us = unordered_set<int>();
                    us.insert(edge[0]);
                    um.insert(pair(edge[1], us));
                } else {
                    um[edge[1]].insert(edge[0]);
                }
            }
            auto pq = priority_queue<status>();
            pq.push(status(1, 0));
            bool flag = false;//已经到达一次终点
            int prev  = 0;
            while(!pq.empty()) {
                status current = pq.top();
                pq.pop();
                if(current.position == n) {
                    if(!flag) {
                        flag = true;
                        prev = current.time;
                    } else {
                        if(current.time != prev) {
                            return current.time;
                        }
                    }
                }
 
                if(record[current.position].empty() || record[current.position].size() == 1 && current.time != *record[current.position].rbegin()) {
                    //可以继续
                    record[current.position].push_back(current.time);
                } else {
                    continue;
                }
 
                for(int next: um[current.position]) {
                    int next_time;
                    if(current.time / change % 2 == 1) {
                        //当前为红灯
                        next_time = (current.time / change + 1) * change + time;
                    } else {
                        next_time = current.time + time;
                    }
                    auto next_status = status(next, next_time);
                    if(record[next_status.position].empty() || record[next_status.position].size() == 1 && next_status.time != *record[next_status.position].rbegin()) {
                        //可以继续
                        pq.push(next_status);
                    }
                }
            }
            return 0;
        }
 
        bool status::operator<(const status &s) const { return this->time > s.time; }
    }// namespace second_minimum_time_to_reach_destination
 
    namespace count_of_matches_in_tournament {
        int Solution::numberOfMatches(int n) { return n - 1; }
    }// namespace count_of_matches_in_tournament
 
    namespace detect_squares {
        DetectSquares::DetectSquares() { ms = multiset<pair<int, int>>(); }
 
        void DetectSquares::add(vector<int> point) { ms.insert(pair(point[0], point[1])); }
 
        int DetectSquares::count(vector<int> point) const {
            int count = 0;
            for(auto p: ms) {
                if(p.first != point[0] && p.second != point[1] && abs(p.first - point[0]) == abs(p.second - point[1])) {
                    count += ms.count(pair(p.first, point[1])) * ms.count(pair(point[0], p.second));
                }
            }
            return count;
        }
    }// namespace detect_squares
 
    namespace number_of_valid_words_in_a_sentence {
        int Solution::countValidWords(const string &sentence) {
            auto *str = new char[sentence.length() + 1];
            strcpy(str, sentence.c_str());
            int count = 0;
            for(const char *token = strtok(str, " "); token != nullptr; token = strtok(nullptr, " ")) {
                bool is_valid = true; 
                bool hyphen   = false;
                for(int i = 0; token[i] != '\0'; i++) {
                    const char ch = token[i];
                    if(ch == '-') {
                        //当前字符是连接符'-'
                        if(hyphen) {
                            //已经存在过连接符'-'
                            is_valid = false;
                            break;
                        }
                        hyphen = true;
                        if(i == 0 || token[i + 1] == '\0') {
                            //是否在字符串的开头或结尾
                            is_valid = false;
                            break;
                        }
                        if(isalpha(token[i - 1]) == 0 || isalpha(token[i + 1]) == 0) {
                            //前后是否是字母
                            is_valid = false;
                            break;
                        }
                    } else if(token[i + 1] != '\0' && isalpha(ch) == 0) {
                        //不是最后一个字符是否不是字母
                        is_valid = false;
                        break;
                    } else if(isdigit(ch) != 0) {
                        //是否是数字
                        is_valid = false;
                        break;
                    }
                }
                if(is_valid) {
                    count++;
                }
            }
            delete[] str;
            return count;
        }
    }// namespace number_of_valid_words_in_a_sentence
 
    namespace the_number_of_weak_characters_in_the_game {
        int Solution::numberOfWeakCharacters(vector<vector<int>> &properties) {
            //按攻击值从大到小排序。攻击值相同时，按照其防御值从小到大排序
            sort(properties.begin(), properties.end(), [](const vector<int> &a, const vector<int> &b) { return a[0] == b[0] ? a[1] < b[1] : a[0] > b[0]; });
 
            int maxDef = 0;
            int count  = 0;
            for(const auto &p: properties) {
                if(p[1] < maxDef) {
                    count++;
                } else {
                    maxDef = p[1];
                }
            }
            return count;
        }
    }// namespace the_number_of_weak_characters_in_the_game
 
    namespace pattern_matching_lcci {
        bool Solution::patternMatching(const string &pattern, const string &value) {
            int a_count = 0;
            int b_count = 0;
            for(const char ch: pattern) {
                if(ch == 'a') {
                    a_count++;
                } else {
                    b_count++;
                }
            }
            if(a_count == 0 || b_count == 0) {
                int size  = 0;
                int count = 0;
                if(b_count == 0) {
                    if(value.length() % a_count != 0) {
                        return false;
                    }
                    size  = value.length() / a_count;
                    count = a_count;
                } else {
                    if(value.length() % b_count != 0) {
                        return false;
                    }
                    size  = value.length() / b_count;
                    count = b_count;
                }
                const string str = value.substr(0, size);
                for(int i = 0; i < count; i++) {
                    auto s = value.substr(i * size, size);
                    if(s != str) {
                        return false;
                    }
                }
                return true;
            }
            for(int a_size = 0; a_size <= value.length() / a_count; a_size++) {
                string a;
                string b;
                if((value.length() - a_size * a_count) % b_count == 0) {
                    const int b_size   = (value.length() - a_size * a_count) / b_count;
                    string value_local = value;
                    for(const char ch: pattern) {
                        if(ch == 'a') {
                            string a_local = value_local.substr(0, a_size);
                            if(a.empty()) {
                                a = a_local;
                            } else if(a_local != a) {
                                goto next_loop;
                            }
                            value_local = value_local.substr(a_size);
                        } else {
                            string b_local = value_local.substr(0, b_size);
                            if(b.empty()) {
                                b = b_local;
                            } else if(b_local != b) {
                                goto next_loop;
                            }
                            value_local = value_local.substr(b_size);
                        }
                    }
                    if(a == b) {
                        goto next_loop;
                    }
                    return true;
                }
            next_loop:;
            }
            return false;
        }
    }// namespace pattern_matching_lcci
 
    namespace map_of_highest_peak {
        vector<vector<int>> Solution::highestPeak(vector<vector<int>> &isWater) {
            const int m    = isWater.size();
            const int n    = isWater[0].size();
            auto *occupied = new bool *[m];
            for(int i = 0; i < m; i++) {
                occupied[i] = new bool[n];
                memset(occupied[i], 0, n * sizeof(bool));
            }
            auto que = queue<pair<int, int>>();
            for(int i = 0; i < m; i++) {
                for(int j = 0; j < n; j++) {
                    if(isWater[i][j] == 1) {
                        que.push(pair(i, j));
                        isWater[i][j]  = 0;
                        occupied[i][j] = true;
                    } else {
                        isWater[i][j] = 1;
                    }
                }
            }
            while(!que.empty()) {
                pair<int, int> current = que.front();
                que.pop();
                pair<int, int> nexts[4] = {pair(current.first + 1, current.second),
                                           pair(current.first - 1, current.second),
                                           pair(current.first, current.second + 1),
                                           pair(current.first, current.second - 1)};
                for(auto next: nexts) {
                    if(0 <= next.first && next.first < m && 0 <= next.second && next.second < n && !occupied[next.first][next.second]) {
                        isWater[next.first][next.second]  = isWater[current.first][current.second] + 1;
                        occupied[next.first][next.second] = true;
                        que.push(next);
                    }
                }
            }
            delete[] occupied;
            return isWater;
        }
    }// namespace map_of_highest_peak
 
    namespace uncommon_words_from_two_sentences {
        vector<string> Solution::uncommonFromSentences(const string &s1, const string &s2) {
            auto ans           = vector<string>();
            auto um            = unordered_map<string, unsigned int>();
            auto *const s1_str = new char[s1.length() + 1];
            auto *const s2_str = new char[s2.length() + 1];
            strcpy(s1_str, s1.c_str());
            strcpy(s2_str, s2.c_str());
            for(char *word = strtok(s1_str, " "); word != nullptr; word = strtok(nullptr, " ")) {
                auto word_str = string(word);
                if(!um.contains(word_str)) {
                    um.insert(pair(word_str, 1));
                } else {
                    um[word_str]++;
                }
            }
            for(char *word = strtok(s2_str, " "); word != nullptr; word = strtok(nullptr, " ")) {
                auto word_str = string(word);
                if(!um.contains(word_str)) {
                    um.insert(pair(word_str, 1));
                } else {
                    um[word_str]++;
                }
            }
            for(const auto &p: um) {
                if(p.second == 1) {
                    ans.push_back(p.first);
                }
            }
            delete[] s1_str;
            delete[] s2_str;
            return ans;
        }
    }// namespace uncommon_words_from_two_sentences
 
    namespace keep_multiplying_found_values_by_two {
        int Solution::findFinalValue(vector<int> &nums, int original) {
        restart:;
            for(const auto num: nums) {
                if(num == original) {
                    original *= 2;
                    goto restart;
                }
            }
            return original;
        }
    }// namespace keep_multiplying_found_values_by_two
 
    namespace all_divisions_with_the_highest_score_of_a_binary_array {
        vector<int> Solution::maxScoreIndices(vector<int> &nums) {
            const auto n       = nums.size();
            auto left_0_count  = vector<int>();
            auto right_1_count = vector<int>();
            left_0_count.push_back(0);
            right_1_count.push_back(0);
            int count = 0;
            for(int i = 0; i < n; i++) {
                if(nums[i] == 0) {
                    count++;
                }
                left_0_count.push_back(count);
            }
            count = 0;
            for(int i = n - 1; i >= 0; i--) {
                if(nums[i] == 1) {
                    count++;
                }
                right_1_count.push_back(count);
            }
            right_1_count = vector(right_1_count.rbegin(), right_1_count.rend());
            int maximum   = 0;
            for(int i = 0; i <= n; i++) {
                maximum = max(maximum, left_0_count[i] + right_1_count[i]);
            }
            auto ans = vector<int>();
            for(int i = 0; i <= n; i++) {
                if(maximum == left_0_count[i] + right_1_count[i]) {
                    ans.push_back(i);
                }
            }
            return ans;
        }
    }// namespace all_divisions_with_the_highest_score_of_a_binary_array
 
    namespace find_substring_with_given_hash_value {
        string Solution::subStrHash(string s, int power, int modulo, int k, int hashValue) {
            power %= modulo;
            auto *const pn = new int[k];
            pn[0]          = 1;
            for(int i = 1; i < k; i++) {
                pn[i] = static_cast<unsigned long long>(pn[i - 1]) * static_cast<unsigned long long>(power) % modulo;
            }
 
            for(int i = 0; i < s.length(); i++) {
                unsigned long long hash = 0;
                for(int j = 0; j < k; j++) {
                    hash += static_cast<unsigned long long>((s[i + j] - 'a' + 1) % modulo) * pn[j];
                    hash %= modulo;
                }
                if(hash == hashValue) {
                    return s.substr(i, k);
                }
            }
            delete[] pn;
            return "";
        }
    }// namespace find_substring_with_given_hash_value
 
    namespace groups_of_strings {
        vector<int> Solution::groupStrings(vector<string> &words) {
            auto ans  = vector<int>();
            auto nums = vector<unsigned int>();
            for(const auto &word: words) {
                auto num = compress(word);
                nums.push_back(num);
                insert(num);
            }
            for(const auto num: nums) {
                for(int i = 0; i < 26; i++) {
                    auto next = num ^ 1 << i;//添加或删除字符 i
                    if(parent.contains(next)) {
                        to_union(num, next);
                    }
                    if((num >> i & 1) == 1) {
                        //存在字符i
                        for(int j = 0; j < 26; j++) {
                            if((num >> j & 1) == 0) {
                                //不存在字符j
                                auto next = num ^ 1 << i | 1 << j;
                                if(parent.contains(next)) {
                                    to_union(num, num ^ 1 << i | 1 << j);// 替换字符 i 为 j
                                }
                            }
                        }
                    }
                }
            }
            ans.push_back(groups);
            ans.push_back(max_size);
            return ans;
        }
 
        unsigned int Solution::compress(const string &word) {
            unsigned int ans = 0;
            for(const char ch: word) {
                ans |= 1 << ch - 'a';
            }
            return ans;
        }
 
        void Solution::insert(unsigned int num) {
            parent.insert(pair(num, num));
            rank.insert(pair(num, 0));
            if(!size.contains(num)) {
                size.insert(pair(num, 1));
                groups++;
            } else {
                size[num]++;
                max_size = size[num];
            }
        }
 
        unsigned int Solution::find(unsigned int x) { return x == parent[x] ? x : parent[x] = find(parent[x]); }
 
        void Solution::to_union(unsigned int x1, unsigned int x2) {
            const int f1 = find(x1);
            const int f2 = find(x2);
            if(f1 == f2) {
                return;
            }
            groups--;
            if(rank[f1] > rank[f2]) {
                parent[f2] = f1;
                size[f1] += size[f2];
                max_size = max(max_size, size[f1]);
            } else {
                parent[f1] = f2;
                size[f2] += size[f1];
                max_size = max(max_size, size[f2]);
                if(rank[f1] == rank[f2]) {
                    ++rank[f2];
                }
            }
        }
    }// namespace groups_of_strings
 
    namespace number_of_steps_to_reduce_a_number_to_zero {
        int Solution::numberOfSteps(int num) {
            if(num == 0) {
                return 0;
            }
            int count = 0;
            while(num != 0) {
                if((num & 1) == 0) {
                    count += 1;
                } else {
                    count += 2;
                }
                num >>= 1;
            }
            return count - 1;
        }
    }// namespace number_of_steps_to_reduce_a_number_to_zero
 
    namespace longest_nice_substring {
        string Solution::longestNiceSubstring(const string &s) {
            auto [max_start, max_len] = dfs(s, 0, s.length() - 1);
            if(max_len == 0) {
                return "";
            }
            return s.substr(max_start, max_len);
        }
 
        pair<int, int> Solution::dfs(string s, int start, int end) {
            if(start == end) {
                return {start, 0};
            }
            int lower     = 0;
            int upper     = 0;
            int max_start = 0;
            int max_len   = 0;
            for(int i = start; i <= end; i++) {
                const char ch = s[i];
                if(islower(ch) != 0) {
                    lower |= 1 << ch - 'a';
                } else {
                    //isupper
                    upper |= 1 << ch - 'A';
                }
            }
            if(lower == upper) {
                //是美好字符串
                return {start, end - start + 1};
            }
            //不是美好字符串
            const int not_nice = lower ^ upper;//无法构成美好字符串的字符
            int i              = start;
            while(i <= end) {
                if((not_nice >> tolower(s[i]) - 'a' & 1) == 1) {
                    //在not_nice中
                    i++;
                    continue;
                }
                int j = i + 1;
                while(j <= end && (not_nice >> tolower(s[j]) - 'a' & 1) != 1) {
                    j++;
                }
                auto [next_start, next_len] = dfs(s, i, j - 1);
                if(max_len < next_len) {
                    max_len   = next_len;
                    max_start = next_start;
                }
                i = j;
            }
            return {max_start, max_len};
        }
    }// namespace longest_nice_substring
 
    namespace reverse_prefix_of_word {
        string Solution::reversePrefix(string word, char ch) {
            int i = 0;
            for(; i < word.length(); i++) {
                if(ch == word[i]) {
                    break;
                }
            }
            if(i == word.length()) {
                return word;
            }
            string prefix       = word.substr(0, i + 1);
            const string suffix = word.substr(i + 1);
            const auto xiferp   = string(prefix.rbegin(), prefix.rend());
            return xiferp + suffix;
        }
    }// namespace reverse_prefix_of_word
 
    namespace find_the_minimum_number_of_fibonacci_numbers_whose_sum_is_k {
        int Solution::findMinFibonacciNumbers(int k) {
            auto fibb = set<int, greater<>>();
            fibb.insert(1);
            int prev_1 = 1;
            int next   = 2;
            while(next <= k) {
                fibb.insert(next);
                const int prev_2 = prev_1;
                prev_1           = next;
                next             = prev_1 + prev_2;
            }
            return find_min(fibb, k, fibb.begin());
        }
 
        int Solution::find_min(set<int, greater<>> &fibb, int k, set<int, greater<>>::iterator begin) {
            const auto i = lower_bound(begin, fibb.end(), k, greater<int>());
            if(k == *i) {
                return 1;
            }
            return 1 + find_min(fibb, k - *i, i);
        }
    }// namespace find_the_minimum_number_of_fibonacci_numbers_whose_sum_is_k
 
    namespace number_of_rectangles_that_can_form_the_largest_square {
        int Solution::countGoodRectangles(vector<vector<int>> &rectangles) {
            auto m = map<int, int>();
            for(auto rectangle: rectangles) {
                int k = min(rectangle[0], rectangle[1]);
                m[k]++;
            }
            return (*m.rbegin()).second;
        }
    }// namespace number_of_rectangles_that_can_form_the_largest_square
 
    namespace path_with_maximum_gold {
        int Solution::getMaximumGold(vector<vector<int>> &grid) {
            const int m = grid.size();
            const int n = grid[0].size();
            int ans     = 0;
            for(int i = 0; i < m; i++) {
                for(int j = 0; j < n; j++) {
                    if(grid[i][j] != 0) {
                        auto *occupied = new bool *[m];
                        for(int k = 0; k < m; k++) {
                            occupied[k] = new bool[n];
                            memset(occupied[k], 0, n * sizeof(bool));
                        }
                        occupied[i][j] = true;
                        ans            = max(ans, get_sum(grid[i][j], i, j, m, n, grid, occupied));
                        for(int k = 0; k < m; k++) {
                            delete[] occupied[k];
                        }
                        delete[] occupied;
                    }
                }
            }
            return ans;
        }
 
        int Solution::get_sum(int current, int x, int y, int m, int n, vector<vector<int>> &grid, bool **occupied) {
            pair<int, int> nexts[] = {make_pair(x + 1, y), make_pair(x - 1, y), make_pair(x, y + 1), make_pair(x, y - 1)};
            int maximum            = current;
            for(auto [next_x, next_y]: nexts) {
                if(0 <= next_x && next_x < m && 0 <= next_y && next_y < n && grid[next_x][next_y] != 0 && !occupied[next_x][next_y]) {
                    auto *occupied_cpy = new bool *[m];
                    for(int i = 0; i < m; i++) {
                        occupied_cpy[i] = new bool[n];
                        memcpy(occupied_cpy[i], occupied[i], n * sizeof(bool));
                    }
                    occupied_cpy[next_x][next_y] = true;
                    maximum                      = max(maximum, get_sum(current + grid[next_x][next_y], next_x, next_y, m, n, grid, occupied_cpy));
                    for(int i = 0; i < m; i++) {
                        delete[] occupied_cpy[i];
                    }
                    delete[] occupied_cpy;
                }
            }
            return maximum;
        }
    }// namespace path_with_maximum_gold
 
    namespace minimum_sum_of_four_digit_number_after_splitting_digits {
        int Solution::minimumSum(int num) {
            auto oss = ostringstream();
            oss << num;
            const string str = oss.str();
            int nums[4];
            for(int i = 0; i < 4; i++) {
                nums[i] = str[i] - '0';
            }
            sort(nums, nums + 4);
            return nums[0] * 10 + nums[1] * 10 + nums[2] + nums[3];
        }
    }// namespace minimum_sum_of_four_digit_number_after_splitting_digits
 
    namespace partition_array_according_to_given_pivot {
        vector<int> Solution::pivotArray(vector<int> &nums, int pivot) {
            auto less    = vector<int>();
            auto equal   = vector<int>();
            auto greater = vector<int>();
            for(auto num: nums) {
                if(num < pivot) {
                    less.push_back(num);
                } else if(num == pivot) {
                    equal.push_back(num);
                } else {
                    greater.push_back(num);
                }
            }
            less.insert(less.end(), equal.begin(), equal.end());
            less.insert(less.end(), greater.begin(), greater.end());
            return less;
        }
    }// namespace partition_array_according_to_given_pivot
 
    namespace minimum_cost_to_set_cooking_time {
        int Solution::minCostSetTime(int startAt, int moveCost, int pushCost, int targetSeconds) {
            int ans    = (moveCost + pushCost) * 4;
            int minute = targetSeconds / 60;
            int second = targetSeconds % 60;
            while(minute > 99) {
                minute -= 1;
                second += 60;
            }
            const int num[4] = {minute / 10, minute % 10, second / 10, second % 10};
            ans              = min(ans, get_cost(startAt, moveCost, pushCost, num));
            if(second + 60 < 100 && minute - 1 >= 0) {
                second += 60;
                minute -= 1;
                const int num[4] = {minute / 10, minute % 10, second / 10, second % 10};
                ans              = min(ans, get_cost(startAt, moveCost, pushCost, num));
            }
            return ans;
        }
 
        int Solution::get_cost(int startAt, int moveCost, int pushCost, const int num[4]) {
            int cost    = 0;
            int current = startAt;
            bool flag   = true;
            for(int i = 0; i < 4; i++) {
                if(num[i] == 0 && flag) {
                    continue;
                }
                flag = false;
                if(num[i] != current) {
                    cost += moveCost;
                    current = num[i];
                }
                cost += pushCost;
            }
            return cost;
        }
    }// namespace minimum_cost_to_set_cooking_time
 
    namespace minimum_difference_in_sums_after_removal_of_elements {
        long long Solution::minimumDifference(vector<int> &nums) {
            const int n         = nums.size() / 3;
            auto *left_sum      = new long long[n];
            auto *right_sum     = new long long[n];
            long long left_min  = 0;
            long long right_max = 0;
            auto left_n         = priority_queue<int>();
            auto right_n        = priority_queue<int, vector<int>, greater<>>();
            for(int i = 0; i < n; i++) {
                left_n.push(nums[i]);
                left_min += nums[i];
            }
            for(int i = 3 * n - 1; i >= 2 * n; i--) {
                right_n.push(nums[i]);
                right_max += nums[i];
            }
            const long long left_min_preserve  = left_min;
            const long long right_max_preserve = right_max;
            left_sum[0]                        = left_min;
            right_sum[n - 1]                   = right_max;
            for(int i = n; i < 2 * n; i++) {
                if(nums[i] < left_n.top()) {
                    left_min += nums[i] - left_n.top();
                    left_n.pop();
                    left_n.push(nums[i]);
                }
                left_sum[i - n] = left_min;
            }
            for(int i = 2 * n - 1; i >= n; i--) {
                if(nums[i] > right_n.top()) {
                    right_max += nums[i] - right_n.top();
                    right_n.pop();
                    right_n.push(nums[i]);
                }
                right_sum[i - n] = right_max;
            }
            long long ans = left_min_preserve - right_sum[0];
            for(int i = 0; i < n - 1; i++) {
                ans = min(ans, left_sum[i] - right_sum[i + 1]);
            }
            ans = min(ans, left_sum[n - 1] - right_max_preserve);
            delete[] left_sum;
            delete[] right_sum;
            return ans;
        }
    }// namespace minimum_difference_in_sums_after_removal_of_elements
 
    namespace sum_of_unique_elements {
        int Solution::sumOfUnique(vector<int> &nums) {
            auto um = unordered_map<int, int>();
            for(auto num: nums) {
                um[num]++;
            }
            int ans = 0;
            for(auto [k, v]: um) {
                if(v == 1) {
                    ans += k;
                }
            }
            return ans;
        }
    }// namespace sum_of_unique_elements
 
    namespace sort_even_and_odd_indices_independently {
        vector<int> Solution::sortEvenOdd(vector<int> &nums) {
            vector<int> even;
            vector<int> odd; 
            vector<int> ans;
            for(int i = 0; i < nums.size(); i++) {
                if(i % 2 == 0) {
                    even.push_back(nums[i]);
                } else {
                    odd.push_back(nums[i]);
                }
            }
            sort(even.begin(), even.end());
            sort(odd.begin(), odd.end(), greater<int>());
            for(int i = 0; i < odd.size(); i++) {
                ans.push_back(even[i]);
                ans.push_back(odd[i]);
            }
            if(even.size() > odd.size()) {
                ans.push_back(even.back());
            }
            return ans;
        }
    }// namespace sort_even_and_odd_indices_independently
 
    namespace smallest_value_of_the_rearranged_number {
        long long Solution::smallestNumber(long long num) {
            bool positive = num > 0;
            auto oss      = ostringstream();
            num           = abs(num);
            oss << num;
            vector<int> n;
            for(char ch: oss.str()) {
                n.push_back(ch - '0');
            }
            sort(n.begin(), n.end());
            vector<int> ans;
            if(positive) {
                for(auto i: n) {
                    if(i != 0) {
                        ans.push_back(i);
                    }
                }
                for(auto i: n) {
                    if(i == 0) {
                        ans.insert(ans.begin() + 1, i);
                    }
                }
            } else {
                for(int i = n.size() - 1; i >= 0; i--) {
                    ans.push_back(n[i]);
                }
            }
            oss = ostringstream();
            if(!positive) {
                oss << '-';
            }
            for(auto i: ans) {
                oss << i;
            }
            auto iss = istringstream(oss.str());
            long long a;
            iss >> a;
            return a;
        }
    }// namespace smallest_value_of_the_rearranged_number
 
    namespace design_bitset {
        Bitset::Bitset(int size) {
            this->size = size;
            one1       = new set<unsigned int>();
            zero0      = new set<unsigned int>();
            for(int i = 0; i < size; i++) {
                zero0->insert(i);
            }
        }
 
        void Bitset::fix(int idx) const {
            zero0->erase(idx);
            one1->insert(idx);
        }
 
        void Bitset::unfix(int idx) const {
            zero0->insert(idx);
            one1->erase(idx);
        }
 
        void Bitset::flip() {
            auto *const tmp = one1;
            one1            = zero0;
            zero0           = tmp;
        }
 
        bool Bitset::all() const { return zero0->empty(); }
 
        bool Bitset::one() const { return !one1->empty(); }
 
        int Bitset::count() const { return one1->size(); }
 
        string Bitset::toString() const {
            auto oss = ostringstream();
            auto c1  = one1->begin();
            auto c0  = zero0->begin();
            for(int i = 0; i < size; i++) {
                if(c1 != one1->end() && *c1 == i) {
                    oss << 1;
                    ++c1;
                } else if(c0 != zero0->end() && *c0 == i) {
                    oss << 0;
                    ++c0;
                }
            }
            return oss.str();
        }
    }// namespace design_bitset
 
    namespace longest_happy_string {
        string Solution::longestDiverseString(int a, int b, int c) {
            auto oss   = ostringstream();
            int count  = 0;
            char prev  = '0';
            char ch[3] = {};
            sort(ch, a, b, c);
            while(a != 0 || b != 0 || c != 0) {
                if(!(count == 2 && prev == ch[2] && *get_p(ch[2], &a, &b, &c) > 0)) {
                    oss << ch[2];
                    (*get_p(ch[2], &a, &b, &c))--;
                    if(prev == ch[2]) {
                        count++;
                    } else {
                        prev  = ch[2];
                        count = 1;
                    }
                } else if(!(count == 2 && prev == ch[1]) && *get_p(ch[1], &a, &b, &c) > 0) {
                    oss << ch[1];
                    (*get_p(ch[1], &a, &b, &c))--;
                    if(prev == ch[1]) {
                        count++;
                    } else {
                        prev  = ch[1];
                        count = 1;
                    }
                } else if(!(count == 2 && prev == ch[0]) && *get_p(ch[0], &a, &b, &c) > 0) {
                    oss << ch[0];
                    (*get_p(ch[0], &a, &b, &c))--;
                    if(prev == ch[0]) {
                        count++;
                    } else {
                        prev  = ch[0];
                        count = 1;
                    }
                } else {
                    return oss.str();
                }
                sort(ch, a, b, c);
            }
            return oss.str();
        }
 
        void Solution::sort(char *ch, int a, int b, int c) {
            int minimum = a;
            ch[0]       = 'a';
            int maximum = b;
            ch[2]       = 'b';
            if(minimum > b) {
                minimum = b;
                ch[0]   = 'b';
            }
            if(minimum > c) {
                minimum = c;
                ch[0]   = 'c';
            }
            if(maximum < a) {
                maximum = a;
                ch[2]   = 'a';
            }
            if(maximum < c) {
                maximum = c;
                ch[2]   = 'c';
            }
            ch[1] = 'a' + 'b' + 'c' - ch[0] - ch[2];
        }
 
        int *Solution::get_p(char ch, int *a, int *b, int *c) {
            switch(ch) {
                case 'a': return a;
                case 'b': return b;
                case 'c': return c;
                default: return nullptr;
            }
        }
    }// namespace longest_happy_string
 
    namespace grid_illumination {
        vector<int> Solution::gridIllumination(int n, vector<vector<int>> &lamps, vector<vector<int>> &queries) {
            auto ls        = unordered_set<pair<int, int>, pair_hash>();
            auto row       = unordered_map<int, int>();
            auto col       = unordered_map<int, int>();
            auto diag_down = unordered_map<int, int>();
            auto diag_up   = unordered_map<int, int>();
            for(auto lamp: lamps) {
                int x  = lamp[0];
                int y  = lamp[1];
                auto p = make_pair(x, y);
                if(!ls.contains(p)) {
                    ls.insert(p);
                    row[x]++;
                    col[y]++;
                    diag_down[n - x + y]++;
                    diag_up[x + y]++;
                }
            }
            auto ans = vector<int>();
            for(auto query: queries) {
                int query_x = query[0];
                int query_y = query[1];
                if(row[query_x] > 0 || col[query_y] > 0 || diag_down[n - query_x + query_y] > 0 || diag_up[query_x + query_y] > 0) {
                    ans.push_back(1);
                } else {
                    ans.push_back(0);
                }
                pair<int, int> adjacents[9] = {make_pair(query_x + 1, query_y + 1), make_pair(query_x + 1, query_y), make_pair(query_x + 1, query_y - 1),
                                               make_pair(query_x, query_y + 1), make_pair(query_x, query_y), make_pair(query_x, query_y - 1),
                                               make_pair(query_x - 1, query_y + 1), make_pair(query_x - 1, query_y), make_pair(query_x - 1, query_y - 1)};
                for(auto adjacent: adjacents) {
                    if(ls.contains(adjacent)) {
                        ls.erase(adjacent);
                        auto [x, y] = adjacent;
                        row[x]--;
                        col[y]--;
                        diag_down[n - x + y]--;
                        diag_up[x + y]--;
                    }
                }
            }
            return ans;
        }
 
        unsigned long long pair_hash::operator()(const pair<int, int> &p) const { return static_cast<unsigned long long>(p.first) * 1000000000 + p.second; }
    }// namespace grid_illumination
 
    namespace count_number_of_pairs_with_absolute_difference_k {
        int Solution::countKDifference(vector<int> &nums, int k) {
            int ans = 0;
            for(int i = 0; i < nums.size(); i++) {
                for(int j = i + 1; j < nums.size(); j++) {
                    if(abs(nums[i] - nums[j]) == k) {
                        ans++;
                    }
                }
            }
            return ans;
        }
    }// namespace count_number_of_pairs_with_absolute_difference_k
 
    namespace simplified_fractions {
        vector<string> Solution::simplifiedFractions(int n) {
            auto ans = vector<string>();
            for(int denominator = 2; denominator <= n; denominator++) {
                for(int numerator = 1; numerator < denominator; numerator++) {
                    if(gcd(denominator, numerator) != 1) {
                        continue;
                    }
                    auto oss = ostringstream();
                    oss << numerator << "/" << denominator;
                    ans.push_back(oss.str());
                }
            }
            return ans;
        }
 
        int Solution::gcd(int m, int n) { return n != 0 ? gcd(n, m % n) : m; }
    }// namespace simplified_fractions
 
    namespace minimum_difference_between_highest_and_lowest_of_k_scores {
        int Solution::minimumDifference(vector<int> &nums, int k) {
            int ans = 100000;
            sort(nums.begin(), nums.end());
            for(int i = 0; i + k - 1 < nums.size(); i++) {
                ans = min(ans, nums[i + k - 1] - nums[i]);
            }
            return ans;
        }
    }// namespace minimum_difference_between_highest_and_lowest_of_k_scores
 
    namespace number_of_enclaves {
        int Solution::numEnclaves(vector<vector<int>> &grid) {
            int sum     = 0;
            const int m = grid.size();
            const int n = grid[0].size();
            auto que    = queue<pair<int, int>>();
            for(int i = 0; i < m; i++) {
                for(int j = 0; j < n; j++) {
                    if(grid[i][j] == 1) {
                        sum++;
                        if(i == 0 || i == m - 1 || j == 0 || j == n - 1) {
                            que.push(make_pair(i, j));
                            grid[i][j] = 0;
                        }
                    }
                }
            }
            while(!que.empty()) {
                auto [x, y] = que.front();
                sum--;
                que.pop();
                pair<int, int> nexts[4] = {make_pair(x + 1, y), make_pair(x - 1, y), make_pair(x, y + 1), make_pair(x, y - 1)};
                for(auto next: nexts) {
                    auto [next_x, next_y] = next;
                    if(0 <= next_x && next_x < m && 0 <= next_y && next_y < n && grid[next_x][next_y] != 0) {
                        que.push(next);
                        grid[next_x][next_y] = 0;
                    }
                }
            }
            return sum;
        }
    }// namespace number_of_enclaves
 
    namespace maximum_number_of_balloons {
        int Solution::maxNumberOfBalloons(const string &text) {
            int b = 0;
            int a = 0;
            int l = 0;
            int o = 0;
            int n = 0;
            for(const char ch: text) {
                switch(ch) {
                    case 'b':
                        b++;
                        break;
                    case 'a':
                        a++;
                        break;
                    case 'l':
                        l++;
                        break;
                    case 'o':
                        o++;
                        break;
                    case 'n':
                        n++;
                        break;
                }
            }
            l /= 2;
            o /= 2;
            int ans = b;
            ans     = min(ans, a);
            ans     = min(ans, l);
            ans     = min(ans, o);
            ans     = min(ans, n);
            return ans;
        }
    }// namespace maximum_number_of_balloons
 
    namespace swap_adjacent_in_lr_string {
        bool Solution::canTransform(const string &start, const string &end) {
            auto oss_start = ostringstream();
            auto oss_end   = ostringstream();
            auto i_start   = vector<int>();
            auto i_end     = vector<int>();
            for(int i = 0; i < start.size(); i++) {
                char ch = start[i];
                if(ch == 'R' || ch == 'L') {
                    oss_start << ch;
                    i_start.push_back(i);
                }
            }
            for(int i = 0; i < end.size(); i++) {
                char ch = end[i];
                if(ch == 'R' || ch == 'L') {
                    oss_end << ch;
                    i_end.push_back(i);
                }
            }
            string str_start = oss_start.str();
            string str_end   = oss_end.str();
            if(str_start != str_end) {
                return false;
            }
            for(int i = 0; i < i_start.size(); i++) {
                if(str_start[i] == 'R') {
                    if(i_start[i] > i_end[i]) {
                        return false;
                    }
                } else {
                    //L
                    if(i_start[i] < i_end[i]) {
                        return false;
                    }
                }
            }
            return true;
        }
    }// namespace swap_adjacent_in_lr_string
 
    namespace count_operations_to_obtain_zero {
        int Solution::countOperations(int num1, int num2) {
            int count = 0;
            while(num1 != 0 && num2 != 0) {
                if(num1 > num2) {
                    count += num1 / num2;
                    num1 = num1 % num2;
                } else {
                    count += num2 / num1;
                    num2 = num2 % num1;
                }
            }
            return count;
        }
    }// namespace count_operations_to_obtain_zero
 
    namespace minimum_operations_to_make_the_array_alternating {
        int Solution::minimumOperations(vector<int> &nums) {
            int a_sum = 0;
            int b_sum = 0;
            auto a    = unordered_map<int, int>();
            auto b    = unordered_map<int, int>();
            for(int i = 0; i < nums.size(); i++) {
                if(i % 2 == 0) {
                    a[nums[i]]++;
                    a_sum++;
                } else {
                    b[nums[i]]++;
                    b_sum++;
                }
            }
            int max_num = 0;
            int maximum = 0;
            int ans1    = 0;
            for(const auto i: a) {
                if(maximum < i.second) {
                    maximum = i.second;
                    max_num = i.first;
                }
            }
            ans1 += a_sum - maximum;
            maximum = 0;
            for(const auto i: b) {
                if(i.first != max_num && maximum < i.second) {
                    maximum = i.second;
                }
            }
            ans1 += b_sum - maximum;
 
            int ans2 = 0;
            max_num  = 0;
            maximum  = 0;
            for(const auto i: b) {
                if(maximum < i.second) {
                    maximum = i.second;
                    max_num = i.first;
                }
            }
            ans2 += b_sum - maximum;
            maximum = 0;
            for(const auto i: a) {
                if(i.first != max_num && maximum < i.second) {
                    maximum = i.second;
                }
            }
            ans2 += a_sum - maximum;
            return min(ans1, ans2);
        }
    }// namespace minimum_operations_to_make_the_array_alternating
 
    namespace removing_minimum_number_of_magic_beans {
        long long Solution::minimumRemoval(vector<int> &beans) {
            sort(beans.begin(), beans.end());
            long long sum     = 0;
            long long maximum = 0;
            for(int i = 0; i < beans.size(); i++) {
                sum += beans[i];
                maximum = max(maximum, static_cast<long long>(beans[i] * (beans.size() - i)));
            }
            return sum - maximum;
        }
    }// namespace removing_minimum_number_of_magic_beans
 
    namespace maximum_and_sum_of_array {
        int Solution::maximumANDSum(vector<int> &nums, int numSlots) {
            int ans = 0;
            vector<int> max_and_sum_of_status(1 << numSlots * 2);
            for(unsigned int status = 0; status < max_and_sum_of_status.size(); ++status) {
                //status:已经放置数字的篮子的集合
                const int one_count = popcount(status);
                if(one_count >= nums.size()) {
                    continue;
                }
                for(int next_slot = 0; next_slot < numSlots * 2; ++next_slot) {
                    if((status & 1 << next_slot) == 0) {
                        // next_slot是空的
                        const int next_status              = status | 1 << next_slot;                                                                              
                        const auto slot_num                = next_slot / 2 + 1;                                                                                    
                        max_and_sum_of_status[next_status] = max(max_and_sum_of_status[next_status], max_and_sum_of_status[status] + (slot_num & nums[one_count]));//放置第onecount个数字
                        ans                                = max(ans, max_and_sum_of_status[next_status]);
                    }
                }
            }
            return ans;
        }
    }// namespace maximum_and_sum_of_array
 
    namespace single_element_in_a_sorted_array {
        int Solution::singleNonDuplicate(vector<int> &nums) {
            int l = 0;
            int r = nums.size() - 1;
            while(l < r) {
                if(l + 1 == r) {
                    if(l == 0) {
                        return nums[l];
                    }
                    if(r == nums.size() - 1) {
                        return nums[r];
                    }
                    if(nums[l - 1] == nums[l]) {
                        return nums[r];
                    }
                    return nums[l];
                }
                const int m = (l + r) / 2;
                int tmp     = m;
                if(nums[m + 1] == nums[m]) {
                    tmp = m + 1;
                }
                if(tmp % 2 == 0) {
                    //在左边
                    r = m;
                } else {
                    //在右边
                    l = m;
                }
            }
            return nums[l];
        }
    }// namespace single_element_in_a_sorted_array
 
    namespace lucky_numbers_in_a_matrix {
        vector<int> Solution::luckyNumbers(vector<vector<int>> &matrix) {
            auto ans      = vector<int>();
            const auto m  = matrix.size();
            const auto n  = matrix[0].size();
            auto *minimum = new int[m];
            memset(minimum, 50, m * sizeof(int));
            auto *maximum = new int[n];
            memset(maximum, 0, n * sizeof(int));
            for(int i = 0; i < m; i++) {
                for(int j = 0; j < n; j++) {
                    minimum[i] = min(minimum[i], matrix[i][j]);
                    maximum[j] = max(maximum[j], matrix[i][j]);
                }
            }
            for(int i = 0; i < m; i++) {
                for(int j = 0; j < n; j++) {
                    if(matrix[i][j] == minimum[i] && matrix[i][j] == maximum[j]) {
                        ans.push_back(matrix[i][j]);
                    }
                }
            }
            delete[] minimum;
            delete[] maximum;
            return ans;
        }
    }// namespace lucky_numbers_in_a_matrix
 
    namespace number_of_ways_to_reconstruct_a_tree {
        int Solution::checkWays(vector<vector<int>> &pairs) {
            unordered_map<int, unordered_set<int>> adj;
            for(auto &p: pairs) {
                adj[p[0]].emplace(p[1]);
                adj[p[1]].emplace(p[0]);
            }
            /* 检测是否存在根节点*/
            int root = -1;
            for(auto &[node, neighbours]: adj) {
                if(neighbours.size() == adj.size() - 1) {
                    root = node;
                    break;
                }
            }
            if(root == -1) {
                return 0;
            }
 
            int res = 1;
            for(auto &[node, neighbours]: adj) {
                if(node == root) {
                    continue;
                }
                const int currDegree = neighbours.size();
                int parent           = -1;
                int parentDegree     = INT_MAX;
 
                /* 根据 degree 的大小找到 node 的父节点 parent */
                for(const auto &neighbour: neighbours) {
                    if(adj[neighbour].size() < parentDegree && adj[neighbour].size() >= currDegree) {
                        parent       = neighbour;
                        parentDegree = adj[neighbour].size();
                    }
                }
                if(parent == -1) {
                    return 0;
                }
 
                /* 检测 neighbours 是否是 adj[parent] 的子集 */
                for(const auto &neighbour: neighbours) {
                    if(neighbour == parent) {
                        continue;
                    }
                    if(static_cast<unsigned int>(adj[parent].contains(neighbour)) == 0U) {
                        return 0;
                    }
                }
                if(parentDegree == currDegree) {
                    res = 2;
                }
            }
            return res;
        }
    }// namespace number_of_ways_to_reconstruct_a_tree
 
    namespace find_center_of_star_graph {
        int Solution::findCenter(vector<vector<int>> &edges) {
            auto um = unordered_map<int, int>();
            for(auto edge: edges) {
                um[edge[0]]++;
                um[edge[1]]++;
                if(um[edge[0]] > 1) {
                    return edge[0];
                }
                if(um[edge[1]] > 1) {
                    return edge[1];
                }
            }
            return 0;
        }
    }// namespace find_center_of_star_graph
 
    namespace knight_probability_in_chessboard {
        double Solution::knightProbability(int n, int k, int row, int column) {
            if(k == 0) {
                return 1;
            }
            const auto s = status(k, row, column);
            if(um.count(s) == 1) {
                return um[s];
            }
            int off                 = 0;
            pair<int, int> nexts[8] = {make_pair(row - 2, column - 1),
                                       make_pair(row - 2, column + 1),
                                       make_pair(row + 2, column - 1),
                                       make_pair(row + 2, column + 1),
                                       make_pair(row - 1, column - 2),
                                       make_pair(row - 1, column + 2),
                                       make_pair(row + 1, column - 2),
                                       make_pair(row + 1, column + 2)};
            double sum              = 0;
            for(auto [next_x, next_y]: nexts) {
                if(0 <= next_x && next_x < n && 0 <= next_y && next_y < n) {
                    sum += knightProbability(n, k - 1, next_x, next_y);
                }
            }
            const double ans = sum / 8;
            um[s]            = ans;
            return ans;
        }
 
        unsigned int status_hash::operator()(const status &s) const { return s.k * 25 * 25 + s.row * 25 + s.column; }
 
        bool status_equal::operator()(const status &s1, const status &s2) const { return s1.k == s2.k && s1.row == s2.row && s1.column == s2.column; }
    }// namespace knight_probability_in_chessboard
 
    namespace pancake_sorting {
        vector<int> Solution::pancakeSort(vector<int> &arr) {
            auto ans      = vector<int>();
            const int n   = arr.size();
            auto *current = new int[n];
            auto *sorted  = new int[n];
            for(int i = 0; i < n; i++) {
                current[i] = arr[i];
                sorted[i]  = arr[i];
            }
            sort(sorted, sorted + n);
        RESTART:
            for(int i = n - 1; i >= 0; i--) {
                if(current[i] != sorted[i]) {
                    const int target = sorted[i];
                    int target_i     = -1;
                    for(int j = 0; j <= i; j++) {
                        if(current[j] == target) {
                            target_i = j + 1;
                            break;
                        }
                    }
                    if(target_i == 1) {
                        target_i = i + 1;
                    }
                    ans.push_back(target_i);
                    for(int j = 0; j < target_i / 2; j++) {
                        swap(current[j], current[target_i - j - 1]);
                    }
                    goto RESTART;
                }
            }
            delete[] current;
            delete[] sorted;
            return ans;
        }
    }// namespace pancake_sorting
 
    namespace count_equal_and_divisible_pairs_in_an_array {
        int Solution::countPairs(vector<int> &nums, int k) {
            int ans = 0;
            for(int i = 0; i + 1 < nums.size(); i++) {
                for(int j = i + 1; j < nums.size(); j++) {
                    if(nums[i] == nums[j] && i * j % k == 0) {
                        ans++;
                    }
                }
            }
            return ans;
        }
    }// namespace count_equal_and_divisible_pairs_in_an_array
 
    namespace find_three_consecutive_integers_that_sum_to_a_given_number {
        vector<long long> Solution::sumOfThree(long long int num) {
            if(num % 3 == 0) {
                const long long mid = num / 3;
                vector ans          = {mid - 1, mid, mid + 1};
                return ans;
            }
            return {};
        }
    }// namespace find_three_consecutive_integers_that_sum_to_a_given_number
 
    namespace maximum_split_of_positive_even_integers {
        vector<long long> Solution::maximumEvenSplit(long long int finalSum) {
            if(finalSum % 2 != 0) {
                return {};
            }
            if(finalSum == 4) {
                return {4};
            }
            auto ans = vector<long long int>();
            ans.push_back(2);
            finalSum -= 2;
            for(long long i = 4; i <= finalSum; i += 2) {
                const long long int next = finalSum - i;
                if(next > i) {
                    ans.push_back(i);
                    finalSum = next;
                } else {
                    ans.push_back(finalSum);
                    break;
                }
            }
            return ans;
        }
    }// namespace maximum_split_of_positive_even_integers
 
    namespace count_good_triplets_in_an_array {
        long long Solution::goodTriplets(vector<int> &nums1, vector<int> &nums2) {
            const int n = nums1.size();
            FenwickTree<int> occur(n);
            unordered_map<int, int> pos;
            for(int i = 0; i < n; ++i) {
                pos[nums2[i]] = i + 1;
            }
            long long ans = 0;
            for(int i = 0; i < n; ++i) {
                const int idx   = pos[nums1[i]];
                const int left  = occur.query(idx);
                const int right = n - idx - (occur.query(n) - occur.query(idx));
                ans += 1LL * left * right;
                occur.update(idx, 1);
            }
 
            return ans;
        }
    }// namespace count_good_triplets_in_an_array
 
    namespace count_integers_with_even_digit_sum {
        int Solution::countEven(int num) {
            int ans = 0;
            for(int i = 1; i <= num; i++) {
                stringstream ss;
                ss << i;
                char ch;
                int sum = 0;
                while(ss >> ch) {
                    sum += ch - '0';
                }
                if(sum % 2 == 0) {
                    ans++;
                }
            }
            return ans;
        }
    }// namespace count_integers_with_even_digit_sum
 
    namespace merge_nodes_in_between_zeros {
        ListNode *Solution::mergeNodes(ListNode *head) {
            while(head != nullptr && head->val == 0) {
                head = head->next;
            }
            auto *prev = head;
            while(head != nullptr && head->next != nullptr) {
                if(head->next->val != 0) {
                    head->val += head->next->val;
                    head->next = head->next->next;
                } else {
                    head->next = head->next->next;
                    head       = head->next;
                }
            }
            return prev;
        }
    }// namespace merge_nodes_in_between_zeros
 
    namespace construct_string_with_repeat_limit {
        string Solution::repeatLimitedString(const string &s, int repeatLimit) {
            int ch[26] = {};
            for(const char c: s) {
                ch[c - 'a']++;
            }
            auto oss = ostringstream();
            for(int i = 25; i >= 0; i--) {
                int repeat = 0;
                while(ch[i] != 0) {
                    oss << static_cast<char>(i + 'a');
                    repeat++;
                    ch[i]--;
                    if(repeat == repeatLimit && ch[i] != 0) {
                        for(int j = i - 1; j >= 0; j--) {
                            if(ch[j] > 0) {
                                oss << static_cast<char>(j + 'a');
                                ch[j]--;
                                repeat = 0;
                                break;
                            }
                        }
                        if(repeat != 0) {
                            return oss.str();
                        }
                    }
                }
            }
            return oss.str();
        }
    }// namespace construct_string_with_repeat_limit
 
    namespace count_array_pairs_divisible_by_k {
        long long Solution::coutPairs(vector<int> &nums, int k) {
            long long ans = 0;
            // 统计每个数的倍数出现的次数
            auto count = unordered_map<int, int>();
            for(const auto num: nums) {
                count[num]++;
            }
            const int maximum = *max_element(nums.begin(), nums.end());
            // 为什么这个算法是 O(nlnn) 的？因为这个算法的循环次数是 n(1 + 1/2 + 1/3 + ...)，由调和级数可知括号内趋向 lnn
            for(int i = 1; i <= maximum; i++) {
                for(int j = i * 2; j <= maximum; j += i) {
                    count[i] += count[j];
                }
            }
            for(const auto num: nums) {
                // 对于每个数统计与它形成好二元组的数有几个
                ans += count[k / gcd(k, num)];
                if(static_cast<long long>(num) * num % k == 0) {
                    // 排除自己和自己形成好二元组的情况
                    ans--;
                }
            }
            return ans / 2;
        }
    }// namespace count_array_pairs_divisible_by_k
 
    namespace leetcode717_1_bit_and_2_bit_characters {
        bool Solution::isOneBitCharacter(vector<int> &bits) {
            for(int i = 0; i < bits.size();) {
                int next = i;
                if(bits[i] == 1) {
                    next += 2;
                } else {
                    next += 1;
                }
                if(next >= bits.size()) {
                    return i == bits.size() - 1;
                }
                i = next;
            }
            return false;
        }
    }// namespace leetcode717_1_bit_and_2_bit_characters
 
    namespace longest_mountain_in_array {
        int Solution::longestMountain(vector<int> &arr) {
            if(arr.size() < 3) {
                return 0;
            }
            auto up_down = vector<int>(arr.size() - 1);
            for(int i = 0; i + 1 < arr.size(); i++) {
                if(arr[i] < arr[i + 1]) {
                    up_down[i] = 1;
                } else if(arr[i] > arr[i + 1]) {
                    up_down[i] = 0;
                } else {
                    up_down[i] = 2;
                }
            }
            auto sector_size = vector<pair<int, int>>();
            int prev         = up_down[0];
            int count        = 1;
            for(int i = 1; i < up_down.size(); i++) {
                if(up_down[i] != prev) {
                    sector_size.emplace_back(prev, count);
                    count = 1;
                } else {
                    count++;
                }
                prev = up_down[i];
            }
            sector_size.emplace_back(prev, count);
            if(sector_size.size() < 2) {
                return 0;
            }
            int maximum = 0;
            for(int i = 0; i + 1 < sector_size.size(); i++) {
                if(sector_size[i].first == 1 && sector_size[i + 1].first == 0) {
                    maximum = max(maximum, sector_size[i].second + sector_size[i + 1].second + 1);
                }
            }
            return maximum;
        }
    }// namespace longest_mountain_in_array
 
    namespace push_dominoes {
        string Solution::pushDominoes(string dominoes) {
            const int n      = dominoes.length();
            auto *left_to_r  = new int[n];
            auto *right_to_l = new int[n];
            auto *left_is    = new char[n];
            auto *right_is   = new char[n];
            int l2r          = 0;
            int r2l          = 0;
            char ch          = '.';
            for(int i = 0; i < n; i++) {
                if(dominoes[i] != '.') {
                    ch = dominoes[i];
                }
                left_is[i] = ch;
            }
            ch = '.';
            for(int i = n - 1; i >= 0; i--) {
                if(dominoes[i] != '.') {
                    ch = dominoes[i];
                }
                right_is[i] = ch;
            }
            for(int i = 0; i < n; i++) {
                if(dominoes[i] == 'R') {
                    l2r = 0;
                } else {
                    l2r++;
                }
                left_to_r[i] = l2r;
            }
            for(int i = n - 1; i >= 0; i--) {
                if(dominoes[i] == 'L') {
                    r2l = 0;
                } else {
                    r2l++;
                }
                right_to_l[i] = r2l;
            }
            for(int i = 0; i < n; i++) {
                if(dominoes[i] == '.') {
                    if(left_is[i] == 'R' && right_is[i] == 'L') {
                        if(right_to_l[i] > left_to_r[i]) {
                            dominoes[i] = 'R';
                        } else if(left_to_r[i] > right_to_l[i]) {
                            dominoes[i] = 'L';
                        }
                    } else if(right_is[i] == 'L') {
                        dominoes[i] = 'L';
                    } else if(left_is[i] == 'R') {
                        dominoes[i] = 'R';
                    }
                }
            }
            delete[] left_to_r;
            delete[] right_to_l;
            delete[] left_is;
            delete[] right_is;
            return dominoes;
        }
    }// namespace push_dominoes
 
    namespace the_number_of_good_subsets {
        int Solution::numberOfGoodSubsets(vector<int> &nums) {
            vector<int> freq(num_max + 1);
            for(const int num: nums) {
                freq[num]++;
            }
 
            vector<int> f(mask_max);
            f[0] = 1;
            for(int i = 0; i < freq[1]; ++i) {
                f[0] = f[0] * 2 % mod;
            }
 
            for(int i = 2; i <= num_max; ++i) {
                if(freq[i] == 0) {
                    continue;
                }
 
                // 检查 i 的每个质因数是否均不超过 1 个
                int subset  = 0;
                const int x = i;
                bool check  = true;
                for(int j = 0; j < primes.size(); j++) {
                    const int prime = primes[j];
                    if(x % (prime * prime) == 0) {
                        check = false;
                        break;
                    }
                    if(x % prime == 0) {
                        subset |= 1 << j;
                    }
                }
                if(!check) {
                    continue;
                }
 
                // 动态规划
                for(int mask = mask_max - 1; mask > 0; mask--) {
                    if((mask & subset) == subset) {
                        f[mask] = (f[mask] + static_cast<long long>(f[mask ^ subset]) * freq[i]) % mod;
                    }
                }
            }
            int ans = 0;
            for(int mask = 1; mask < mask_max; mask++) {
                ans = (ans + f[mask]) % mod;
            }
            return ans;
        }
    }// namespace the_number_of_good_subsets
 
    namespace reverse_only_letters {
        string Solution::reverseOnlyLetters(string s) {
            for(int i = 0, j = s.length() - 1; i < j && i < s.length() && j >= 0;) {
                if(isalpha(s[i]) != 0 && isalpha(s[j]) != 0) {
                    const char temp = s[i];
                    s[i]            = s[j];
                    s[j]            = temp;
                    i++;
                    j--;
                } else {
                    while(i < s.length() && isalpha(s[i]) == 0) {
                        i++;
                    }
                    while(j >= 0 && isalpha(s[j]) == 0) {
                        j--;
                    }
                }
            }
            return s;
        }
    }// namespace reverse_only_letters
 
    namespace where_will_the_ball_fall {
        vector<int> Solution::findBall(vector<vector<int>> &grid) {
            const int m = grid.size();
            const int n = grid[0].size();
            vector<int> ans(n);
            for(int i = 0; i < n; i++) {
                int current_x = 0;
                int current_y = i;
                int dir       = 1;// 0 - 左, 1 - 下, 2 - 右
                while(true) {
                    if(current_x == m) {
                        ans[i] = current_y;
                        break;
                    }
                    if(current_x < 0 || current_y < 0 || current_y >= n) {
                        ans[i] = -1;
                        break;
                    }
                    if(dir == 0) {
                        //左
                        if(grid[current_x][current_y] == 1) {
                            ans[i] = -1;
                            break;
                        }
                        dir = 1;
                    } else if(dir == 1) {
                        //下
                        if(grid[current_x][current_y] == 1) {
                            dir = 2;
                        } else {
                            dir = 0;
                        }
                    } else {
                        //右
                        if(grid[current_x][current_y] == 1) {
                            dir = 1;
                        } else {
                            ans[i] = -1;
                            break;
                        }
                    }
                    if(dir == 0) {
                        //左
                        current_y--;
                    } else if(dir == 1) {
                        //下
                        current_x++;
                    } else {
                        //右
                        current_y++;
                    }
                }
            }
            return ans;
        }
    }// namespace where_will_the_ball_fall
 
    namespace complex_number_multiplication {
        string Solution::complexNumberMultiply(const string &num1, const string &num2) {
            auto ss = stringstream();
            ss << num1 << num2;
            int r1;
            int i1;
            int r2;
            int i2;
            ss >> r1;
            ss.get();
            ss >> i1;
            ss.get();
            ss >> r2;
            ss.get();
            ss >> i2;
            const int r = r1 * r2 - i1 * i2;
            const int i = r1 * i2 + r2 * i1;
            ss          = stringstream();
            ss << r << '+' << i << 'i';
            return ss.str();
        }
    }// namespace complex_number_multiplication
 
    namespace maximum_difference_between_increasing_elements {
        int Solution::maximumDifference(vector<int> &nums) {
            int minn     = nums[0];
            int max_diff = -1;
            for(int i = 1; i < nums.size(); i++) {
                if(nums[i] > minn) {
                    max_diff = max(max_diff, nums[i] - minn);
                }
                minn = min(minn, nums[i]);
            }
            return max_diff;
        }
    }// namespace maximum_difference_between_increasing_elements
 
    namespace optimal_division {
        string Solution::optimalDivision(vector<int> &nums) {
            auto oss = ostringstream();
            if(nums.size() == 1) {
                oss << nums[0];
            } else if(nums.size() == 2) {
                oss << nums[0] << '/' << nums[1];
            } else {
                oss << nums[0] << "/(";
                for(int i = 1; i < nums.size() - 1; i++) {
                    oss << nums[i] << '/';
                }
                oss << nums[nums.size() - 1] << ')';
            }
            return oss.str();
        }
    }// namespace optimal_division
 
    namespace counting_words_with_a_given_prefix {
        int Solution::prefixCount(vector<string> &words, string pref) {
            int ans = 0;
            for(auto word: words) {
                bool ok = true;
                for(int i = 0; i < pref.length(); i++) {
                    if(pref[i] != word[i]) {
                        ok = false;
                        break;
                    }
                }
                if(ok) {
                    ans++;
                }
            }
            return ans;
        }
    }// namespace counting_words_with_a_given_prefix
 
    namespace minimum_number_of_steps_to_make_two_strings_anagram_ii {
        int Solution::minSteps(const string &s, const string &t) {
            int ans       = 0;
            int s_num[26] = {};
            int t_num[26] = {};
            for(const char ch: s) {
                s_num[ch - 'a']++;
            }
            for(const char ch: t) {
                t_num[ch - 'a']++;
            }
            for(int i = 0; i < 26; i++) {
                ans += abs(s_num[i] - t_num[i]);
            }
            return ans;
        }
    }// namespace minimum_number_of_steps_to_make_two_strings_anagram_ii
 
    namespace minimum_time_to_complete_trips {
        long long Solution::minimumTime(vector<int> &time, int totalTrips) {
            int max_t = 1;
            int min_t = 100000;
            for(auto t: time) {
                max_t = max(max_t, t);
                min_t = min(min_t, t);
            }
            long long l = static_cast<long long>(totalTrips) / max_t / time.size();
            long long r = static_cast<long long>(totalTrips) * max_t;
            while(l <= r) {
                const long long m = (l + r) / 2;
                long long sum     = 0;
                for(const auto t: time) {
                    sum += m / t;
                }
                if(l == r || l + 1 == r) {
                    return r;
                }
                if(sum >= totalTrips) {
                    r = m;
                } else if(sum < totalTrips) {
                    l = m;
                }
            }
            return 0;
        }
    }// namespace minimum_time_to_complete_trips
 
    namespace minimum_time_to_finish_the_race {
        int Solution::minimumFinishTime(vector<vector<int>> &tires, int changeTime, int numLaps) {
            /* min_times[i] = 用一个轮胎跑 i 圈的最小花费 */
            vector<long long> min_times(20, 1e9);
            for(auto &v: tires) {
                const long long f    = v[0];
                const long long r    = v[1];
                const long long cost = f + changeTime;
                long long current    = f;
                long long sum        = cost;
                for(int i = 1; i <= 19; i++) {
                    min_times[i] = min(min_times[i], sum);
                    current *= r;
                    if(current > cost) {
                        current = f;
                        sum += cost;
                    } else {
                        sum += current;
                    }
                }
            }
            /* dp[i] = 跑 i 圈的最小花费 */
            vector<long long> dp(numLaps + 1, 1e9);
            dp[0] = 0;
            for(int i = 1; i <= numLaps; i++) {
                for(int j = 1; j <= min(19, i); j++) {
                    dp[i] = min(dp[i], dp[i - j] + min_times[j]);
                }
            }
            /* 最后需要减去一次换轮胎的时间 */
            return dp[numLaps] - changeTime;
        }
    }// namespace minimum_time_to_finish_the_race
 
    namespace maximum_number_of_achievable_transfer_requests {
        int Solution::maximumRequests(int n, vector<vector<int>> &requests) {
            int ans = 0;
            for(unsigned int i = 0; i < 1 << requests.size(); i++) {
                auto *in  = new int[n];
                auto *out = new int[n];
                memset(in, 0, n * sizeof(int));
                memset(out, 0, n * sizeof(int));
                for(unsigned int j = 0; j < requests.size(); j++) {
                    if((i & 1 << j) != 0) {
                        out[requests[j][0]]++;
                        in[requests[j][1]]++;
                    }
                }
                bool ok = true;
                for(int j = 0; j < n; j++) {
                    if(out[j] != in[j]) {
                        ok = false;
                        break;
                    }
                }
                if(ok) {
                    ans = max(ans, popcount(i));
                }
                delete[] in;
                delete[] out;
            }
            return ans;
        }
    }// namespace maximum_number_of_achievable_transfer_requests
 
    namespace zigzag_conversion {
        string Solution::convert(string s, int numRows) {
            if(numRows == 1) {
                return s;
            }
            auto oss = ostringstream();
            auto *m  = new char *[numRows];
            for(int i = 0; i < numRows; i++) {
                m[i] = new char[s.length()];
                memset(m[i], ' ', s.length() * sizeof(char));
            }
            int current_x = 0;
            int current_y = 0;
            bool dir      = true;// true = 下, false = 斜
            for(const char ch: s) {
                m[current_x][current_y] = ch;
                if(dir && current_x == numRows - 1 || !dir && current_x == 0) {
                    dir = !dir;
                }
                if(dir) {
                    current_x++;
                } else {
                    current_x--;
                    current_y++;
                }
            }
            for(int i = 0; i < numRows; i++) {
                for(int j = 0; j <= min(current_y, static_cast<int>(s.length() - 1)); j++) {
                    if(m[i][j] != ' ') {
                        oss << m[i][j];
                    }
                }
            }
            for(int i = 0; i < numRows; i++) {
                delete[] m[i];
            }
            delete[] m;
            return oss.str();
        }
    }// namespace zigzag_conversion
 
    namespace find_the_closest_palindrome {
        string Solution::nearestPalindromic(const string &n) {
            const long long num = stoll(n);
            if(num == 10 || num == 11) {
                return "9";
            }
            if(num < 10) {
                return to_string(num - 1);
            }
            int len         = n.length();
            const bool even = n.length() % 2 == 0;
            string prefix   = n.substr(0, n.length() / 2 + (even ? 0 : 1));
            string option_str[3];
            auto rev                      = string(prefix.rbegin() + (even ? 0 : 1), prefix.rend());
            option_str[2]                 = prefix + rev;
            const long long prefix_int[2] = {stoll(prefix) - 1, stoll(prefix) + 1};
            string prefix_str[2]          = {to_string(prefix_int[0]), to_string(prefix_int[1])};
            for(int i = 0; i < 2; i++) {
                if(prefix_str[i].length() == prefix.length()) {
                    rev           = string(prefix_str[i].rbegin() + (even ? 0 : 1), prefix_str[i].rend());
                    option_str[i] = prefix_str[i] + rev;
                } else if(prefix_str[i].length() > prefix.length()) {
                    rev           = string(prefix_str[i].rbegin() + (even ? 1 : 2), prefix_str[i].rend());
                    option_str[i] = prefix_str[i] + rev;
                } else if(prefix_str[i].length() < prefix.length()) {
                    rev           = string(prefix_str[i].rbegin(), prefix_str[i].rend());
                    option_str[i] = prefix_str[i] + (even ? "9" : "") + rev;
                }
            }
            long long option_int[3] = {stoll(option_str[0]), stoll(option_str[1]), stoll(option_str[2])};
            sort(option_int, option_int + 3);
            long long minimum = option_int[0];
            for(int i = 1; i < 3; i++) {
                if(abs(option_int[i] - num) < abs(minimum - num) && option_int[i] != num) {
                    minimum = option_int[i];
                }
            }
            return to_string(minimum);
        }
    }// namespace find_the_closest_palindrome
 
    namespace add_digits {
        int Solution::addDigits(int num) { return (num - 1) % 9 + 1; }
    }// namespace add_digits
 
    namespace sum_of_subarray_ranges {
        long long Solution::subArrayRanges(vector<int> &nums) {
            long long ans = 0;
            for(int i = 0; i + 1 < nums.size(); i++) {
                int minimum = nums[i];
                int maximum = nums[i];
                for(int j = i + 1; j < nums.size(); j++) {
                    minimum = min(minimum, nums[j]);
                    maximum = max(maximum, nums[j]);
                    ans += maximum - minimum;
                }
            }
            return ans;
        }
    }// namespace sum_of_subarray_ranges
 
    namespace longest_uncommon_subsequence_i {
        int Solution::findLUSlength(const string &a, const string &b) {
            if(a.length() != b.length() || b.find(a) == string::npos && a.find(b) == string::npos) {
                return max(a.length(), b.length());
            }
            return -1;
        }
    }// namespace longest_uncommon_subsequence_i
 
    namespace most_frequent_number_following_key_in_an_array {
        int Solution::mostFrequent(vector<int> &nums, int key) {
            unordered_map<int, int> um;
            for(int i = 0; i + 1 < nums.size(); i++) {
                if(nums[i] == key) {
                    um[nums[i + 1]]++;
                }
            }
            int max_v = 0;
            int max_k = 0;
            for(auto [k, v]: um) {
                if(v > max_v) {
                    max_v = v;
                    max_k = k;
                }
            }
            return max_k;
        }
    }// namespace most_frequent_number_following_key_in_an_array
 
    namespace sort_the_jumbled_numbers {
        vector<int> Solution::sortJumbled(vector<int> &mapping, vector<int> &nums) {
            vector<tuple<int, int, int>> vec;
            for(int i = 0; i < nums.size(); i++) {
                string str = to_string(nums[i]);
                ostringstream oss;
                for(const char ch: str) {
                    oss << mapping[ch - '0'];
                }
                vec.emplace_back(i, nums[i], stoi(oss.str()));
            }
            sort(vec.begin(), vec.end(), cmp());
            vector<int> ans;
            ans.reserve(vec.size());
            for(auto [i, num, rev]: vec) {
                ans.push_back(num);
            }
            return ans;
        }
    }// namespace sort_the_jumbled_numbers
 
    namespace all_ancestors_of_a_node_in_a_directed_acyclic_graph {
        vector<vector<int>> Solution::getAncestors(int n, vector<vector<int>> &edges) {
            for(int i = 0; i < n; i++) {
                nexts[i]     = unordered_set<int>();
                ancestors[i] = set<int>();
            }
            for(auto edge: edges) {
                nexts[edge[0]].insert(edge[1]);
            }
            for(int i = 0; i < n; i++) {
                for(const auto next: nexts[i]) {
                    auto *dfsd = new bool[n];
                    memset(dfsd, 0, n * sizeof(bool));
                    dfs(dfsd, i, next);
                    delete[] dfsd;
                }
            }
            vector<vector<int>> ans;
            for(int i = 0; i < n; i++) {
                vector<int> vec;
                for(auto i: ancestors[i]) {
                    vec.push_back(i);
                }
                ans.push_back(vec);
            }
            return ans;
        }
 
        void Solution::dfs(bool *dfsd, int v, int i) {
            ancestors[i].insert(v);
            dfsd[i] = true;
            for(const auto next: nexts[i]) {
                if(!dfsd[next]) {
                    dfs(dfsd, v, next);
                }
            }
        }
    }// namespace all_ancestors_of_a_node_in_a_directed_acyclic_graph
 
    namespace minimum_number_of_moves_to_make_palindrome {
        int Solution::minMovesToMakePalindrome(string s) {
            int ans = 0;
            for(int left = 0, right = s.size() - 1; left < right; left++) {
                bool even = false;
                for(int i = right; left != i; i--) {
                    if(s[left] == s[i]) {
                        even = true;
                        // 字母出现偶数次的情况，模拟交换
                        for(; i < right; i++) {
                            swap(s[i], s[i + 1]);
                            ans++;
                        }
                        right--;
                        break;
                    }
                }
                if(!even) {
                    // 字母出现奇数次的情况，计算它距离中间还有多少距离
                    ans += s.size() / 2 - left;
                }
            }
            return ans;
        }
    }// namespace minimum_number_of_moves_to_make_palindrome
 
    namespace cells_in_a_range_on_an_excel_sheet {
        vector<string> Solution::cellsInRange(const string &s) {
            vector<string> ans;
            istringstream ss(s);
            char col1;
            char col2;
            int row1;
            int row2;
            ss >> col1 >> row1;
            ss.get();
            ss >> col2 >> row2;
            for(char col = col1; col <= col2; col++) {
                for(int row = row1; row <= row2; row++) {
                    ostringstream oss;
                    oss << col << row;
                    ans.push_back(oss.str());
                }
            }
            return ans;
        }
    }// namespace cells_in_a_range_on_an_excel_sheet
 
    namespace append_k_integers_with_minimal_sum {
        long long Solution::minimalKSum(vector<int> &nums, int k) {
            long long ans = 0;
            set<int> s;
            for(auto num: nums) {
                s.insert(num);
            }
            long long limit = k;
            for(auto i = s.begin(); i != s.end() && *i <= limit; ++i) {
                limit++;
            }
            ans += limit + limit * (limit - 1) / 2;
            for(auto i = s.begin(); i != s.end() && *i < limit; ++i) {
                ans -= *i;
            }
            return ans;
        }
    }// namespace append_k_integers_with_minimal_sum
 
    namespace create_binary_tree_from_descriptions {
        TreeNode *Solution::createBinaryTree(vector<vector<int>> &descriptions) {
            unordered_map<int, TreeNode *> um;
            unordered_set<int> nodes;
            unordered_set<int> childs;
            for(auto description: descriptions) {
                nodes.insert(description[0]);
                nodes.insert(description[1]);
                childs.insert(description[1]);
            }
            for(auto node: nodes) {
                um[node] = new TreeNode();
            }
            for(auto description: descriptions) {
                if(description[2] == 1) {
                    //childi 是 parenti 的左子节点
                    um[description[0]]->left = um[description[1]];
                } else {
                    //childi 是 parenti 的右子节点。
                    um[description[0]]->right = um[description[1]];
                }
            }
            for(auto node: nodes) {
                if(!childs.contains(node)) {
                    return um[node];
                }
            }
            return nullptr;
        }
    }// namespace create_binary_tree_from_descriptions
 
    namespace replace_non_coprime_numbers_in_array {
        vector<int> Solution::replaceNonCoprimes(vector<int> &nums) {
            vector<int> ans;
            for(int i = 0; i < nums.size(); i++) {
                int num = nums[i];
                while(!ans.empty() && gcd(num, ans.back()) > 1) {
                    num = num / gcd(num, ans.back()) * ans.back();
                    ans.pop_back();
                }
                ans.push_back(num);
            }
            return ans;
        }
    }// namespace replace_non_coprime_numbers_in_array
 
    namespace find_good_days_to_rob_the_bank {
        vector<int> Solution::goodDaysToRobBank(vector<int> &security, int time) {
            if(security.size() < 2 * time + 1) {
                return {};
            }
            vector<int> ans;
            if(time == 0) {
                for(int i = 0; i < security.size(); i++) {
                    ans.push_back(i);
                }
                return ans;
            }
            vector non_increasing(security.size(), 0);
            vector non_decreasing(security.size(), 0);
            for(int i = 1; i < security.size(); i++) {
                if(security[i] >= security[i - 1]) {
                    non_decreasing[i] = non_decreasing[i - 1] + 1;
                } else {
                    non_decreasing[i] = 0;
                }
                if(security[i] <= security[i - 1]) {
                    non_increasing[i] = non_increasing[i - 1] + 1;
                } else {
                    non_increasing[i] = 0;
                }
            }
            for(int i = time; i + time < security.size(); i++) {
                if(non_decreasing[i + time] >= time && non_increasing[i] >= time) {
                    ans.push_back(i);
                }
            }
            return ans;
        }
    }// namespace find_good_days_to_rob_the_bank
 
    namespace base_7 {
        string Solution::convertToBase7(int num) {
            bool pos = true;
            if(num < 0) {
                pos = false;
                num = -num;
            }
            if(num == 0) {
                return "0";
            }
            deque<int> deq;
            while(num != 0) {
                deq.push_front(num % 7);
                num /= 7;
            }
            ostringstream oss;
            if(!pos) {
                oss << '-';
            }
            for(const int n: deq) {
                oss << n;
            }
            return oss.str();
        }
    }// namespace base_7
 
    namespace plates_between_candles {
        vector<int> Solution::platesBetweenCandles(string s, vector<vector<int>> &queries) {
            vector<int> ans;
            vector<int> plate_count(s.length());
            vector<int> candle_pos;
            if(s[0] == '*') {
                plate_count[0] = 1;
            } else {
                plate_count[0] = 0;
                candle_pos.push_back(0);
            }
            for(int i = 1; i < s.length(); i++) {
                plate_count[i] = plate_count[i - 1];
                if(s[i] == '*') {
                    plate_count[i]++;
                } else {
                    candle_pos.push_back(i);
                }
            }
            for(auto query: queries) {
                int left  = query[0];
                int right = query[1];
                auto li   = lower_bound(candle_pos.begin(), candle_pos.end(), left);
                if(li == candle_pos.end() || *li > right) {
                    ans.push_back(0);
                    continue;
                }
                auto ri = lower_bound(candle_pos.rbegin(), candle_pos.rend(), right, greater<int>());
                if(ri == candle_pos.rend() || *ri < left) {
                    ans.push_back(0);
                    continue;
                }
                ans.push_back(plate_count[*ri] - plate_count[*li]);
            }
            return ans;
        }
    }// namespace plates_between_candles
 
    namespace smallest_rotation_with_highest_score {
        int Solution::bestRotation(vector<int> &nums) {
            const int n = nums.size();
            vector k_score_diff(n + 1, 0);
            for(int i = 0; i < n; i++) {
                const int low  = (i + 1) % n;
                const int high = (i - nums[i] + n) % n;
                k_score_diff[low]++;
                k_score_diff[high + 1]--;
                if(low > high) {
                    k_score_diff[0]++;
                    k_score_diff[n]--;
                }
            }
            int ans       = 0;
            int max_score = 0;
            int score     = 0;
            for(int i = 0; i < n; i++) {
                score += k_score_diff[i];
                if(score > max_score) {
                    ans       = i;
                    max_score = score;
                }
            }
            return ans;
        }
    }// namespace smallest_rotation_with_highest_score
 
    namespace n_ary_tree_preorder_traversal {
        vector<int> Solution::preorder(Node *root) {
            if(root == nullptr) {
                return {};
            }
            vector<int> ans;
            ans.push_back(root->val);
            for(auto *child: root->children) {
                auto preorder_child = preorder(child);
                ans.insert(ans.end(), preorder_child.begin(), preorder_child.end());
            }
            return ans;
        }
    }// namespace n_ary_tree_preorder_traversal
 
    namespace count_nodes_with_the_highest_score {
        int Solution::countHighestScoreNodes(vector<int> &parents) {
            int ans     = 0;
            auto nodes  = vector<TreeNode *>(parents.size(), nullptr);
            auto edges  = vector(parents.size(), vector<int>());
            auto scores = vector<unsigned long long>(parents.size(), 0);
            for(int i = 0; i < parents.size(); i++) {
                nodes[i] = new TreeNode(i);
                if(parents[i] != -1) {
                    edges[i].push_back(parents[i]);
                    edges[parents[i]].push_back(i);
                }
            }
            TreeNode *root = nullptr;
            for(int i = 0; i < parents.size(); i++) {
                if(parents[i] != -1) {
                    nodes[parents[i]]->add_child(nodes[i]);
                } else {
                    root = nodes[i];
                }
            }
            root->dfs();
            unsigned long long max_score = 0;
            for(int i = 0; i < parents.size(); i++) {
                unsigned long long score = 1;
                const auto *node         = nodes[i];
                for(const auto *child: node->get_children()) {
                    score *= child->get_count();
                }
                if(node->get_parent() != nullptr) {
                    score *= root->get_count() - node->get_count();
                }
                max_score = max(max_score, score);
                scores[i] = score;
            }
            return count(scores.begin(), scores.end(), max_score);
        }
 
        void TreeNode::add_child(TreeNode *node) {
            this->children.push_back(node);
            node->parent = this;
        }
 
        int TreeNode::dfs() {
            int ans = 1;
            for(auto *child: this->children) {
                ans += child->dfs();
            }
            this->count = ans;
            return ans;
        }
 
        const vector<TreeNode *> &TreeNode::get_children() const { return children; }
 
        int TreeNode::get_count() const { return count; }
 
        TreeNode *TreeNode::get_parent() const { return parent; }
    }// namespace count_nodes_with_the_highest_score
 
    namespace n_ary_tree_postorder_traversal {
        vector<int> Solution::postorder(Node *root) {
            if(root == nullptr) {
                return {};
            }
            vector<int> ans;
            for(auto *child: root->children) {
                auto res = postorder(child);
                ans.insert(ans.end(), res.begin(), res.end());
            }
            ans.push_back(root->val);
            return ans;
        }
    }// namespace n_ary_tree_postorder_traversal
 
    namespace max_area_of_island {
        int Solution::maxAreaOfIsland(vector<vector<int>> &grid) {
            const int m = grid.size();
            const int n = grid[0].size();
            auto uf     = UnionFind(m, n);
            int ans     = 0;
            for(int i = 0; i < m; i++) {
                for(int j = 0; j < n; j++) {
                    if(grid[i][j] == 1) {
                        const pair<int, int> p     = make_pair(i, j);
                        ans                        = max(ans, uf.get_size(p));
                        pair<int, int> siblings[4] = {
                                make_pair(i + 1, j),
                                make_pair(i - 1, j),
                                make_pair(i, j + 1),
                                make_pair(i, j - 1),
                        };
                        for(const auto sibling: siblings) {
                            if(uf.contains(sibling) && grid[sibling.first][sibling.second] == 1 && !uf.same(p, sibling)) {
                                uf.merge(p, sibling);
                                ans = max(ans, uf.get_size(p));
                            }
                        }
                    }
                }
            }
            return ans;
        }
 
        UnionFind::UnionFind(int m, int n)
            : m(m), n(n) {
            parent = unordered_map<pair<int, int>,
                                   pair<int, int>,
                                   function<unsigned int(const pair<int, int> &)>>(
                    m * n,
                    [](const pair<int, int> &p) { return static_cast<unsigned int>(p.first * 50 + p.second); });
            size = unordered_map<pair<int, int>,
                                 int,
                                 function<unsigned int(const pair<int, int> &)>>(
                    m * n,
                    [](const pair<int, int> &p) { return static_cast<unsigned int>(p.first * 50 + p.second); });
            rank = unordered_map<pair<int, int>,
                                 int,
                                 function<unsigned int(const pair<int, int> &)>>(
                    m * n,
                    [](const pair<int, int> &p) { return static_cast<unsigned int>(p.first * 50 + p.second); });
            for(int i = 0; i < m; i++) {
                for(int j = 0; j < n; j++) {
                    pair<int, int> p = make_pair(i, j);
                    parent[p]        = p;
                    size[p]          = 1;
                    rank[p]          = 0;
                }
            }
        }
 
        pair<int, int> UnionFind::find(pair<int, int> val) {
            if(parent[val] != val) {
                parent[val] = find(parent[val]);
            }
            return parent[val];
        }
 
        void UnionFind::merge(pair<int, int> a, pair<int, int> b) {
            const auto pa = find(a);
            const auto pb = find(b);
            if(pa != pb) {
                const int sum = size[pa] + size[pb];
                if(rank[pa] > rank[pb]) {
                    parent[pb] = pa;
                } else {
                    parent[pa] = pb;
                    if(rank[pa] == rank[pb]) {
                        ++rank[pb];
                    }
                }
                size[pa] = sum;
                size[pb] = sum;
            }
        }
 
        bool UnionFind::same(pair<int, int> a, pair<int, int> b) { return find(a) == find(b); }
 
        bool UnionFind::contains(pair<int, int> p) const { return parent.contains(p); }
 
        int UnionFind::get_size(pair<int, int> p) { return size[find(p)]; }
    }// namespace max_area_of_island
 
    namespace find_all_k_distant_indices_in_an_array {
        vector<int> Solution::findKDistantIndices(vector<int> &nums, int key, int k) {
            set<int> key_set;
            set<int> ans_set;
            for(int i = 0; i < nums.size(); i++) {
                if(nums[i] == key) {
                    key_set.insert(i);
                }
            }
            for(const auto ks: key_set) {
                for(int i = ks - k; i <= ks + k; i++) {
                    if(0 <= i && i < nums.size()) {
                        ans_set.insert(i);
                    }
                }
            }
            return vector(ans_set.begin(), ans_set.end());
        }
    }// namespace find_all_k_distant_indices_in_an_array
 
    namespace count_artifacts_that_can_be_extracted {
        int Solution::digArtifacts(int n, vector<vector<int>> &artifacts, vector<vector<int>> &dig) {
            auto *grid = new bool *[n];
            for(int i = 0; i < n; i++) {
                grid[i] = new bool[n];
                memset(grid[i], 0, n * sizeof(bool));
            }
            for(auto i: dig) {
                grid[i[0]][i[1]] = true;
            }
            int ans = 0;
            for(auto artifact: artifacts) {
                bool flag = true;
                for(int i = artifact[0]; i <= artifact[2]; i++) {
                    for(int j = artifact[1]; j <= artifact[3]; j++) {
                        if(!grid[i][j]) {
                            flag = false;
                            break;
                        }
                    }
                    if(!flag) {
                        break;
                    }
                }
                if(flag) {
                    ans++;
                }
            }
            for(int i = 0; i < n; i++) {
                delete[] grid[i];
            }
            delete[] grid;
            return ans;
        }
    }// namespace count_artifacts_that_can_be_extracted
 
    namespace maximize_the_topmost_element_after_k_moves {
        int Solution::maximumTop(vector<int> &nums, int k) {
            if(nums.size() == 1 && k % 2 == 1) {
                return -1;
            }
            if(k > nums.size()) {
                int ans = -1;
                for(auto num: nums) {
                    ans = max(ans, num);
                }
                return ans;
            }
            unordered_map<int, int> element_count;
            set<int> poped_elements;
            for(auto num: nums) {
                element_count[num]++;
            }
            for(int i = 0; i < nums.size() && i < k - 1; i++) {
                poped_elements.insert(nums[i]);
                element_count[nums[i]]--;
            }
            int ans = -1;
            if(k < nums.size()) {
                ans = nums[k];
            }
            int maximum = -1;
            for(const auto i = poped_elements.rbegin(); i != poped_elements.rend();) {
                maximum = *i;
                break;
            }
            return max(ans, maximum);
        }
    }// namespace maximize_the_topmost_element_after_k_moves
 
    namespace minimum_weighted_subgraph_with_the_required_paths {
        long long Solution::minimumWeight(int n, vector<vector<int>> &edges, int src1, int src2, int dest) {
            auto *graph     = new vector<pair<int, int>>[n];
            auto *graph_rev = new vector<pair<int, int>>[n];
            for(int i = 0; i < n; i++) {
                graph[i]     = vector<pair<int, int>>();
                graph_rev[i] = vector<pair<int, int>>();
            }
            for(auto &edge: edges) {
                auto from   = edge[0];
                auto to     = edge[1];
                auto weight = edge[2];
                graph[from].emplace_back(to, weight);
                graph_rev[to].emplace_back(from, weight);
            }
 
            long long a = LLONG_MAX;
            vector dist_src1(n, LLONG_MAX);
            vector dist_src2(n, LLONG_MAX);
            vector dist_dest(n, LLONG_MAX);
 
            calc_dist(src1, graph, dist_src1);
            calc_dist(src2, graph, dist_src2);
            calc_dist(dest, graph_rev, dist_dest);
 
            long long ans = LLONG_MAX;
 
            for(int i = 0; i < n; ++i) {
                if(dist_src1[i] != LLONG_MAX && dist_src2[i] != LLONG_MAX && dist_dest[i] != LLONG_MAX) {
                    ans = min(ans, dist_src1[i] + dist_src2[i] + dist_dest[i]);
                }
            }
            if(ans == LLONG_MAX) {
                ans = -1;
            }
            delete[] graph;
            delete[] graph_rev;
            return ans;
        }
 
        void Solution::calc_dist(int s, vector<pair<int, int>> *graph, vector<long long int> &dist) {
            priority_queue<pair<long long, int>, vector<pair<long long, int>>, greater<>> pq;
            dist[s] = 0;
            pq.emplace(0, s);
            while(!pq.empty()) {
                auto [weight, node] = pq.top();
                pq.pop();
                if(weight > dist[node]) {
                    continue;
                }
                for(auto [next_node, next_weight]: graph[node]) {
                    if(weight + next_weight < dist[next_node]) {
                        dist[next_node] = weight + next_weight;
                        pq.emplace(weight + next_weight, next_node);
                    }
                }
            }
        }
    }// namespace minimum_weighted_subgraph_with_the_required_paths
 
    namespace utf_8_validation {
        bool Solution::validUtf8(vector<int> &data) {
            vector<int> len;
            for(const auto num: data) {
                if(num >> 7 == 0) {
                    //0xxxxxxx
                    len.push_back(1);
                } else if(num >> 3 == 30) {
                    //11110xxx
                    len.push_back(4);
                } else if(num >> 4 == 14) {
                    //1110xxxx
                    len.push_back(3);
                } else if(num >> 5 == 6) {
                    //110xxxxx
                    len.push_back(2);
                } else if(num >> 6 == 2) {
                    //10xxxxxx
                    len.push_back(-1);
                } else {
                    return false;
                }
            }
            int count = 0;
            for(int i = 0; i < len.size(); i++) {
                if(count != 0) {
                    if(len[i] != -1) {
                        return false;
                    }
                } else {
                    count = len[i];
                    if(count == -1) {
                        return false;
                    }
                }
                count--;
            }
            return count == 0;
        }
    }// namespace utf_8_validation
 
    namespace minimum_index_sum_of_two_lists {
        vector<string> Solution::findRestaurant(vector<string> &list1, vector<string> &list2) {
            unordered_map<string, int> restaurants;
            unordered_map<string, int> index1;
            unordered_map<string, int> index2;
            for(int i = 0; i < list1.size(); i++) {
                restaurants[list1[i]]++;
                index1[list1[i]] = i;
            }
            for(int i = 0; i < list2.size(); i++) {
                restaurants[list2[i]]++;
                index2[list2[i]] = i;
            }
            unordered_set<string> optional_restaurants;
            for(auto [restaurant, count]: restaurants) {
                if(count > 1) {
                    optional_restaurants.insert(restaurant);
                }
            }
            int min_index_sum = INT_MAX;
            for(const auto &optional_restaurant: optional_restaurants) {
                int index_sum = index1[optional_restaurant] + index2[optional_restaurant];
                min_index_sum = min(min_index_sum, index_sum);
            }
            vector<string> ans;
            for(const auto &optional_restaurant: optional_restaurants) {
                int index_sum = index1[optional_restaurant] + index2[optional_restaurant];
                if(index_sum == min_index_sum) {
                    ans.push_back(optional_restaurant);
                }
            }
            return ans;
        }
    }// namespace minimum_index_sum_of_two_lists
 
    namespace count_number_of_maximum_bitwise_or_subsets {
        int Solution::countMaxOrSubsets(vector<int> &nums) {
            int max = 0;
            for(const auto num: nums) {
                max |= num;
            }
            return dfs(0, max, nums);
        }
 
        int Solution::dfs(int current, int target, vector<int> nums) {
            if((current | target) == current) {
                return 1 << nums.size();
            }
            int sum         = 0;
            vector nums_cpy = nums;
            for(int i = 0; i < nums.size(); i++) {
                nums_cpy.erase(nums_cpy.begin());
                sum += dfs(current | nums[i], target, nums_cpy);
            }
            return sum;
        }
    }// namespace count_number_of_maximum_bitwise_or_subsets
 
    namespace all_oone_data_structure {
        AllOne::AllOne() {
            str_count = unordered_map<string, int>();
            count_str = map<int, unordered_set<string>>();
        }
 
        void AllOne::inc(const string &key) {
            const int prev = str_count[key]++;
            count_str[prev].erase(key);
            count_str[prev + 1].insert(key);
            if(count_str[prev].empty()) {
                count_str.erase(prev);
            }
            if(!count_str.empty()) {
                min = count_str.begin()->first;
                max = count_str.rbegin()->first;
            } else {
                min = 50000;
                max = 0;
            }
        }
 
        void AllOne::dec(const string &key) {
            const int prev = str_count[key]--;
            if(str_count[key] == 0) {
                str_count.erase(key);
            }
            count_str[prev].erase(key);
            if(count_str[prev].empty()) {
                count_str.erase(prev);
            }
            if(prev != 1) {
                count_str[prev - 1].insert(key);
            }
            if(!count_str.empty()) {
                min = count_str.begin()->first;
                max = count_str.rbegin()->first;
            } else {
                min = 50000;
                max = 0;
            }
        }
 
        string AllOne::getMaxKey() {
            if(str_count.empty()) {
                return "";
            }
            return *count_str[max].begin();
        }
 
        string AllOne::getMinKey() {
            if(str_count.empty()) {
                return "";
            }
            return *count_str[min].begin();
        }
    }// namespace all_oone_data_structure
 
    namespace longest_word_in_dictionary {
        string Solution::longestWord(vector<string> &words) {
            auto root = TrieNode('0');
            for(const auto &word: words) {
                root.insert(word);
            }
            return dfs("", &root);
        }
 
        string Solution::dfs(const string &str, TrieNode *node) {
            string ans = str;
            for(auto *next: node->nexts) {
                if(next != nullptr && next->end_of_word) {
                    string ret = dfs(str + next->ch, next);
                    if(ans.length() < ret.length()) {
                        ans = ret;
                    }
                }
            }
            return ans;
        }
    }// namespace longest_word_in_dictionary
 
    namespace simple_bank_system {
        Bank::Bank(vector<long long int> &balance) {
            accounts = unordered_map<int, long long>(balance.size());
            for(int i = 0; i < balance.size(); i++) {
                accounts[i + 1] = balance[i];
            }
        }
 
        bool Bank::transfer(int account1, int account2, long long int money) {
            if(!accounts.contains(account1) || !accounts.contains(account2)) {
                return false;
            }
            if(accounts[account1] < money) {
                return false;
            }
            accounts[account1] -= money;
            accounts[account2] += money;
            return true;
        }
 
        bool Bank::deposit(int account, long long int money) {
            if(!accounts.contains(account)) {
                return false;
            }
            accounts[account] += money;
            return true;
        }
 
        bool Bank::withdraw(int account, long long int money) {
            if(!accounts.contains(account)) {
                return false;
            }
            if(accounts[account] < money) {
                return false;
            }
            accounts[account] -= money;
            return true;
        }
    }// namespace simple_bank_system
 
    namespace construct_string_from_binary_tree {
        string Solution::tree2str(TreeNode *root) {
            ostringstream oss;
            oss << root->val;
            if(root->left != nullptr) {
                oss << '(' << tree2str(root->left) << ')';
            } else if(root->right != nullptr) {
                oss << "()";
            }
            if(root->right != nullptr) {
                oss << '(' << tree2str(root->right) << ')';
            }
            return oss.str();
        }
    }// namespace construct_string_from_binary_tree
 
    namespace maximize_number_of_subsequences_in_a_string {
        long long Solution::maximumSubsequenceCount(string text, string pattern) {
            long long ans   = 0;
            long long count = 0;
            vector<long long> p1count(text.length());
            long long p0count          = 0;
            long long p1c              = 0;
            p1count[text.length() - 1] = 0;
            for(int i = text.length() - 1; i >= 0; i--) {
                if(text[i] == pattern[1]) {
                    count++;
                } else if(text[i] == pattern[0]) {
                    p0count++;
                }
                if(i - 1 >= 0) {
                    p1count[i - 1] = count;
                }
            }
            for(int i = 0; i < text.length(); i++) {
                if(text[i] == pattern[0]) {
                    ans += p1count[i];
                }
            }
            ans += max(p0count, count);
            return ans;
        }
    }// namespace maximize_number_of_subsequences_in_a_string
 
    namespace minimum_operations_to_halve_array_sum {
        int Solution::halveArray(vector<int> &nums) {
            long double sum = 0;
            int ans         = 0;
            priority_queue<long double> pq;
            for(const auto num: nums) {
                pq.push(num);
                sum += num;
            }
            const long double target = sum / 2;
            while(sum > target) {
                auto num = pq.top();
                pq.pop();
                num /= 2;
                sum -= num;
                pq.push(num);
                ans++;
            }
            return ans;
        }
    }// namespace minimum_operations_to_halve_array_sum
 
    namespace minimum_white_tiles_after_covering_with_carpets {
        int Solution::minimumWhiteTiles(string floor, int numCarpets, int carpetLen) {
            const int n = floor.length();
            vector f(numCarpets + 1, vector<int>(n));
            f[0][0] = floor[0] % 2;
            for(int i = 1; i < n; ++i) {
                f[0][i] = f[0][i - 1] + floor[i] % 2;
            }
            for(int i = 1; i <= numCarpets; ++i) {
                // j < carpetLen 的 f[i][j] 均为 0
                for(int j = carpetLen; j < n; ++j) {
                    f[i][j] = min(f[i][j - 1] + floor[j] % 2, f[i - 1][j - carpetLen]);
                }
            }
            return f[numCarpets][n - 1];
        }
    }// namespace minimum_white_tiles_after_covering_with_carpets
 
    namespace count_hills_and_valleys_in_an_array {
        int Solution::countHillValley(vector<int> &nums) {
            int ans      = 0;
            const auto u = unique(nums.begin(), nums.end());
            nums.erase(u, nums.end());
            for(int i = 1; i + 1 < nums.size(); i++) {
                if(nums[i] > nums[i - 1] && nums[i] > nums[i + 1] || nums[i] < nums[i - 1] && nums[i] < nums[i + 1]) {
                    ans++;
                }
            }
            return ans;
        }
    }// namespace count_hills_and_valleys_in_an_array
 
    namespace count_collisions_on_a_road {
        int Solution::countCollisions(const string &directions) {
            int ans = 0;
            vector<char> status;
            vector<int> count;
            int current = 0;
            for(char ch: directions) {
                if(status.empty()) {
                    status.push_back(ch);
                    current++;
                } else {
                    if(status.back() == ch) {
                        current++;
                    } else {
                        status.push_back(ch);
                        count.push_back(current);
                        current = 1;
                    }
                }
            }
            count.push_back(current);
            for(int i = 0; i + 1 < status.size(); i++) {
                if(status[i] == 'R' && status[i + 1] == 'L') {
                    ans += count[i] + count[i + 1];
                } else if(status[i] == 'R' && status[i + 1] == 'S') {
                    ans += count[i];
                } else if(status[i] == 'S' && status[i + 1] == 'L') {
                    ans += count[i + 1];
                }
            }
            return ans;
        }
    }// namespace count_collisions_on_a_road
 
    namespace maximum_points_in_an_archery_competition {
        vector<int> Solution::maximumBobPoints(int numArrows, vector<int> &aliceArrows) {
            int maximum = 0;
            int max_n   = 0;
            for(unsigned int n = 1; n < 1 << 11; n++) {
                int rest  = numArrows;
                int score = 0;
                for(int i = 0; i <= 10; i++) {
                    if((n & 1 << i) != 0) {
                        score += 11 - i;
                        rest -= aliceArrows[11 - i] + 1;
                    }
                    if(rest < 0) {
                        goto NEXT_N;
                    }
                }
                if(maximum < score) {
                    maximum = score;
                    max_n   = n;
                }
            NEXT_N:;
            }
            vector ans(aliceArrows.size(), 0);
            for(int i = 0; i <= 10; i++) {
                if((max_n & 1 << i) != 0) {
                    numArrows -= aliceArrows[11 - i] + 1;
                    ans[11 - i] = aliceArrows[11 - i] + 1;
                }
            }
            ans[0] += numArrows;
            return ans;
        }
    }// namespace maximum_points_in_an_archery_competition
 
    namespace the_time_when_the_network_becomes_idle {
        int Solution::networkBecomesIdle(vector<vector<int>> &edges, vector<int> &patience) {
            unordered_map<int, Node *> um;
            unordered_set<int> nodes;
            for(int i = 0; i < patience.size(); i++) {
                um[i] = new Node(i, patience[i]);
                nodes.insert(i);
            }
            for(auto edge: edges) {
                um[edge[0]]->linked.insert(edge[1]);
                um[edge[1]]->linked.insert(edge[0]);
            }
            auto comp = [](const pair<int, int> &s1, const pair<int, int> &s2) -> bool { return s1.second > s2.second; };
            priority_queue<pair<int, int>, vector<pair<int, int>>, decltype(comp)> pq;
            pq.push(make_pair(0, 0));
            while(!nodes.empty()) {
                auto [num, len] = pq.top();
                pq.pop();
                if(nodes.contains(num)) {
                    nodes.erase(num);
                    Node *node = um[num];
                    node->time = len;
                    for(auto next: node->linked) {
                        if(nodes.contains(next)) {
                            pq.push(make_pair(next, len + 1));
                        }
                    }
                }
            }
            int ans = 0;
            for(auto [num, node]: um) {
                if(num != 0) {
                    int resent_num = node->time * 2 / node->patience;
                    if(node->time * 2 % node->patience == 0) {
                        resent_num--;
                    }
                    ans = max(ans, resent_num * node->patience + 2 * node->time + 1);
                }
            }
            return ans;
        }
    }// namespace the_time_when_the_network_becomes_idle
 
    namespace two_sum_iv_input_is_a_bst {
        bool Solution::findTarget(TreeNode *root, int k) {
            set<int> s;
            unordered_map<int, int> count;
            queue<TreeNode *> que;
            que.push(root);
            while(!que.empty()) {
                const auto *node = que.front();
                que.pop();
                s.insert(node->val);
                count[node->val]++;
                if(node->left != nullptr) {
                    que.push(node->left);
                }
                if(node->right != nullptr) {
                    que.push(node->right);
                }
            }
            bool ans = false;
            for(auto it = s.begin(); it != s.end(); ++it) {
                int other = k - *it;
                if(other == *it) {
                    if(count[other] > 1) {
                        ans = true;
                        break;
                    }
                } else if(s.contains(other)) {
                    ans = true;
                    break;
                }
            }
            return ans;
        }
    }// namespace two_sum_iv_input_is_a_bst
 
    namespace remove_colored_pieces_if_both_neighbors_are_the_same_color {
        bool Solution::winnerOfGame(string colors) {
            int a_count = 0;
            int b_count = 0;
            vector vec(colors.length(), true);
            vec[0]                   = false;
            vec[colors.length() - 1] = false;
            for(int i = 0; i + 1 < colors.length(); i++) {
                if(colors[i] != colors[i + 1]) {
                    vec[i]     = false;
                    vec[i + 1] = false;
                }
            }
            for(int i = 0; i + 1 < colors.length(); i++) {
                if(vec[i]) {
                    if(colors[i] == 'A') {
                        a_count++;
                    } else {
                        b_count++;
                    }
                }
            }
            return a_count > b_count;
        }
    }// namespace remove_colored_pieces_if_both_neighbors_are_the_same_color
 
    namespace k_th_smallest_in_lexicographical_order {
        int Solution::findKthNumber(int n, int k) {
            int curr = 1;
            k--;
            while(k > 0) {
                const int steps = getSteps(curr, n);
                if(steps <= k) {
                    k -= steps;
                    curr++;
                } else {
                    curr = curr * 10;
                    k--;
                }
            }
            return curr;
        }
 
        int Solution::getSteps(int curr, long n) {
            int steps  = 0;
            long first = curr;
            long last  = curr;
            while(first <= n) {
                steps += min(last, n) - first + 1;
                first = first * 10;
                last  = last * 10 + 9;
            }
            return steps;
        }
    }// namespace k_th_smallest_in_lexicographical_order
 
    namespace image_smoother {
        vector<vector<int>> Solution::imageSmoother(vector<vector<int>> &img) {
            const int m = img.size();
            const int n = img[0].size();
            auto ans    = vector(m, vector<int>(n));
            for(int i = 0; i < m; i++) {
                for(int j = 0; j < n; j++) {
                    pair<int, int> cells[9] = {make_pair(i - 1, j - 1), make_pair(i - 1, j), make_pair(i - 1, j + 1),
                                               make_pair(i, j - 1), make_pair(i, j), make_pair(i, j + 1),
                                               make_pair(i + 1, j - 1), make_pair(i + 1, j), make_pair(i + 1, j + 1)};
                    int sum                 = 0;
                    int count               = 0;
                    for(int k = 0; k < 9; k++) {
                        auto [x, y] = cells[k];
                        if(0 <= x && x < m && 0 <= y && y < n) {
                            count++;
                            sum += img[x][y];
                        }
                    }
                    ans[i][j] = sum / count;
                }
            }
            return ans;
        }
    }// namespace image_smoother
 
    namespace factorial_trailing_zeroes {
        int Solution::trailingZeroes(int n) {
            unsigned int pow5   = 5;
            unsigned int pow2   = 2;
            unsigned int count5 = 0;
            unsigned int count2 = 0;
            while(n / pow5 != 0) {
                count5 += n / pow5;
                pow5 *= 5;
            }
            while(n / pow2 != 0) {
                count2 += n / pow2;
                pow2 *= 2;
            }
            return min(count2, count5);
        }
    }// namespace factorial_trailing_zeroes
 
    namespace baseball_game {
        int Solution::calPoints(vector<string> &ops) {
            vector<int> stk;
            for(const string &op: ops) {
                if(op == "+") {
                    const int score1 = stk.back();
                    const int score2 = *(stk.rbegin() + 1);
                    stk.push_back(score1 + score2);
                } else if(op == "D") {
                    stk.push_back(2 * stk.back());
                } else if(op == "C") {
                    stk.pop_back();
                } else {
                    stringstream ss;
                    ss << op;
                    int score;
                    ss >> score;
                    stk.push_back(score);
                }
            }
            int ans = 0;
            for(const auto score: stk) {
                ans += score;
            }
            return ans;
        }
    }// namespace baseball_game
 
    namespace minimum_deletions_to_make_array_beautiful {
        int Solution::minDeletion(vector<int> &nums) {
            vector<int> indexes;
            for(int i = 0; i + 1 < nums.size(); i++) {
                if(nums[i] == nums[i + 1]) {
                    indexes.push_back(i);
                }
            }
            int ans   = 0;
            bool even = true;
            for(const auto index: indexes) {
                if(even && index % 2 == 0 || !even && index % 2 != 0) {
                    ans++;
                    even = !even;
                }
            }
            if((nums.size() - ans) % 2 != 0) {
                ans++;
            }
            return ans;
        }
    }// namespace minimum_deletions_to_make_array_beautiful
 
    namespace find_palindrome_with_fixed_length {
        unsigned long long qmi(unsigned long long m, unsigned long long k) {
            unsigned long long res = 1;
            unsigned long long t   = m;
            while(k != 0U) {
                if((k & 1) != 0U) {
                    res = res * t;
                }
                t = t * t;
                k >>= 1;
            }
            return res;
        }
 
        vector<long long> Solution::kthPalindrome(vector<int> &queries, int intLength) {
            vector<long long> ans;
            if(intLength == 1) {
                for(auto query: queries) {
                    if(query < 10) {
                        ans.push_back(query);
                    } else {
                        ans.push_back(-1);
                    }
                }
                return ans;
            }
            if(intLength == 2) {
                for(auto query: queries) {
                    if(query < 10) {
                        ans.push_back(query * 10 + query);
                    } else {
                        ans.push_back(-1);
                    }
                }
                return ans;
            }
            int n = (intLength + 1) / 2;
            vector<unsigned long long> q10(n + 1);
            for(int i = 1; i <= n; i++) {
                q10[i] = qmi(10, n - i);
            }
            for(auto query: queries) {
                vector<unsigned long long> num;
                int n1 = query / q10[1] + 1;
                if(n1 == 10 && query % q10[1] == 0) {
                    stringstream ss;
                    for(int i = 0; i < intLength; i++) {
                        ss << 9;
                    }
                    long long res;
                    ss >> res;
                    ans.push_back(res);
                    continue;
                }
                if(n1 > 9) {
                    ans.push_back(-1);
                    continue;
                }
                if(n1 < 10 && query % q10[1] == 0) {
                    n1--;
                    query = (query - 1) % q10[1] + 1;
                } else {
                    query %= q10[1];
                }
                num.push_back(n1);
                for(int i = 2; i <= n; i++) {
                    int digit = query / q10[i];
                    if(i == n) {
                        digit--;
                    } else if(query != q10[i] && query % q10[i] == 0) {
                        digit--;
                    } else if(query == q10[i]) {
                        digit = 0;
                    }
                    query %= q10[i];
                    num.push_back((digit + 10) % 10);
                }
                stringstream ss;
                for(int digit: num) {
                    ss << digit;
                }
                int i = num.size() - 1;
                if(intLength % 2 != 0) {
                    i--;
                }
                while(i >= 0) {
                    ss << num[i];
                    --i;
                }
                long long res;
                ss >> res;
                ans.push_back(res);
            }
            return ans;
        }
    }// namespace find_palindrome_with_fixed_length
 
    namespace find_missing_observations {
        vector<int> Solution::missingRolls(vector<int> &rolls, int mean, int n) {
            const int m = rolls.size();
            int sum     = (m + n) * mean;
            for(const auto roll: rolls) {
                sum -= roll;
            }
            if(sum < n || sum > 6 * n) {
                return {};
            }
            vector ans(n, sum / n);
            sum %= n;
            for(int i = 0; i < sum; i++) {
                ans[i]++;
            }
            return ans;
        }
    }// namespace find_missing_observations
 
    namespace binary_number_with_alternating_bits {
        bool Solution::hasAlternatingBits(int n) {
            stringstream ss;
            while(n != 0) {
                ss << n % 2;
                n /= 2;
            }
            string str;
            ss >> str;
            for(int i = 0; i + 1 < str.length(); i++) {
                if(str[i] == str[i + 1]) {
                    return false;
                }
            }
            return true;
        }
    }// namespace binary_number_with_alternating_bits
 
    namespace maximize_the_confusion_of_an_exam {
        int Solution::maxConsecutiveAnswers(string answerKey, int k) {
            if(answerKey.length() == 1) {
                return 1;
            }
            vector<int> t_count(answerKey.length());
            vector<int> f_count(answerKey.length());
            int t_current = 0;
            int f_current = 0;
            for(int i = 0; i < t_count.size(); i++) {
                if(answerKey[i] == 'T') {
                    t_current++;
                } else {
                    f_current++;
                }
                t_count[i] = t_current;
                f_count[i] = f_current;
            }
            int l      = 1;
            int r      = answerKey.size();
            auto check = [&answerKey, &t_count, &f_count, &k](int len) -> bool {
                for(int i = 0; i + len <= answerKey.length(); i++) {
                    int tc = t_count[i + len - 1] - (i - 1 >= 0 ? t_count[i - 1] : 0);
                    int fc = f_count[i + len - 1] - (i - 1 >= 0 ? f_count[i - 1] : 0);
                    if(min(tc, fc) <= k) {
                        return true;
                    }
                }
                return false;
            };
            while(l < r) {
                if(l + 1 == r) {
                    if(check(r)) {
                        return r;
                    }
                    return l;
                }
                const int mid = (l + r) / 2;
                if(check(mid)) {
                    l = mid;
                } else {
                    r = mid;
                }
            }
            return -1;
        }
    }// namespace maximize_the_confusion_of_an_exam
 
    namespace find_servers_that_handled_most_number_of_requests {
        vector<int> Solution::busiestServers(int k, vector<int> &arrival, vector<int> &load) {
            vector<int> ans;
            vector count(k, 0);
            set<int> available;
            for(int i = 0; i < k; i++) {
                available.insert(i);
            }
            priority_queue<event> events;
            for(int i = 0; i < arrival.size(); i++) {
                event e = {arrival[i], true, i};
                events.push(e);
            }
            while(!events.empty()) {
                event e = events.top();
                events.pop();
                if(e.start) {
                    if(!available.empty()) {
                        auto it = available.lower_bound(e.index % k);
                        if(it == available.end()) {
                            it = available.begin();
                        }
                        event next = {e.time + load[e.index], false, e.index, *it};
                        events.push(next);
                        available.erase(it);
                    }
                } else {
                    //end
                    available.insert(e.server_index);
                    count[e.server_index]++;
                }
            }
            const int maximum = *max_element(count.begin(), count.end());
            for(int i = 0; i < k; i++) {
                if(count[i] == maximum) {
                    ans.push_back(i);
                }
            }
            return ans;
        }
 
        bool event::operator<(const event &e) const {
            if(this->time != e.time) {
                return this->time > e.time;
            }
            return this->start;
        }
    }// namespace find_servers_that_handled_most_number_of_requests
 
    namespace self_dividing_numbers {
        vector<int> Solution::selfDividingNumbers(int left, int right) {
            vector<int> ans;
            for(int i = left; i <= right; ++i) {
                stringstream ss;
                ss << i;
                char ch;
                bool flag = true;
                while(ss >> ch) {
                    const int num = ch - '0';
                    if(num == 0) {
                        flag = false;
                        break;
                    }
                    if(i % num != 0) {
                        flag = false;
                        break;
                    }
                }
                if(flag) {
                    ans.push_back(i);
                }
            }
            return ans;
        }
    }// namespace self_dividing_numbers
 
    namespace array_of_doubled_pairs {
        bool Solution::canReorderDoubled(vector<int> &arr) {
            multiset<int> positive;
            multiset<int, greater<>> negative;
            for(auto num: arr) {
                if(num >= 0) {
                    positive.insert(num);
                } else {
                    negative.insert(num);
                }
            }
            while(!positive.empty()) {
                const int num = *positive.begin();
                positive.erase(positive.begin());
                auto it = positive.find(num * 2);
                if(it == positive.end()) {
                    return false;
                }
                positive.erase(it);
            }
            while(!negative.empty()) {
                const int num = *negative.begin();
                negative.erase(negative.begin());
                auto it = negative.find(num * 2);
                if(it == negative.end()) {
                    return false;
                }
                negative.erase(it);
 
                negative.erase(it);
            }
            return true;
        }
    }// namespace array_of_doubled_pairs
 
    namespace strong_password_checker {
        int Solution::strongPasswordChecker(const string &password) {
            const int n    = password.length();
            bool has_lower = false;
            bool has_upper = false;
            bool has_digit = false;
            for(const char ch: password) {
                if(islower(ch) != 0) {
                    has_lower = true;
                } else if(isupper(ch) != 0) {
                    has_upper = true;
                } else if(isdigit(ch) != 0) {
                    has_digit = true;
                }
            }
            const int categories = static_cast<int>(has_lower) + static_cast<int>(has_upper) + static_cast<int>(has_digit);
 
            if(n < 6) {
                return max(6 - n, 3 - categories);
            }
            if(n <= 20) {
                int replace  = 0;
                int count    = 0;
                char current = '#';
 
                for(const char ch: password) {
                    if(ch == current) {
                        ++count;
                    } else {
                        replace += count / 3;
                        count   = 1;
                        current = ch;
                    }
                }
                replace += count / 3;
                return max(replace, 3 - categories);
            }
            // 替换次数和删除次数
            int replace = 0;
            int remove  = n - 20;
            // k mod 3 = 1 的组数，即删除 2 个字符可以减少 1 次替换操作
            int rm2   = 0;
            int count = 0;
            char cur  = '#';
 
            for(const char ch: password) {
                if(ch == cur) {
                    ++count;
                } else {
                    if(remove > 0 && count >= 3) {
                        if(count % 3 == 0) {
                            // 如果是 k % 3 = 0 的组，那么优先删除 1 个字符，减少 1 次替换操作
                            --remove;
                            --replace;
                        } else if(count % 3 == 1) {
                            // 如果是 k % 3 = 1 的组，那么存下来备用
                            ++rm2;
                        }
                        // k % 3 = 2 的组无需显式考虑
                    }
                    replace += count / 3;
                    count = 1;
                    cur   = ch;
                }
            }
            if(remove > 0 && count >= 3) {
                if(count % 3 == 0) {
                    --remove;
                    --replace;
                } else if(count % 3 == 1) {
                    ++rm2;
                }
            }
            replace += count / 3;
 
            // 使用 k % 3 = 1 的组的数量，由剩余的替换次数、组数和剩余的删除次数共同决定
            const int use2 = min({replace, rm2, remove / 2});
            replace -= use2;
            remove -= use2 * 2;
            // 由于每有一次替换次数就一定有 3 个连续相同的字符（k / 3 决定），因此这里可以直接计算出使用 k % 3 = 2 的组的数量
            const int use3 = min(replace, remove / 3);
            replace -= use3;
            remove -= use3 * 3;
            return n - 20 + max(replace, 3 - categories);
        }
    }// namespace strong_password_checker
 
    namespace number_of_ways_to_select_buildings {
        long long Solution::numberOfWays(string s) {
            const unsigned int n = s.length();
            vector<unsigned int> prev0(n, 0);
            vector<unsigned int> prev1(n, 0);
            vector<unsigned int> post0(n, 0);
            vector<unsigned int> post1(n, 0);
            unsigned current0 = 0;
            unsigned current1 = 0;
            for(int i = 0; i < n; i++) {
                prev0[i] = current0;
                prev1[i] = current1;
                if(s[i] == '0') {
                    current0++;
                } else {
                    current1++;
                }
            }
            current0 = 0;
            current1 = 0;
            for(int i = n - 1; i >= 0; i--) {
                post0[i] = current0;
                post1[i] = current1;
                if(s[i] == '0') {
                    current0++;
                } else {
                    current1++;
                }
            }
            long long ans = 0;
            for(unsigned i = 0; i < n; i++) {
                if(s[i] == '0') {
                    ans += static_cast<long long>(prev1[i]) * post1[i];
                } else {
                    ans += static_cast<long long>(prev0[i]) * post0[i];
                }
            }
            return ans;
        }
    }// namespace number_of_ways_to_select_buildings
 
    namespace sum_of_scores_of_built_strings {
        long long Solution::sumScores(string s) {
            const int n   = s.length();
            long long ans = n;
            int l         = 0;
            int r         = 0;
            vector z(n, 0);
            for(int i = 1; i < n; ++i) {
                if(i <= r && z[i - l] < r - i + 1) {
                    z[i] = z[i - l];
                } else {
                    z[i] = max(0, r - i + 1);
                    while(i + z[i] < n && s[z[i]] == s[i + z[i]]) {
                        ++z[i];
                    }
                }
                if(i + z[i] - 1 > r) {
                    l = i;
                    r = i + z[i] - 1;
                }
                ans += z[i];
            }
            return ans;
        }
    }// namespace sum_of_scores_of_built_strings
 
    namespace minimum_number_of_operations_to_convert_time {
        int Solution::convertTime(string current, string correct) {
            const int current_h = (current[0] - '0') * 10 + (current[1] - '0');
            const int current_m = (current[3] - '0') * 10 + (current[4] - '0');
            const int correct_h = (correct[0] - '0') * 10 + (correct[1] - '0');
            const int correct_m = (correct[3] - '0') * 10 + (correct[4] - '0');
            int diff            = correct_h * 60 + correct_m - (current_h * 60 + current_m);
            if(diff < 0) {
                diff += 24 * 60;
            }
            int ans = 0;
            ans += diff / 60;
            diff %= 60;
            ans += diff / 15;
            diff %= 15;
            ans += diff / 5;
            diff %= 5;
            ans += diff;
            return ans;
        }
    }// namespace minimum_number_of_operations_to_convert_time
 
    namespace find_players_with_zero_or_one_losses {
        vector<vector<int>> Solution::findWinners(vector<vector<int>> &matches) {
            map<unsigned, unsigned> lose;
            for(auto match: matches) {
                lose[match[0]] += 0;
                lose[match[1]] += 1;
            }
            vector<vector<int>> ans(2);
            vector<int> ans1;
            vector<int> ans2;
            for(auto [player, count]: lose) {
                if(count == 0) {
                    ans1.push_back(player);
                } else if(count == 1) {
                    ans2.push_back(player);
                }
            }
            ans[0] = ans1;
            ans[1] = ans2;
            return ans;
        }
    }// namespace find_players_with_zero_or_one_losses
 
    namespace maximum_candies_allocated_to_k_children {
        int Solution::maximumCandies(vector<int> &candies, long long k) {
            sort(candies.begin(), candies.end());
            long long sum = 0;
            for(const auto candy: candies) {
                sum += candy;
            }
            int l = 1;
            int r = sum / k;
            if(sum < k) {
                return 0;
            }
            while(l < r) {
                if(l + 1 == r) {
                    unsigned long long count = 0;
                    for(auto it = candies.rbegin(); it != candies.rend() && *it >= r; ++it) {
                        count += *it / r;
                        if(count > k) {
                            break;
                        }
                    }
                    if(count > k) {
                        return r;
                    }
                    return l;
                }
                const int m              = (l + r) / 2;
                unsigned long long count = 0;
                for(auto it = candies.rbegin(); it != candies.rend() && *it >= m; ++it) {
                    count += *it / m;
                    if(count > k) {
                        break;
                    }
                }
                if(count >= k) {
                    l = m;
                } else if(count < k) {
                    r = m;
                }
            }
            return (l + r) / 2;
        }
    }// namespace maximum_candies_allocated_to_k_children
 
    namespace encrypt_and_decrypt_strings {
        Encrypter::Encrypter(vector<char> &keys, vector<string> &values, vector<string> &dictionary) {
            for(int i = 0; i < keys.size(); ++i) {
                mp[keys[i] - 'a'] = values[i];
            }
            for(const auto &s: dictionary) {
                ++count[encrypt(s)];
            }
        }
 
        string Encrypter::encrypt(const string &word1) const {
            string res;
            for(const char ch: word1) {
                const auto &s = mp[ch - 'a'];
                if(s.empty()) {
                    return "";
                }
                res += s;
            }
            return res;
        }
 
        int Encrypter::decrypt(const string &word2) {
            if(count.contains(word2)) {
                count[word2] += 0;
                return count[word2];
            }
            // 防止把不在 cnt 中的字符串加进去
            return 0;
        }
    }// namespace encrypt_and_decrypt_strings
 
    namespace range_sum_query_mutable {
        NumArray::NumArray(vector<int> &nums)
            : nums(nums) {
            const int n = nums.size();
            size        = sqrt(n);
            sum.resize((n + size - 1) / size);// n/size 向上取整
            for(int i = 0; i < n; i++) {
                sum[i / size] += nums[i];
            }
        }
 
        void NumArray::update(int index, int val) {
            sum[index / size] += val - nums[index];
            nums[index] = val;
        }
 
        int NumArray::sumRange(int left, int right) const {
            const int b1 = left / size;
            const int i1 = left % size;
            const int b2 = right / size;
            const int i2 = right % size;
            if(b1 == b2) {
                // 区间 [left, right] 在同一块中
                return accumulate(nums.begin() + b1 * size + i1, nums.begin() + b1 * size + i2 + 1, 0);
            }
            const int sum1 = accumulate(nums.begin() + b1 * size + i1, nums.begin() + b1 * size + size, 0);
            const int sum2 = accumulate(nums.begin() + b2 * size, nums.begin() + b2 * size + i2 + 1, 0);
            const int sum3 = accumulate(sum.begin() + b1 + 1, sum.begin() + b2, 0);
            return sum1 + sum2 + sum3;
        }
    }// namespace range_sum_query_mutable
 
    namespace process_restricted_friend_requests {
        vector<bool> Solution::friendRequests(int n, vector<vector<int>> &restrictions, vector<vector<int>> &requests) {
            UnionFind uf(n);
            vector<bool> ans(requests.size());
            auto check = [&uf, &restrictions](int x, int y) -> bool {
                x = uf.find(x);
                y = uf.find(y);
                if(x > y) {
                    swap(x, y);
                }
                for(auto &restriction: restrictions) {
                    int i = uf.find(restriction[0]);
                    int j = uf.find(restriction[1]);
                    if(i > j) {
                        swap(i, j);
                    }
                    if(i == x && j == y) {
                        return false;
                    }
                }
                return true;
            };
            for(int i = 0; i < requests.size(); i++) {
                if(check(requests[i][0], requests[i][1])) {
                    uf.unite(requests[i][0], requests[i][1]);
                    ans[i] = true;
                } else {
                    ans[i] = false;
                }
            }
            return ans;
        }
    }// namespace process_restricted_friend_requests
 
    namespace prime_number_of_set_bits_in_binary_representation {
        int Solution::countPrimeSetBits(int left, int right) {
            int ans = 0;
            const unordered_set primes{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61};
            for(unsigned i = left; i <= right; i++) {
                if(primes.contains(popcount(i))) {
                    ans++;
                }
            }
            return ans;
        }
    }// namespace prime_number_of_set_bits_in_binary_representation
 
    namespace minimum_height_trees {
        vector<int> Solution::findMinHeightTrees(int n, vector<vector<int>> &edges) {
            if(n == 1) {
                return {0};
            }
            vector<vector<int>> adj(n);
            for(auto &edge: edges) {
                adj[edge[0]].emplace_back(edge[1]);
                adj[edge[1]].emplace_back(edge[0]);
            }
 
            vector parent(n, -1);
            /* 找到与节点 0 最远的节点 x */
            const int x = findLongestNode(0, parent, adj);
            /* 找到与节点 x 最远的节点 y */
            int y = findLongestNode(x, parent, adj);
            /* 求出节点 x 到节点 y 的路径 */
            vector<int> path;
            parent[x] = -1;
            while(y != -1) {
                path.emplace_back(y);
                y = parent[y];
            }
            const int m = path.size();
            if(m % 2 == 0) {
                return {path[m / 2 - 1], path[m / 2]};
            }
            return {path[m / 2]};
        }
 
        int Solution::findLongestNode(int u, vector<int> &parent, vector<vector<int>> &adj) {
            const int n = adj.size();
            queue<int> qu;
            vector<bool> visit(n);
            qu.emplace(u);
            visit[u] = true;
            int node = -1;
 
            while(!qu.empty()) {
                const int curr = qu.front();
                qu.pop();
                node = curr;
                for(auto &v: adj[curr]) {
                    if(!visit[v]) {
                        visit[v]  = true;
                        parent[v] = curr;
                        qu.emplace(v);
                    }
                }
            }
            return node;
        }
    }// namespace minimum_height_trees
 
    namespace rotate_string {
        bool Solution::rotateString(string s, const string &goal) {
            if(s.length() != goal.length()) {
                return false;
            }
            s += s;
            return s.find(goal) != string::npos;
        }
    }// namespace rotate_string
 
    namespace n_ary_tree_level_order_traversal {
        vector<vector<int>> Solution::levelOrder(Node *root) {
            queue<pair<int, Node *>> q;
            vector<vector<int>> ans;
            if(root == nullptr) {
                return ans;
            }
            q.push(make_pair(0, root));
            while(!q.empty()) {
                auto [level, node] = q.front();
                if(ans.size() == level) {
                    ans.emplace_back();
                }
                ans[level].push_back(node->val);
                q.pop();
                for(auto *next: node->children) {
                    q.push(make_pair(level + 1, next));
                }
            }
            return ans;
        }
    }// namespace n_ary_tree_level_order_traversal
 
    namespace reaching_points {
        bool Solution::reachingPoints(int sx, int sy, int tx, int ty) {
            while(tx > sx && ty > sy && tx != ty) {
                if(tx > ty) {
                    tx %= ty;
                } else {
                    ty %= tx;
                }
            }
            if(tx == sx && ty == sy) {
                return true;
            }
            if(tx == sx) {
                return ty > sy && (ty - sy) % tx == 0;
            }
            if(ty == sy) {
                return tx > sx && (tx - sx) % ty == 0;
            }
            return false;
        }
    }// namespace reaching_points
 
    namespace maximum_product_after_k_increments {
        int Solution::maximumProduct(vector<int> &nums, int k) {
            priority_queue<int, vector<int>, greater<int>> pq;
            for(auto num: nums) {
                pq.push(num);
            }
            while(k-- != 0) {
                const int num = pq.top();
                pq.pop();
                pq.push(num + 1);
            }
            long long ans = 1;
            while(!pq.empty()) {
                const int num = pq.top();
                pq.pop();
                ans *= num;
                ans %= 1000000007;
            }
            return ans;
        }
    }// namespace maximum_product_after_k_increments
 
    namespace maximum_total_beauty_of_the_gardens {
        long long Solution::maximumBeauty(vector<int> &flowers, long long newFlowers, int target, int full, int partial) {
            const int n = flowers.size();
            sort(flowers.begin(), flowers.end());
            for(int i = 0; i < n; i++) {
                flowers[i] = min(flowers[i], target);
            }
            long long ans = 0;
            vector<long long> sum(n + 1, 0);
            for(int i = 0; i < n; i++) {
                sum[i + 1] = sum[i] + flowers[i];
            }
            for(int i = 0, j = 0; i <= n; i++) {
                const long long rest = newFlowers - (static_cast<long long>(target) * (n - i) - (sum[n] - sum[i]));
                if(rest >= 0) {
                    while(j < i && rest >= static_cast<long long>(flowers[j]) * j - sum[j]) {
                        //将前j项补齐到flowers[j]
                        j++;
                    }
                    ans = max(ans, static_cast<long long>(full) * (n - i) + (j == 0 ? 0 : static_cast<long long>(partial) * min(static_cast<long long>(target - 1), (rest + sum[j]) / j)));
                }
                if(i < n && flowers[i] == target) {
                    break;
                }
            }
            return ans;
        }
    }// namespace maximum_total_beauty_of_the_gardens
 
    namespace count_numbers_with_unique_digits {
        int Solution::countNumbersWithUniqueDigits(int n) {
            if(n == 0) {
                return 1;
            }
            vector<int> dp(n + 1);
            dp[1] = 9;
            for(int i = 2; i <= n; ++i) {
                dp[i] = dp[i - 1] * (10 - (i - 1));
            }
            int ans = 0;
            for(int i = 1; i <= n; ++i) {
                ans += dp[i];
            }
            return ans + 1;
        }
    }// namespace count_numbers_with_unique_digits
 
    namespace number_of_lines_to_write_string {
        vector<int> Solution::numberOfLines(vector<int> &widths, string s) {
            int lines   = 1;
            int current = 0;
            for(int i = 0; i < s.length(); i++) {
                if(current + widths[s[i] - 'a'] > 100) {
                    current = 0;
                    lines++;
                }
                current += widths[s[i] - 'a'];
            }
            return {lines, current};
        }
    }// namespace number_of_lines_to_write_string
 
    namespace permutation_in_string {
        bool Solution::checkInclusion(const string &s1, string s2) {
            if(s1.length() > s2.length()) {
                return false;
            }
            unordered_map<char, int> um1;
            unordered_map<char, int> um2;
            for(char ch: s1) {
                um1[ch]++;
            }
            for(int i = 0; i < s1.length(); i++) {
                um2[s2[i]]++;
            }
            if(um2 == um1) {
                return true;
            }
            for(int i = 0; i + s1.length() < s2.length(); i++) {
                um2[s2[i]]--;
                um2[s2[i + s1.length()]]++;
                if(um2[s2[i]] == 0) {
                    um2.erase(s2[i]);
                }
                if(um2 == um1) {
                    return true;
                }
            }
            return false;
        }
    }// namespace permutation_in_string
 
    namespace insert_delete_getrandom_o1 {
        RandomizedSet::RandomizedSet() {
            generator    = default_random_engine(time(nullptr));
            distribution = uniform_int_distribution(0, INT_MAX);
        }
 
        bool RandomizedSet::insert(int val) {
            if(static_cast<unsigned int>(map.contains(val)) != 0U) {
                return false;
            }
            nums.push_back(val);
            map[val] = nums.size() - 1;
            return true;
        }
 
        bool RandomizedSet::remove(int val) {
            if(static_cast<unsigned int>(map.contains(val)) == 0U) {
                return false;
            }
            const int index = map[val];
            const int last  = nums.back();
            nums[index]     = last;
            map[last]       = index;
            nums.pop_back();
            map.erase(val);
            return true;
        }
 
        int RandomizedSet::getRandom() { return nums[distribution(generator) % nums.size()]; }
    }// namespace insert_delete_getrandom_o1
 
    namespace projection_area_of_3d_shapes {
        int Solution::projectionArea(vector<vector<int>> &grid) {
            const int n  = grid.size();
            int xy       = 0;
            int xz       = 0;
            int yz       = 0;
            auto grid_xz = vector(51, vector(51, 0));
            auto grid_yz = vector(51, vector(51, 0));
            for(int i = 0; i < n; i++) {
                for(int j = 0; j < n; j++) {
                    if(grid[i][j] != 0) {
                        xy++;
                    }
                    for(int k = 0; k < grid[i][j]; k++) {
                        grid_xz[i][k] = 1;
                        grid_yz[j][k] = 1;
                    }
                }
            }
            for(int i = 0; i < 51; i++) {
                for(int j = 0; j < 51; j++) {
                    if(grid_xz[i][j] != 0) {
                        xz++;
                    }
                    if(grid_yz[i][j] != 0) {
                        yz++;
                    }
                }
            }
            return xy + yz + xz;
        }
    }// namespace projection_area_of_3d_shapes
 
    namespace design_parking_system {
        ParkingSystem::ParkingSystem(int big, int medium, int small)
            : big(big), medium(medium), small(small) {}
 
        bool ParkingSystem::addCar(int carType) {
            switch(carType) {
                case 1: {
                    if(big > 0) {
                        big--;
                        return true;
                    }
                    return false;
                }
                case 2: {
                    if(medium > 0) {
                        medium--;
                        return true;
                    }
                    return false;
                }
                case 3: {
                    if(small > 0) {
                        small--;
                        return true;
                    }
                    return false;
                }
                default: return false;
            }
        }
    }// namespace design_parking_system
 
    namespace range_sum_query_immutable {
        NumArray::NumArray(vector<int> &nums) {
            pref_sum    = vector<int>(nums.size());
            pref_sum[0] = nums[0];
            for(int i = 1; i < nums.size(); i++) {
                pref_sum[i] = pref_sum[i - 1] + nums[i];
            }
        }
 
        int NumArray::sumRange(int left, int right) const { return pref_sum[right] - (left - 1 >= 0 ? pref_sum[left - 1] : 0); }
    }// namespace range_sum_query_immutable
 
    namespace house_robber {
        int Solution::rob(vector<int> &nums) {
            if(nums.size() == 1) {
                return nums[0];
            }
            vector<int> dp(nums.size());
            dp[0] = nums[0];
            dp[1] = max(nums[0], nums[1]);
            for(int i = 2; i < nums.size(); i++) {
                dp[i] = max(dp[i - 2] + nums[i], dp[i - 1]);
            }
            return dp[nums.size() - 1];
        }
    }// namespace house_robber
 
    namespace triangle {
        int Solution::minimumTotal(vector<vector<int>> &triangle) {
            vector<vector<int>> dp = triangle;
            for(int i = 1; i < triangle.size(); i++) {
                for(int j = 0; j < triangle[i].size(); j++) {
                    if(j == 0) {
                        dp[i][j] = dp[i - 1][j] + triangle[i][j];
                    } else if(j == triangle[i].size() - 1) {
                        dp[i][j] = dp[i - 1][j - 1] + triangle[i][j];
                    } else {
                        dp[i][j] = min(dp[i - 1][j], dp[i - 1][j - 1]) + triangle[i][j];
                    }
                }
            }
            int ans = dp.back()[0];
            for(int i = 0; i < dp.back().size(); i++) {
                ans = min(ans, dp.back()[i]);
            }
            return ans;
        }
    }// namespace triangle
 
    namespace lowest_common_ancestor_of_a_binary_search_tree {
        TreeNode *Solution::lowestCommonAncestor(TreeNode *root, TreeNode *p, TreeNode *q) {
            auto *const tnp = new TreeNodeP(root->val);
            TreeNodeP *pp;
            TreeNodeP *qq;
            copy(root, tnp, p->val, q->val, &pp, &qq);
            TreeNodeP *current = pp;
            while(current != nullptr) {
                current->ed = true;
                current     = current->parent;
            }
            current = qq;
            while(current != nullptr) {
                if(current->ed) {
                    return current->mirror;
                }
                current = current->parent;
            }
            return root;
        }
 
        void Solution::copy(TreeNode *tn, TreeNodeP *tnp, int low, int high, TreeNodeP **p, TreeNodeP **q) {
            tnp->mirror = tn;
            if(tn->val == low) {
                *p = tnp;
            } else if(tn->val == high) {
                *q = tnp;
            }
            if(tn->left != nullptr) {
                tnp->left         = new TreeNodeP(tn->left->val);
                tnp->left->parent = tnp;
                copy(tn->left, tnp->left, low, high, p, q);
            }
            if(tn->right != nullptr) {
                tnp->right         = new TreeNodeP(tn->right->val);
                tnp->right->parent = tnp;
                copy(tn->right, tnp->right, low, high, p, q);
            }
        }
    }// namespace lowest_common_ancestor_of_a_binary_search_tree
 
    namespace shuffle_an_array {
        vector<int> Solution::reset() { return nums; }
 
        vector<int> Solution::shuffle() const {
            vector<int> ans;
            vector<int> cpy = nums;
            while(!cpy.empty()) {
                const int idx = rand() % cpy.size();
                ans.emplace_back(cpy[idx]);
                cpy.erase(cpy.begin() + idx);
            }
            return ans;
        }
 
        Solution::Solution(vector<int> &nums)
            : nums(nums) { srand(time(nullptr)); }
    }// namespace shuffle_an_array
 
    namespace find_all_anagrams_in_a_string {
        vector<int> Solution::findAnagrams(string s, const string &p) {
            vector<int> ans;
            unordered_map<char, int> um_p;
            for(char ch: p) {
                um_p[ch]++;
            }
            unordered_map<char, int> um_s;
            for(int i = 0; i < p.length(); i++) {
                um_s[s[i]]++;
            }
            if(um_s == um_p) {
                ans.emplace_back(0);
            }
            for(int i = p.length(); i < s.length(); i++) {
                um_s[s[i]]++;
                um_s[s[i - p.length()]]--;
                if(um_s[s[i - p.length()]] == 0) {
                    um_s.erase(s[i - p.length()]);
                }
                if(um_s == um_p) {
                    ans.emplace_back(i - p.length() + 1);
                }
            }
            return ans;
        }
    }// namespace find_all_anagrams_in_a_string
 
    namespace subarray_product_less_than_k {
        int Solution::numSubarrayProductLessThanK(vector<int> &nums, int k) {
            int ans  = 0;
            int prod = 1;
            int i    = 0;
            for(int j = 0; j < nums.size(); j++) {
                prod *= nums[j];
                while(i <= j && prod >= k) {
                    prod /= nums[i];
                    i++;
                }
                ans += j - i + 1;
            }
            return ans;
        }
    }// namespace subarray_product_less_than_k
 
    namespace minimum_size_subarray_sum {
        int Solution::minSubArrayLen(int target, vector<int> &nums) {
            int r   = nums.size() - 1;
            int l   = r;
            int sum = nums[r];
            int ans = 0;
            while(l >= 0 && l <= r) {
                if(nums[l] >= target) {
                    return 1;
                }
                while(l - 1 >= 0 && sum + nums[l - 1] < target) {
                    sum += nums[--l];
                }
                if(l - 1 >= 0) {
                    l--;
                    sum += nums[l];
                    if(ans == 0) {
                        ans = r - l + 1;
                    } else {
                        ans = min(ans, r - l + 1);
                    }
                } else {
                    break;
                }
                do {
                    sum -= nums[r--];
                    if(sum >= target) {
                        ans = min(ans, r - l + 1);
                    }
                } while(sum >= target && r >= l);
            }
            return ans;
        }
    }// namespace minimum_size_subarray_sum
 
    namespace populating_next_right_pointers_in_each_node_ii {
        Node *Solution::connect(Node *root) {
            if(root == nullptr) {
                return nullptr;
            }
            int prev_level  = 0;
            Node *prev_node = root;
            queue<pair<int, Node *>> q;
            if(root->left != nullptr) {
                q.emplace(1, root->left);
            }
            if(root->right != nullptr) {
                q.emplace(1, root->right);
            }
            while(!q.empty()) {
                auto [level, node] = q.front();
                q.pop();
                if(level == prev_level) {
                    prev_node->next = node;
                }
                prev_level = level;
                prev_node  = node;
                if(node->left != nullptr) {
                    q.emplace(level + 1, node->left);
                }
                if(node->right != nullptr) {
                    q.emplace(level + 1, node->right);
                }
            }
            return root;
        }
    }// namespace populating_next_right_pointers_in_each_node_ii
 
    namespace subtree_of_another_tree {
        bool Solution::isSubtree(TreeNode *root, TreeNode *subRoot) {
            if(root == nullptr) {
                return false;
            }
            queue<TreeNode *> q;
            q.push(root);
            while(!q.empty()) {
                auto *const node = q.front();
                q.pop();
                if(equal(node, subRoot)) {
                    return true;
                }
                if(node->left != nullptr) {
                    q.push(node->left);
                }
                if(node->right != nullptr) {
                    q.push(node->right);
                }
            }
            return false;
        }
 
        bool Solution::equal(TreeNode *tn1, TreeNode *tn2) {
            if(static_cast<int>(tn1 == nullptr) + static_cast<int>(tn2 == nullptr) == 1) {
                return false;
            }
            if(tn1 == nullptr && tn2 == nullptr) {
                return true;
            }
            if(tn1->val != tn2->val) {
                return false;
            }
            if(static_cast<int>(tn1->left == nullptr) + static_cast<int>(tn2->left == nullptr) == 1) {
                return false;
            }
            if(static_cast<int>(tn1->right == nullptr) + static_cast<int>(tn2->right == nullptr) == 1) {
                return false;
            }
            return equal(tn1->left, tn2->left) && equal(tn1->right, tn2->right);
        }
    }// namespace subtree_of_another_tree
 
    namespace shortest_path_in_binary_matrix {
        int Solution::shortestPathBinaryMatrix(vector<vector<int>> &grid) {
            int n       = grid.size();
            auto levels = vector(n, vector(n, -1));
            auto cmp    = [&n](const tuple<int, int, int> &t1, const tuple<int, int, int> &t2) {
                const auto &[level1, x1, y1] = t1;
                const auto &[level2, x2, y2] = t2;
                const int dx1                = abs(n - 1 - x1);
                const int dy1                = abs(n - 1 - y1);
                const int dx2                = abs(n - 1 - x2);
                const int dy2                = abs(n - 1 - y2);
                return level1 + dx1 + dy1 - min(dx1, dy1) > level2 + dx2 + dy2 - min(dx2, dy2);
            };
            priority_queue<tuple<int, int, int>, vector<tuple<int, int, int>>, decltype(cmp)> pq(cmp);
            if(grid[0][0] == 0 && grid[n - 1][n - 1] == 0) {
                pq.push(make_tuple(1, 0, 0));
            } else {
                return -1;
            }
            while(!pq.empty()) {
                auto [level, x, y] = pq.top();
                if(x == n - 1 && y == n - 1) {
                    return level;
                }
                pq.pop();
                if(levels[x][y] == -1 || levels[x][y] > level) {
                    levels[x][y] = level;
                } else {
                    continue;
                }
                pair<int, int> nexts[8] = {make_pair(x - 1, y - 1), make_pair(x - 1, y), make_pair(x - 1, y + 1),
                                           make_pair(x, y - 1), make_pair(x, y + 1),
                                           make_pair(x + 1, y - 1), make_pair(x + 1, y), make_pair(x + 1, y + 1)};
                for(auto [next_x, next_y]: nexts) {
                    if(next_x >= 0 && next_x < n && next_y >= 0 && next_y < n && grid[next_x][next_y] == 0 && (levels[next_x][next_y] == -1 || levels[next_x][next_y] > level + 1)) {
                        pq.push(make_tuple(level + 1, next_x, next_y));
                    }
                }
            }
            return -1;
        }
    }// namespace shortest_path_in_binary_matrix
 
    namespace surrounded_regions {
        void Solution::solve(vector<vector<char>> &board) {
            const int m = board.size();
            const int n = board[0].size();
            for(int i = 0; i < n; i++) {
                if(board[0][i] == 'O') {
                    dfs(board, 0, i);
                }
                if(board[m - 1][i] == 'O') {
                    dfs(board, m - 1, i);
                }
            }
            for(int j = 0; j < m; j++) {
                if(board[j][0] == 'O') {
                    dfs(board, j, 0);
                }
                if(board[j][n - 1] == 'O') {
                    dfs(board, j, n - 1);
                }
            }
            for(int i = 0; i < m; i++) {
                for(int j = 0; j < n; j++) {
                    if(board[i][j] == 'O') {
                        board[i][j] = 'X';
                    }
                    if(board[i][j] == 'D') {
                        board[i][j] = 'O';
                    }
                }
            }
        }
 
        void Solution::dfs(vector<vector<char>> &board, int x, int y) {
            board[x][y]             = 'D';
            const int m             = board.size();
            const int n             = board[0].size();
            pair<int, int> nexts[4] = {{x - 1, y}, {x + 1, y}, {x, y - 1}, {x, y + 1}};
            for(auto [next_x, next_y]: nexts) {
                if(next_x >= 0 && next_x < m && next_y >= 0 && next_y < n && board[next_x][next_y] == 'O') {
                    dfs(board, next_x, next_y);
                }
            }
        }
    }// namespace surrounded_regions
 
    namespace all_paths_from_source_to_target {
        vector<vector<int>> Solution::allPathsSourceTarget(vector<vector<int>> &graph) {
            vector<vector<int>> ans;
            dfs(graph, ans, 0);
            for(auto &path: ans) {
                path.push_back(0);
                path = vector(path.rbegin(), path.rend());
            }
            return ans;
        }
 
        int Solution::dfs(vector<vector<int>> &graph, vector<vector<int>> &ans, int cur) {
            int ret = 0;
            if(cur == graph.size() - 1) {
                ans.emplace_back(vector(1, cur));
                return 1;
            }
            for(const auto next: graph[cur]) {
                const int n = dfs(graph, ans, next);
                ret += n;
                for(int i = ans.size() - 1, j = 0; j < n; i--, j++) {
                    ans[i].emplace_back(cur);
                }
            }
            return ret;
        }
    }// namespace all_paths_from_source_to_target
 
    namespace permutations_ii {
        vector<vector<int>> Solution::permuteUnique(vector<int> &nums) {
            vector<vector<int>> ans;
            set<vector<int>> s;
            dfs(s, vector<int>(), nums);
            ans.reserve(s.size());
            for(const auto &vec: s) {
                ans.emplace_back(vec);
            }
            return ans;
        }
 
        void Solution::dfs(set<vector<int>> &s, const vector<int> &current, vector<int> rest) {
            if(rest.empty()) {
                s.insert(current);
                return;
            }
            for(auto it = rest.begin(); it != rest.end(); ++it) {
                vector<int> next_current = current;
                vector<int> next_rest    = rest;
                next_current.push_back(*it);
                next_rest.erase(next_rest.begin() + (it - rest.begin()));
                dfs(s, next_current, next_rest);
            }
        }
    }// namespace permutations_ii
 
    namespace combination_sum {
        vector<vector<int>> Solution::combinationSum(vector<int> &candidates, int target) {
            sort(candidates.begin(), candidates.end());
            return recurse(candidates, target, 0);
        }
 
        vector<vector<int>> Solution::recurse(vector<int> &candidates, int target, int index) {
            vector<vector<int>> ans;
            for(int i = index; i < candidates.size(); i++) {
                auto &candidate = candidates[i];
                if(candidate == target) {
                    ans.emplace_back(vector(1, candidate));
                } else if(target - candidate >= 1) {
                    auto res = recurse(candidates, target - candidate, i);
                    for(auto &vec: res) {
                        vec.push_back(candidate);
                        ans.push_back(vec);
                    }
                }
            }
            return ans;
        }
    }// namespace combination_sum
 
    namespace combination_sum_ii {
        vector<vector<int>> Solution::combinationSum2(vector<int> &candidates, int target) {
            sort(candidates.begin(), candidates.end());
            const auto ret = recurse(candidates, target, -10);
            vector<vector<int>> ans(ret.size());
            for(int i = 0; i < ret.size(); i++) {
                ans[i] = vector<int>(ret[i].size());
                for(int j = 0; j < ret[i].size(); j++) {
                    ans[i][j] = candidates[ret[i][j]];
                }
            }
            return ans;
        }
 
        vector<vector<int>> Solution::recurse(vector<int> &candidates, int target, int index) {
            vector<vector<int>> ans;
            for(int i = max(0, index + 1); i < candidates.size(); i++) {
                if(!(i > 0 && candidates[i] == candidates[i - 1] && index != i - 1)) {
                    const auto &candidate = candidates[i];
                    if(candidate == target) {
                        ans.emplace_back(vector(1, i));
                    } else if(target - candidate >= 1) {
                        auto res = recurse(candidates, target - candidate, i);
                        for(auto &vec: res) {
                            vec.push_back(i);
                            ans.push_back(vec);
                        }
                    }
                }
            }
            return ans;
        }
    }// namespace combination_sum_ii
 
    namespace house_robber_ii {
        int Solution::rob(vector<int> &nums) {
            if(nums.size() == 1) {
                return nums[0];
            }
            auto vec1 = vector(nums.begin(), nums.end() - 1);
            auto vec2 = vector(nums.begin() + 1, nums.end());
            return max(house_robber::Solution::rob(vec1), house_robber::Solution::rob(vec2));
        }
    }// namespace house_robber_ii
 
    namespace jump_game {
        bool Solution::canJump(vector<int> &nums) {
            vector can(nums.size(), false);
            can[0]   = true;
            int last = 0;
            for(int i = 0; i < nums.size(); i++) {
                if(can[i] && min(i + nums[i], static_cast<int>(nums.size() - 1)) > last) {
                    for(int j = last + 1; j <= i + nums[i] && j < nums.size(); j++) {
                        can[j] = true;
                    }
                    last = min(i + nums[i], static_cast<int>(nums.size() - 1));
                }
            }
            return can.back();
        }
    }// namespace jump_game
 
    namespace jump_game_ii {
        int Solution::jump(vector<int> &nums) {
            const int n = nums.size();
            int ans     = 0;
            int last    = n - 1;
            while(last != 0) {
                for(int i = 0; i < n; i++) {
                    if(i + nums[i] >= last) {
                        last = i;
                        ans++;
                        break;
                    }
                }
            }
            return ans;
        }
    }// namespace jump_game_ii
 
    namespace unique_paths {
        int Solution::uniquePaths(int m, int n) {
            vector dp(m, vector(n, 0));
            dp[m - 1][n - 1] = 1;
            for(int i = m - 1; i >= 0; i--) {
                for(int j = n - 1; j >= 0; j--) {
                    if(i + 1 < m) {
                        dp[i][j] += dp[i + 1][j];
                    }
                    if(j + 1 < n) {
                        dp[i][j] += dp[i][j + 1];
                    }
                }
            }
            return dp[0][0];
        }
    }// namespace unique_paths
 
    namespace longest_palindromic_substring {
        string Solution::longestPalindrome(string s) {
            const int n = s.size();
            if(n < 2) {
                return s;
            }
 
            int maxLen = 1;
            int begin  = 0;
            // dp[i][j] 表示 s[i..j] 是否是回文串
            vector dp(n, vector<int>(n));
            // 初始化：所有长度为 1 的子串都是回文串
            for(int i = 0; i < n; i++) {
                dp[i][i] = 1;
            }
            // 递推开始
            // 先枚举子串长度
            for(int L = 2; L <= n; L++) {
                // 枚举左边界，左边界的上限设置可以宽松一些
                for(int i = 0; i < n; i++) {
                    // 由 L 和 i 可以确定右边界，即 j - i + 1 = L 得
                    const int j = L + i - 1;
                    // 如果右边界越界，就可以退出当前循环
                    if(j >= n) {
                        break;
                    }
 
                    if(s[i] != s[j]) {
                        dp[i][j] = 0;
                    } else {
                        if(j - i < 3) {
                            dp[i][j] = 1;
                        } else {
                            dp[i][j] = dp[i + 1][j - 1];
                        }
                    }
 
                    // 只要 dp[i][L] == true 成立，就表示子串 s[i..L] 是回文，此时记录回文长度和起始位置
                    if(dp[i][j] != 0 && j - i + 1 > maxLen) {
                        maxLen = j - i + 1;
                        begin  = i;
                    }
                }
            }
            return s.substr(begin, maxLen);
        }
    }// namespace longest_palindromic_substring
 
    namespace arithmetic_slices {
        int Solution::numberOfArithmeticSlices(vector<int> &nums) {
            const int n = nums.size();
            vector<int> diff(n - 1);
            for(int i = 0; i < n - 1; i++) {
                diff[i] = nums[i + 1] - nums[i];
            }
            vector<int> consecutive;
            int prev = 0;
            int cnt  = 0;
            for(int i = 0; i < n - 1; i++) {
                if(diff[i] == diff[prev]) {
                    cnt++;
                } else {
                    consecutive.emplace_back(cnt);
                    prev = i;
                    cnt  = 1;
                }
            }
            consecutive.emplace_back(cnt);
            int ans = 0;
            for(const auto num: consecutive) {
                if(num >= 2) {
                    ans += (num - 1) * num / 2;
                }
            }
            return ans;
        }
    }// namespace arithmetic_slices
 
    namespace decode_ways {
        int Solution::numDecodings(string s) {
            vector dp(s.length(), 0);
            for(int i = 0; i < dp.size(); i++) {
                bool ok = false;
                if('1' <= s[i] && s[i] <= '9') {
                    dp[i] += i - 1 >= 0 ? dp[i - 1] : 1;
                    ok = true;
                }
                if(i - 1 >= 0 && (s[i - 1] == '1' && '0' <= s[i] && s[i] <= '9' || s[i - 1] == '2' && '0' <= s[i] && s[i] <= '6')) {
                    dp[i] += i - 2 >= 0 ? dp[i - 2] : 1;
                    ok = true;
                }
                if(!ok) {
                    return 0;
                }
            }
            return dp.back();
        }
    }// namespace decode_ways
 
    namespace word_break {
        bool Solution::wordBreak(const string &s, vector<string> &wordDict) {
            vector end(s.length(), false);
            TrieNode tn(0);
            for(const auto &word: wordDict) {
                tn.insert(word);
            }
            search(&tn, s, 0, end);
            for(int i = 1; i < s.length(); i++) {
                if(end[i - 1]) {
                    search(&tn, s, i, end);
                    if(end.back()) {
                        return true;
                    }
                }
            }
            return end.back();
        }
 
        void Solution::search(const TrieNode *tn, const string &s, int i, vector<bool> &end) {
            const TrieNode *node = tn;
            for(; i < s.length(); i++) {
                node = node->nexts[s[i] - 'a'];
                if(node == nullptr) {
                    return;
                }
                if(node->end_of_word) {
                    end[i] = true;
                }
            }
        }
    }// namespace word_break
 
    namespace longest_increasing_subsequence {
        int Solution::lengthOfLIS(vector<int> &nums) {
            const int n = nums.size();
            int ans     = 1;
            vector dp(n, 1);//length of longest increasing subsequence end with i
            for(int i = 0; i < n; i++) {
                for(int j = i + 1; j < n; j++) {
                    if(nums[j] > nums[i]) {
                        dp[j] = max(dp[j], dp[i] + 1);
                    }
                }
                ans = max(ans, dp[i]);
            }
            return ans;
        }
    }// namespace longest_increasing_subsequence
 
    namespace number_of_longest_increasing_subsequence {
        int Solution::findNumberOfLIS(vector<int> &nums) {
            const int n = nums.size();
            vector dp(n, map<unsigned, unsigned>());//dp[i][j] = number of increasing subsequence end with i, length is j
            for(int i = 0; i < n; i++) {
                dp[i][1] = 1;
            }
            unsigned max_len = 1;
            for(int i = 0; i < n; i++) {
                for(int j = i + 1; j < n; j++) {
                    auto &[len, cnt] = *dp[i].rbegin();
                    if(nums[j] > nums[i]) {
                        dp[j][len + 1] += cnt;
                        max_len = max(max_len, len + 1);
                    }
                }
            }
            unsigned ans = 0;
            for(int i = 0; i < n; i++) {
                ans += dp[i][max_len];
            }
            return ans;
        }
    }// namespace number_of_longest_increasing_subsequence
 
    namespace longest_common_subsequence {
        int Solution::longestCommonSubsequence(string text1, string text2) {
            vector dp(text1.length(), vector(text2.length(), 0));
            for(int i = 0; i < text1.length(); i++) {
                for(int j = 0; j < text2.length(); j++) {
                    if(text1[i] == text2[j]) {
                        dp[i][j] = (i - 1 < 0 || j - 1 < 0 ? 0 : dp[i - 1][j - 1]) + 1;
                    } else {
                        dp[i][j] = max(i - 1 >= 0 ? dp[i - 1][j] : 0, j - 1 >= 0 ? dp[i][j - 1] : 0);
                    }
                }
            }
            return dp.back().back();
        }
    }// namespace longest_common_subsequence
 
    namespace delete_operation_for_two_strings {
        int Solution::minDistance(const string &word1, const string &word2) {
            const int lcs = longest_common_subsequence::Solution::longestCommonSubsequence(word1, word2);
            return word1.length() + word2.length() - 2 * lcs;
        }
    }// namespace delete_operation_for_two_strings
 
    namespace edit_distance {
        int Solution::minDistance(string word1, string word2) {
            // dp[i][j] is the minimum number of operations required to convert word1[0..i] to word2[0..j]
            vector dp(word1.length() + 1, vector<int>(word2.length() + 1));
            // if word[i] == word2[j], dp[i][j] = dp[i-1][j-1]; else dp[i][j] = min(dp[i-1][j], dp[i][j-1], dp[i-1][j-1]) + 1
            for(int j = 0; j <= word2.length(); j++) {
                dp[0][j] = j;
            }
            for(int i = 0; i <= word1.length(); i++) {
                dp[i][0] = i;
            }
            for(int i = 1; i <= word1.length(); i++) {
                for(int j = 1; j <= word2.length(); j++) {
                    if(word1[i - 1] == word2[j - 1]) {
                        dp[i][j] = dp[i - 1][j - 1];
                    } else {
                        dp[i][j] = min(min(dp[i - 1][j], dp[i][j - 1]), dp[i - 1][j - 1]) + 1;
                    }
                }
            }
            return dp.back().back();
        }
    }// namespace edit_distance
 
    namespace coin_change {
        int Solution::coinChange(vector<int> &coins, int amount) {
            vector dp(amount + 1, -1);
            dp[0] = 0;
            for(const auto &coin: coins) {
                if(coin <= amount) {
                    dp[coin] = 1;
                }
            }
            for(unsigned i = 0; i <= amount; i++) {
                if(dp[i] > 0) {
                    for(const auto &coin: coins) {
                        if(i + coin <= static_cast<unsigned>(amount)) {
                            if(dp[i + coin] == -1) {
                                dp[i + coin] = dp[i] + 1;
                            } else {
                                dp[i + coin] = min(dp[i + coin], dp[i] + 1);
                            }
                        }
                    }
                }
            }
            return dp[amount];
        }
    }// namespace coin_change
 
    namespace integer_break {
        int Solution::integerBreak(int n) {
            // dp[i] is the maximum product of i
            vector<int> dp(n + 1);
            // dp[i] = max(dp[i], dp[j] * dp[i - j])
            dp[2] = 1;
            dp[1] = 1;
            for(int i = 3; i <= n; i++) {
                for(int j = 1; j < i; j++) {
                    dp[i] = max(dp[i], dp[j] * dp[i - j]);
                    dp[i] = max(dp[i], j * dp[i - j]);
                    dp[i] = max(dp[i], dp[j] * (i - j));
                    dp[i] = max(dp[i], j * (i - j));
                }
            }
            return dp[n];
        }
    }// namespace integer_break
 
    namespace max_points_on_a_line {
        int Solution::maxPoints(vector<vector<int>> &points) {
            int ans = 0;
            for(auto &p1: points) {
                unordered_map<long double, int> us;
                int cnt = 0;
                for(auto &p2: points) {
                    if(p2[0] != p1[0]) {
                        us[static_cast<long double>(p2[1] - p1[1]) / static_cast<long double>(p2[0] - p1[0])]++;
                    } else {
                        cnt++;
                    }
                }
                for(auto &[k, v]: us) {
                    cnt = max(cnt, v + 1);
                }
                ans = max(ans, cnt);
            }
            return ans;
        }
    }// namespace max_points_on_a_line
 
    namespace group_anagrams {
        vector<vector<string>> Solution::groupAnagrams(vector<string> &strs) {
            vector<string> strs_sorted = strs;
            unordered_map<string, vector<string>> um;
            for(auto &str: strs_sorted) {
                sort(str.begin(), str.end());
                if(!um.contains(str)) {
                    um[str] = vector<string>();
                }
            }
            for(int i = 0; i < strs.size(); i++) {
                um[strs_sorted[i]].emplace_back(strs[i]);
            }
            vector<vector<string>> ans;
            ans.reserve(um.size());
            for(auto &[k, v]: um) {
                ans.emplace_back(v);
            }
            return ans;
        }
    }// namespace group_anagrams
 
    namespace sort_colors {
        void Solution::sortColors(vector<int> &nums) { qsort(nums, 0, nums.size() - 1); }
 
        void Solution::qsort(vector<int> &nums, int l, int r) {
            if(l >= r) {
                return;
            }
            int lp          = l - 1;
            int rp          = r + 1;
            const int pivot = nums[(l + r) / 2];
            while(lp < rp) {
                while(nums[++lp] < pivot) {}
                while(nums[--rp] > pivot) {}
                if(lp < rp) {
                    swap(nums[lp], nums[rp]);
                }
            }
            qsort(nums, l, rp);
            qsort(nums, rp + 1, r);
        }
    }// namespace sort_colors
 
    namespace top_k_frequent_elements {
        vector<int> Solution::topKFrequent(vector<int> &nums, int k) {
            unordered_map<int, int> um;
            for(auto num: nums) {
                um[num]++;
            }
            vector<int> vec(um.size());
            int i = 0;
            for(auto &[_, v]: um) {
                vec[i++] = v;
            }
            sort(vec.rbegin(), vec.rend());
            unordered_set<int> us;
            for(i = 0; i < k; i++) {
                us.insert(vec[i]);
            }
            vector<int> ans;
            for(auto [num, v]: um) {
                if(us.contains(v)) {
                    ans.emplace_back(num);
                }
            }
            return ans;
        }
    }// namespace top_k_frequent_elements
 
    namespace kth_largest_element_in_an_array {
        int Solution::findKthLargest(vector<int> &nums, int k) {
            sort(nums.rbegin(), nums.rend());
            return nums[k - 1];
        }
    }// namespace kth_largest_element_in_an_array
 
    namespace merge_intervals {
        vector<vector<int>> Solution::merge(vector<vector<int>> &intervals) {
            vector<vector<int>> ans;
            auto comp = [](const vector<int> &a, const vector<int> &b) { return a[0] < b[0]; };
            sort(intervals.begin(), intervals.end(), comp);
            int start = intervals[0][0];
            int end   = intervals[0][1];
            for(int i = 1; i < intervals.size(); i++) {
                if(intervals[i][0] <= end) {
                    end = max(end, intervals[i][1]);
                } else {
                    ans.emplace_back(vector{start, end});
                    start = intervals[i][0];
                    end   = intervals[i][1];
                }
            }
            ans.emplace_back(vector{start, end});
            return ans;
        }
    }// namespace merge_intervals
 
    namespace search_a_2d_matrix_ii {
        bool Solution::searchMatrix(vector<vector<int>> &matrix, int target) { return search(matrix, target, 0, matrix.size() - 1, 0, matrix[0].size() - 1); }
 
        bool Solution::search(const vector<vector<int>> &matrix, int target, int x_start, int x_end, int y_start, int y_end) {
            const int minimum = min(x_end - x_start, y_end - y_start);
            vector<int> diag1(minimum + 1);
            for(int i = 0; i <= minimum; i++) {
                diag1[i] = matrix[x_start + i][y_start + i];
            }
            const auto it = lower_bound(diag1.begin(), diag1.end(), target);
            const int x   = x_start + it - diag1.begin();
            const int y   = y_start + it - diag1.begin();
            if(it != diag1.end()) {
                if(*it == target) {
                    return true;
                }
                if(it == diag1.begin()) {
                    return false;
                }
                if(search(matrix, target, x_start, x - 1, y, y_end)) {
                    return true;
                }
                if(search(matrix, target, x, x_end, y_start, y - 1)) {
                    return true;
                }
                if(search(matrix, target, x, x_end, y, y_end)) {
                    return true;
                }
            } else {
                if(x > x_end && y > y_end) {
                    return false;
                }
                if(x > x_end && search(matrix, target, x_start, x_end, y, y_end)) {
                    return true;
                }
                if(y > y_end && search(matrix, target, x, x_end, y_start, y_end)) {
                    return true;
                }
            }
            return false;
        }
    }// namespace search_a_2d_matrix_ii
 
    namespace serialize_and_deserialize_binary_tree {
        string Codec::serialize(TreeNode *root) {
            if(root == nullptr) {
                return "[]";
            }
            vector<string> vec;
            ostringstream oss;
            oss << '[';
            queue<TreeNode *> q;
            q.push(root);
            while(!q.empty()) {
                const TreeNode *node = q.front();
                q.pop();
                if(node == nullptr) {
                    vec.emplace_back("null");
                    continue;
                }
                vec.emplace_back(to_string(node->val));
                q.push(node->left);
                q.push(node->right);
            }
            int end = vec.size() - 1;
            while(vec[end] == "null" && end > 0) {
                end--;
            }
            oss << vec[0];
            for(int i = 1; i <= end; i++) {
                oss << ',' << vec[i];
            }
            oss << ']';
            return oss.str();
        }
 
        TreeNode *Codec::deserialize(string data) {
            if(data == "[]") {
                return nullptr;
            }
            vector<string> vec;
            data            = data.substr(1, data.size() - 2);
            auto *const str = static_cast<char *>(malloc((data.length() + 1) * sizeof(char)));
            memcpy(str, data.c_str(), (data.length() + 1) * sizeof(char));
            for(const char *item = strtok(str, ","); item != nullptr; item = strtok(nullptr, ",")) {
                vec.emplace_back(string(item));
            }
            queue<TreeNode **> q;
            auto *root = new TreeNode(stoi(vec[0]));
            q.push(&root);
            for(const auto &str: vec) {
                auto *const node = q.front();
                q.pop();
                if(str == "null") {
                    *node = nullptr;
                } else {
                    *node = new TreeNode(stoi(str));
                    q.push(&(*node)->left);
                    q.push(&(*node)->right);
                }
            }
            return root;
        }
    }// namespace serialize_and_deserialize_binary_tree
 
    namespace task_scheduler {
        int Solution::leastInterval(vector<char> &tasks, int n) {
            if(n == 0) {
                return tasks.size();
            }
            int maximum = 0;
            int cycle   = 0;
            unordered_map<char, int> task_cnt;
            unordered_map<char, int> processing;
            for(char task: tasks) {
                task_cnt[task]++;
            }
            while(true) {
                bool finished = true;
                maximum       = 0;
                for(const auto &[task, cnt]: task_cnt) {
                    if(cnt > 0) {
                        finished = false;
                    }
                    if(processing[task] <= 0) {
                        maximum = max(maximum, cnt);
                    }
                }
                if(finished) {
                    return cycle;
                }
                for(auto &[task, rest]: processing) {
                    rest--;
                }
                for(auto &[task, cnt]: task_cnt) {
                    if(maximum == cnt && processing[task] <= 0) {
                        cnt--;
                        processing[task] = n;
                        break;
                    }
                }
                cycle++;
            }
        }
    }// namespace task_scheduler
 
    namespace design_hashmap {
        MyHashMap::MyHashMap() {
            arr = array<list<pair<int, int>>, SZ>();
            for(unsigned i = 0; i < SZ; i++) {
                arr[i] = list<pair<int, int>>();
            }
        }
 
        void MyHashMap::put(int key, int value) {
            const unsigned slot = static_cast<unsigned>(key) % SZ;
            for(auto &[k, v]: arr[slot]) {
                if(k == key) {
                    v = value;
                    return;
                }
            }
            arr[slot].emplace_back(key, value);
        }
 
        int MyHashMap::get(int key) {
            const unsigned slot = static_cast<unsigned>(key) % SZ;
            for(auto &[k, v]: arr[slot]) {
                if(k == key) {
                    return v;
                }
            }
            return -1;
        }
 
        void MyHashMap::remove(int key) {
            const unsigned slot = static_cast<unsigned>(key) % SZ;
            for(auto it = arr[slot].begin(); it != arr[slot].end(); ++it) {
                if(it->first == key) {
                    arr[slot].erase(it);
                    return;
                }
            }
        }
    }// namespace design_hashmap
 
    namespace spiral_matrix_ii {
        vector<vector<int>> Solution::generateMatrix(int n) {
            vector ans(n, vector(n, 0));
            int dir = 0;// 0-right 1-down 2-left 3->up
            int c   = 1;
            int x   = 0;
            int y   = 0;
            for(int i = 0; i < n * n; i++) {
                ans[x][y] = c++;
                bool flag = true;
            SLCT:
                int nx = x;
                int ny = y;
                switch(dir) {
                    case 0:
                        ny++;
                        break;
                    case 1:
                        nx++;
                        break;
                    case 2:
                        ny--;
                        break;
                    case 3:
                        nx--;
                        break;
                }
                if(flag && (nx < 0 || nx >= n || ny < 0 || ny >= n || ans[nx][ny] != 0)) {
                    dir++;
                    dir %= 4;
                    flag = false;
                    goto SLCT;
                }
                x = nx;
                y = ny;
            }
            return ans;
        }
    }// namespace spiral_matrix_ii
 
    namespace non_overlapping_intervals {
        int Solution::eraseOverlapIntervals(vector<vector<int>> &intervals) {
            if(intervals.empty()) {
                return 0;
            }
 
            sort(intervals.begin(), intervals.end(), [](const auto &u, const auto &v) { return u[1] < v[1]; });
 
            const int n = intervals.size();
            int right   = intervals[0][1];
            int ans     = 1;
            for(int i = 1; i < n; ++i) {
                if(intervals[i][0] >= right) {
                    ++ans;
                    right = intervals[i][1];
                }
            }
            return n - ans;
        }
    }// namespace non_overlapping_intervals
 
    namespace product_of_array_except_self {
        vector<int> Solution::productExceptSelf(vector<int> &nums) {
            vector<int> left(nums.size());
            vector<int> right(nums.size());
            int c = 1;
            for(int i = 0; i < left.size(); i++) {
                left[i] = c;
                c *= nums[i];
            }
            c = 1;
            for(int i = left.size() - 1; i >= 0; i--) {
                right[i] = c;
                c *= nums[i];
            }
            vector<int> ans(nums.size());
            for(int i = 0; i < nums.size(); i++) {
                ans[i] = left[i] * right[i];
            }
            return ans;
        }
    }// namespace product_of_array_except_self
 
    namespace subarray_sum_equals_k {
        int Solution::subarraySum(vector<int> &nums, int k) {
            unordered_map<int, int> um;
            um[0]     = 1;
            int count = 0;
            int ps    = 0;
            for(const auto &num: nums) {
                ps += num;
                count += um[ps - k];
                um[ps]++;
            }
            return count;
        }
    }// namespace subarray_sum_equals_k
 
    namespace partition_labels {
        vector<int> Solution::partitionLabels(string s) {
            unordered_map<char, unsigned> last;
            vector<int> ans;
            for(int i = 0; i < s.length(); i++) {
                last[s[i]] = i;
            }
            for(int i = 0; i < s.length();) {
                unsigned last_pos = i;
                char ch           = s[i];
                for(int j = i; j <= last_pos; j++) {
                    last_pos = max(last_pos, last[s[j]]);
                }
                ans.emplace_back(last_pos - i + 1);
                i = last_pos + 1;
            }
            return ans;
        }
    }// namespace partition_labels
 
    namespace repeated_dna_sequences {
        vector<string> Solution::findRepeatedDnaSequences(string s) {
            vector<unsigned short> vec(s.length());
            for(int i = 0; i < s.length(); i++) {
                switch(s[i]) {
                    case 'A':
                        vec[i] = 0;
                        break;
                    case 'C':
                        vec[i] = 1;
                        break;
                    case 'G':
                        vec[i] = 2;
                        break;
                    case 'T':
                        vec[i] = 3;
                        break;
                }
            }
            unsigned hsv = 0;
            if(s.length() < 10) {
                return {};
            }
            unordered_map<unsigned, string> um;
            unordered_map<unsigned, unsigned> cnt;
            for(int i = 0; i < 10; i++) {
                hsv *= 4;
                hsv += vec[i];
            }
            um[hsv]          = s.substr(0, 10);
            cnt[hsv]         = 1;
            const unsigned f = 262144;
            for(int i = 10; i < s.length(); i++) {
                hsv -= vec[i - 10] * f;
                hsv *= 4;
                hsv += vec[i];
                um[hsv] = s.substr(i - 9, 10);
                cnt[hsv]++;
            }
            vector<string> ans;
            for(auto &[k, v]: um) {
                if(cnt[k] > 1) {
                    ans.emplace_back(v);
                }
            }
            return ans;
        }
    }// namespace repeated_dna_sequences
 
    namespace design_linked_list {
        MyLinkedList::MyLinkedList() {
            head = new ListNode();
            tail = head;
        }
 
        int MyLinkedList::get(int index) const {
            index += 1;
            if(index < 1) {
                return -1;
            }
            const ListNode *current = head;
            for(int i = 0; i < index && current != nullptr; i++) {
                current = current->next;
            }
            return current == nullptr ? -1 : current->val;
        }
 
        void MyLinkedList::addAtHead(int val) {
            auto *const node = new ListNode(val);
            node->next       = head->next;
            head->next       = node;
            if(tail == head) {
                tail = node;
            }
        }
 
        void MyLinkedList::addAtTail(int val) {
            auto *const node = new ListNode(val);
            tail->next       = node;
            tail             = node;
        }
 
        void MyLinkedList::addAtIndex(int index, int val) {
            index += 1;
            if(index < 1) {
                return;
            }
            auto *const node  = new ListNode(val);
            ListNode *current = head;
            for(int i = 0; i < index - 1 && current != nullptr; i++) {
                current = current->next;
            }
            if(current == nullptr) {
                delete node;
                return;
            }
            node->next    = current->next;
            current->next = node;
            if(current == tail) {
                tail = node;
            }
        }
 
        void MyLinkedList::deleteAtIndex(int index) {
            index += 1;
            if(index < 1) {
                return;
            }
            ListNode *current = head;
            for(int i = 0; i < index - 1 && current != nullptr; i++) {
                current = current->next;
            }
            if(current == nullptr) {
                return;
            }
            const auto *const p = current->next;
            if(p == tail) {
                tail = current;
            }
            if(p != nullptr) {
                current->next = current->next->next;
                delete p;
            }
        }
    }// namespace design_linked_list
 
    namespace delete_node_in_a_bst {
        TreeNode *Solution::findMaximum(TreeNode *node) {
            TreeNode *current = node;
            while(current->right != nullptr) {
                prev    = current;
                current = current->right;
            }
            return current;
        }
 
        TreeNode *Solution::findMinimum(TreeNode *node) {
            TreeNode *current = node;
            while(current->left != nullptr) {
                prev    = current;
                current = current->left;
            }
            return current;
        }
 
        void Solution::remove(TreeNode *node) {
            if(node->right != nullptr) {
                prev             = node;
                auto *const rmin = findMinimum(node->right);
                node->val        = rmin->val;
                remove(rmin);
                return;
            }
            if(node->left != nullptr) {
                prev             = node;
                auto *const lmax = findMaximum(node->left);
                node->val        = lmax->val;
                remove(lmax);
                return;
            }
            if(prev != nullptr) {
                if(prev->left != nullptr && prev->left->val == node->val) {
                    prev->left = nullptr;
                } else if(prev->right != nullptr && prev->right->val == node->val) {
                    prev->right = nullptr;
                }
            } else {
                exit(-1);
            }
            //delete node;
        }
 
        TreeNode *Solution::deleteNode(TreeNode *root, int key) {
            if(root == nullptr) {
                return root;
            }
            TreeNode *current = root;
            while(current != nullptr && current->val != key) {
                if(current->val == key) {
                    break;
                }
                prev = current;
                if(current->val < key) {
                    current = current->right;
                } else {
                    current = current->left;
                }
            }
            if(current == nullptr) {
                return root;
            }
            if(root->left == nullptr && root->right == nullptr) {
                return nullptr;
            }
            remove(current);
            return root;
        }
    }// namespace delete_node_in_a_bst
 
    namespace missing_element_in_sorted_array {
        int Solution::missingElement(vector<int> &nums, int k) {
            unordered_set<int> us;
            for(auto num: nums) {
                us.insert(num);
            }
            if(missing(nums, nums.size() - 1) < k) {
                return nums[0] + k + nums.size() - 1;
            }
            int l = 0;
            int r = nums.size() - 1;
            while(l < r) {
                if(r == l + 1) {
                    return nums[l] + k - missing(nums, l);
                }
                const int m = (l + r) / 2;
                if(missing(nums, m) < k) {
                    l = m;
                } else if(missing(nums, m) >= k) {
                    r = m;
                }
            }
            return 0;
        }
 
        unsigned Solution::missing(vector<int> &nums, int i) { return nums[i] - nums[0] - i; }
    }// namespace missing_element_in_sorted_array
 
    namespace find_a_peak_element_ii {
        vector<int> Solution::findPeakGridLR(vector<vector<int>> &mat, int l, int r) {
            const int mid = (l + r) / 2;
            int max_col   = mid;
            int max_row   = 0;
            int maximum   = -1;
            for(int i = 0; i < mat.size(); i++) {
                for(int j = mid - 1; j <= mid + 1; j++) {
                    if(maximum < get(mat, i, j)) {
                        maximum = get(mat, i, j);
                        max_col = j;
                        max_row = i;
                    }
                }
            }
            if(max_col == mid || l + 1 == r) {
                return {max_row, max_col};
            }
            if(max_col == mid + 1) {
                return findPeakGridLR(mat, mid, r);
            }
            return findPeakGridLR(mat, l, mid);
        }
 
        vector<int> Solution::findPeakGrid(vector<vector<int>> &mat) { return findPeakGridLR(mat, 0, mat[0].size() - 1); }
 
        int Solution::get(vector<vector<int>> &mat, int i, int j) {
            if(i >= 0 && i < mat.size() && j >= 0 && j < mat[0].size()) {
                return mat[i][j];
            }
            return -1;
        }
    }// namespace find_a_peak_element_ii
 
    namespace divide_chocolate {
        int Solution::maximizeSweetness(vector<int> &sweetness, int k) {
            int l = sweetness[0];
            int r = 0;
            for(auto s: sweetness) {
                l = min(l, s);
                r += s;
            }
            while(l < r) {
                if(l + 1 == r) {
                    return count(sweetness, r) == k + 1 ? r : l;
                }
                const int m = (l + r) / 2;
                const int c = count(sweetness, m);
                if(c < k + 1) {
                    r = m - 1;
                } else {
                    l = m;
                }
            }
            return l;
        }
 
        int Solution::count(vector<int> &sweetness, int x) {
            int ans     = 0;
            int current = 0;
            for(const auto s: sweetness) {
                current += s;
                if(current >= x) {
                    current = 0;
                    ans++;
                }
            }
            return ans;
        }
    }// namespace divide_chocolate
 
    namespace shortest_distance_to_target_color {
        vector<int> Solution::shortestDistanceColor(vector<int> &colors, vector<vector<int>> &queries) {
            vector<int> ans;
            unordered_map<int, vector<int>> um;
            for(int i = 0; i < colors.size(); i++) {
                um[colors[i]].emplace_back(i);
            }
            for(auto &[k, vec]: um) {
                sort(vec.begin(), vec.end());
            }
            for(auto &query: queries) {
                int &i           = query[0];
                int &c           = query[1];
                vector<int> &vec = um[c];
                auto g           = lower_bound(vec.begin(), vec.end(), i, less());
                auto l           = lower_bound(vec.rbegin(), vec.rend(), i, greater());
                if(g == vec.end() && l == vec.rend()) {
                    ans.emplace_back(-1);
                } else if(g == vec.end()) {
                    ans.emplace_back(abs(*l - i));
                } else if(l == vec.rend()) {
                    ans.emplace_back(abs(*g - i));
                } else {
                    ans.emplace_back(min(abs(*l - i), abs(*g - i)));
                }
            }
            return ans;
        }
    }// namespace shortest_distance_to_target_color
 
    namespace meeting_scheduler {
        vector<int> Solution::minAvailableDuration(vector<vector<int>> &slots1, vector<vector<int>> &slots2, int duration) {
            vector<int> ans(2);
            auto cmp = [](const vector<int> &vec1, const vector<int> &vec2) -> bool {
                if(vec1[1] != vec2[1]) {
                    return vec1[1] < vec2[1];
                }
                return vec1[0] < vec2[0];
            };
            sort(slots1.begin(), slots1.end(), cmp);
            sort(slots2.begin(), slots2.end(), cmp);
            for(auto it1 = slots1.begin(), it2 = slots2.begin(); it1 != slots1.end() && it2 != slots2.end();) {
                pair<int, int> p = merge(*it1, *it2);
                if(p.second - p.first >= duration) {
                    return {p.first, p.first + duration};
                }
                if(cmp(*it1, *it2)) {
                    ++it1;
                } else {
                    ++it2;
                }
            }
            return {};
        }
 
        pair<int, int> Solution::merge(const vector<int> &vec1, const vector<int> &vec2) { return {max(vec1[0], vec2[0]), min(vec1[1], vec2[1])}; }
    }// namespace meeting_scheduler
 
    namespace find_the_duplicate_number {
        int Solution::findDuplicate(vector<int> &nums) {
            int maximum = nums[0];
            int minimum = nums[0];
            for(const auto &num: nums) {
                maximum = max(maximum, num);
                minimum = min(minimum, num);
            }
            int l = minimum;
            int r = maximum;
            while(l < r) {
                const int m = (l + r) / 2;
                const int c = countInRange(nums, l, m);
                if(c == m - l + 1) {
                    l = m + 1;
                } else if(c > m - l + 1) {
                    r = m;
                } else {
                    l++;
                }
            }
            return l;
        }
 
        int Solution::countInRange(vector<int> &nums, int l, int r) {
            int ans = 0;
            for(const auto &num: nums) {
                if(l <= num && num <= r) {
                    ans++;
                }
            }
            return ans;
        }
    }// namespace find_the_duplicate_number
 
    namespace trapping_rain_water {
        int Solution::trap(vector<int> &height) {
            vector lmax(height.size(), 0);
            vector rmax(height.size(), 0);
            int maximum = height[0];
            for(int i = 0; i < height.size(); i++) {
                maximum = max(maximum, height[i]);
                lmax[i] = maximum;
            }
            maximum = height.back();
            for(int i = height.size() - 1; i >= 0; i--) {
                maximum = max(maximum, height[i]);
                rmax[i] = maximum;
            }
            int ans = 0;
            for(int i = 0; i < height.size(); i++) {
                ans += min(lmax[i], rmax[i]) - height[i];
            }
            return ans;
        }
    }// namespace trapping_rain_water
 
    namespace product_of_two_run_length_encoded_arrays {
        vector<vector<int>> Solution::findRLEArray(vector<vector<int>> &encoded1, vector<vector<int>> &encoded2) {
            vector<vector<int>> ans;
            int p1 = 0;
            int p2 = 0;
            for(int i1 = 0, i2 = 0; i1 < encoded1.size() && i2 < encoded2.size();) {
                const int len = min(encoded1[i1][1] - p1, encoded2[i2][1] - p2);
                const int v   = encoded1[i1][0] * encoded2[i2][0];
                if(!ans.empty() && ans.back()[0] == v) {
                    ans.back()[1] += len;
                } else {
                    vector vec = {v, len};
                    ans.emplace_back(vec);
                }
                p1 += len;
                p2 += len;
                if(p1 >= encoded1[i1][1]) {
                    i1++;
                    p1 = 0;
                }
                if(p2 >= encoded2[i2][1]) {
                    i2++;
                    p2 = 0;
                }
            }
            return ans;
        }
    }// namespace product_of_two_run_length_encoded_arrays
 
    namespace longest_substring_with_at_most_two_distinct_characters {
        int Solution::getMinUniqueCharCnt(const string &s, int len) {
            unordered_map<char, int> um;
            for(int i = 0; i < len; i++) {
                um[s[i]]++;
            }
            size_t ans = um.size();
            for(int i = 0, j = len; j < s.length(); i++, j++) {
                um[s[i]]--;
                um[s[j]]++;
                if(um[s[i]] == 0) {
                    um.erase(s[i]);
                }
                ans = min(ans, um.size());
            }
            return ans;
        }
 
        int Solution::lengthOfLongestSubstringTwoDistinct(const string &s) {
            int l = 1;
            int r = s.length();
            while(l < r) {
                const int mid = (l + r) / 2 + 1;
                const int res = getMinUniqueCharCnt(s, mid);
                if(res > 2) {
                    r = mid - 1;
                } else {
                    l = mid;
                }
            }
            return l;
        }
    }// namespace longest_substring_with_at_most_two_distinct_characters
 
    namespace longest_substring_with_at_most_k_distinct_characters {
        int Solution::lengthOfLongestSubstringKDistinct(const string &s, int k) {
            if(k == 0) {
                return 0;
            }
            int l = 1;
            int r = s.length();
            while(l < r) {
                const int mid = (l + r) / 2 + 1;
                const int res = longest_substring_with_at_most_two_distinct_characters::Solution::getMinUniqueCharCnt(s, mid);
                if(res > k) {
                    r = mid - 1;
                } else {
                    l = mid;
                }
            }
            return l;
        }
    }// namespace longest_substring_with_at_most_k_distinct_characters
 
    namespace max_consecutive_ones_iii {
        int Solution::longestOnes(vector<int> &nums, int k) {
            int l = 0;
            int r = nums.size();
            while(l < r) {
                const int mid = (l + r) / 2 + 1;
                const int res = cntMinFlip(nums, mid);
                if(res > k) {
                    r = mid - 1;
                } else {
                    l = mid;
                }
            }
            return l;
        }
 
        int Solution::cntMinFlip(vector<int> &nums, int len) {
            if(len == 0) {
                return 0;
            }
            int current = 0;
            for(int i = 0; i < len; i++) {
                if(nums[i] == 0) {
                    current++;
                }
            }
            int ans = current;
            for(int i = 0, j = len; j < nums.size(); i++, j++) {
                if(nums[i] == 0) {
                    current--;
                }
                if(nums[j] == 0) {
                    current++;
                }
                ans = min(ans, current);
            }
            return ans;
        }
    }// namespace max_consecutive_ones_iii
 
    namespace sliding_window_maximum {
        vector<int> Solution::maxSlidingWindow(vector<int> &nums, int k) {
            multiset<int> ms;
            for(int i = 0; i < k; i++) {
                ms.insert(nums[i]);
            }
            vector<int> ans;
            for(int i = 0, j = k; j < nums.size(); i++, j++) {
                ans.emplace_back(*ms.rbegin());
                ms.erase(ms.lower_bound(nums[i]));
                ms.insert(nums[j]);
            }
            ans.emplace_back(*ms.rbegin());
            return ans;
        }
    }// namespace sliding_window_maximum
 
    namespace minimum_window_substring {
        string Solution::minWindow(string s, const string &t) {
            string ans = s;
            int l      = 0;
            int r      = 0;
            unordered_map<char, int> umt;
            unordered_map<char, int> ums;
            ums[s[0]]++;
            for(char ch: t) {
                umt[ch]++;
            }
            bool flag = true;
            while(l <= r && r < s.length() && l < s.length()) {
                while(!valid(ums, umt) && r + 1 < s.length()) {
                    ums[s[++r]]++;
                }
                while(valid(ums, umt) && l < s.length()) {
                    flag = false;
                    if(r - l + 1 < ans.length()) {
                        ans = s.substr(l, r - l + 1);
                    }
                    ums[s[l++]]--;
                }
                if(flag) {
                    return "";
                }
                if(r == s.length() - 1) {
                    break;
                }
            }
            return ans;
        }
 
        bool Solution::valid(unordered_map<char, int> &ums, const unordered_map<char, int> &umt) {
            for(const auto &[k, v]: umt) {
                if(!ums.contains(k) || ums[k] < v) {
                    return false;
                }
            }
            return true;
        }
    }// namespace minimum_window_substring
 
    namespace walls_and_gates {
        void Solution::wallsAndGates(vector<vector<int>> &rooms) {
            const int m = rooms.size();
            const int n = rooms[0].size();
            queue<tuple<int, int, int>> q;
            for(int i = 0; i < m; i++) {
                for(int j = 0; j < n; j++) {
                    if(rooms[i][j] == 0) {
                        q.push({0, i, j});
                    }
                }
            }
            while(!q.empty()) {
                auto [d, x, y] = q.front();
                q.pop();
                pair<int, int> nexts[4] = {{x + 1, y}, {x - 1, y}, {x, y + 1}, {x, y - 1}};
                for(auto &[next_x, next_y]: nexts) {
                    if(next_x >= 0 && next_y >= 0 && next_x < m && next_y < n && rooms[next_x][next_y] != -1 && rooms[next_x][next_y] != 0 && (rooms[next_x][next_y] == INT_MAX || rooms[next_x][next_y] > d + 1)) {
                        rooms[next_x][next_y] = d + 1;
                        q.push({d + 1, next_x, next_y});
                    }
                }
            }
        }
    }// namespace walls_and_gates
 
    namespace pacific_atlantic_waterflow {
        vector<vector<int>> Solution::pacificAtlantic(vector<vector<int>> &heights) {
            const int m = heights.size();
            const int n = heights[0].size();
            unordered_set<pair<int, int>, myhash, myeq> pacific;
            unordered_set<pair<int, int>, myhash, myeq> atlantic;
            queue<pair<int, int>> q;
            vector<vector<int>> ans;
 
            for(int i = 0; i < m; i++) {
                q.push({i, 0});
                pacific.insert({i, 0});
            }
            for(int i = 1; i < n; i++) {
                q.push({0, i});
                pacific.insert({0, i});
            }
            while(!q.empty()) {
                auto [x, y] = q.front();
                q.pop();
                pair<int, int> nexts[4] = {{x + 1, y}, {x - 1, y}, {x, y + 1}, {x, y - 1}};
                for(auto &[next_x, next_y]: nexts) {
                    if(next_x >= 0 && next_y >= 0 && next_x < m && next_y < n && heights[next_x][next_y] >= heights[x][y] && !pacific.contains({next_x, next_y})) {
                        pacific.insert({next_x, next_y});
                        q.push({next_x, next_y});
                    }
                }
            }
 
            for(int i = 0; i < m; i++) {
                q.push({i, n - 1});
                atlantic.insert({i, n - 1});
            }
            for(int i = 0; i < n - 1; i++) {
                q.push({m - 1, i});
                atlantic.insert({m - 1, i});
            }
            while(!q.empty()) {
                auto [x, y] = q.front();
                q.pop();
                pair<int, int> nexts[4] = {{x + 1, y}, {x - 1, y}, {x, y + 1}, {x, y - 1}};
                for(auto &[next_x, next_y]: nexts) {
                    if(next_x >= 0 && next_y >= 0 && next_x < m && next_y < n && heights[next_x][next_y] >= heights[x][y] && !atlantic.contains({next_x, next_y})) {
                        atlantic.insert({next_x, next_y});
                        q.push({next_x, next_y});
                    }
                }
            }
 
            for(const auto &p: atlantic) {
                if(pacific.contains(p)) {
                    vector vec = {p.first, p.second};
                    ans.emplace_back(vec);
                }
            }
            sort(ans.begin(), ans.end());
            return ans;
        }
 
        bool myeq::operator()(const pair<int, int> &p1, const pair<int, int> &p2) const { return p1 == p2; }
 
        size_t myhash::operator()(const pair<int, int> &p) const { return p.first * 200 + p.second; }
    }// namespace pacific_atlantic_waterflow
 
    namespace find_all_the_lonely_nodes {
        vector<int> Solution::getLonelyNodes(TreeNode *root) {
            vector<int> ans;
            queue<TreeNode *> q;
            q.push(root);
            while(!q.empty()) {
                const TreeNode *node = q.front();
                q.pop();
                if(node->left == nullptr && node->right != nullptr) {
                    ans.emplace_back(node->right->val);
                } else if(node->right == nullptr && node->left != nullptr) {
                    ans.emplace_back(node->left->val);
                }
                if(node->left != nullptr) {
                    q.push(node->left);
                }
                if(node->right != nullptr) {
                    q.push(node->right);
                }
            }
            return ans;
        }
    }// namespace find_all_the_lonely_nodes
 
    namespace kill_process {
        vector<int> Solution::killProcess(vector<int> &pid, vector<int> &ppid, int kill) {
            unordered_map<int, Node *> um;
            for(const auto &v: pid) {
                um[v] = new Node(v);
            }
            for(int i = 0; i < pid.size(); i++) {
                if(ppid[i] != 0) {
                    um[ppid[i]]->children.insert(um[pid[i]]);
                }
            }
            vector<int> ans;
            queue<Node *> q;
            q.push(um[kill]);
            while(!q.empty()) {
                Node *node = q.front();
                q.pop();
                ans.emplace_back(node->val);
                for(auto *next: node->children) {
                    q.push(next);
                }
            }
            return ans;
        }
    }// namespace kill_process
 
    namespace all_nodes_distance_k_in_binary_tree {
        vector<int> Solution::distanceK(TreeNode *root, TreeNode *target, int k) {
            if(k == 0) {
                return {target->val};
            }
            unordered_map<TreeNode *, Node *> um;
            vector<int> ans;
            queue<TreeNode *> q1;
            q1.push(root);
            um[root] = new Node(root->val);
            while(!q1.empty()) {
                TreeNode *tn = q1.front();
                q1.pop();
                if(tn->left != nullptr) {
                    q1.push(tn->left);
                    um[tn->left] = new Node(tn->left->val);
                    um[tn->left]->siblings.insert(um[tn]);
                    um[tn]->siblings.insert(um[tn->left]);
                }
                if(tn->right != nullptr) {
                    q1.push(tn->right);
                    um[tn->right] = new Node(tn->right->val);
                    um[tn->right]->siblings.insert(um[tn]);
                    um[tn]->siblings.insert(um[tn->right]);
                }
            }
            Node *node = um[target];
            unordered_set<Node *> vis;
            queue<pair<int, Node *>> q2;
            q2.push({0, node});
            while(!q2.empty()) {
                auto [d, nd] = q2.front();
                q2.pop();
                vis.insert(nd);
                for(auto *sibling: nd->siblings) {
                    if(!vis.contains(sibling)) {
                        vis.insert(sibling);
                        if(d + 1 == k) {
                            ans.emplace_back(sibling->val);
                        } else {
                            q2.push({d + 1, sibling});
                        }
                    }
                }
            }
            return ans;
        }
    }// namespace all_nodes_distance_k_in_binary_tree
 
    namespace open_the_lock {
        int Solution::openLock(vector<string> &deadends, const string &target) {
            unordered_set<string> deads;
            unordered_set<string> vis;
            for(auto &deadend: deadends) {
                deads.insert(deadend);
            }
            auto get_nexts = [](const string &code) {
                vector ans(8, code);
                ans[0][0] = (ans[0][0] - '0' + 10 + 1) % 10 + '0';
                ans[1][0] = (ans[1][0] - '0' + 10 - 1) % 10 + '0';
                ans[2][1] = (ans[2][1] - '0' + 10 + 1) % 10 + '0';
                ans[3][1] = (ans[3][1] - '0' + 10 - 1) % 10 + '0';
                ans[4][2] = (ans[4][2] - '0' + 10 + 1) % 10 + '0';
                ans[5][2] = (ans[5][2] - '0' + 10 - 1) % 10 + '0';
                ans[6][3] = (ans[6][3] - '0' + 10 + 1) % 10 + '0';
                ans[7][3] = (ans[7][3] - '0' + 10 - 1) % 10 + '0';
                return ans;
            };
            queue<pair<int, string>> q;
            q.push({0, "0000"});
            while(!q.empty()) {
                auto [step, code] = q.front();
                if(code == target) {
                    return step;
                }
                vis.insert(code);
                q.pop();
                if(deads.contains(code)) {
                    continue;
                }
                auto nexts = get_nexts(code);
                for(auto &next: nexts) {
                    if(!vis.contains(next)) {
                        vis.insert(next);
                        if(next == target) {
                            return step + 1;
                        }
                        q.push({step + 1, next});
                    }
                }
            }
            return -1;
        }
    }// namespace open_the_lock
 
    namespace number_of_operations_to_make_network_connected {
        int Solution::makeConnected(int n, vector<vector<int>> &connections) {
            vector<unordered_set<int>> g(n);
            for(auto &connection: connections) {
                g[connection[0]].insert(connection[1]);
                g[connection[1]].insert(connection[0]);
            }
            int group_cnt      = 0;
            int free_edges_cnt = 0;
            unordered_set<int> vis;
            for(int i = 0; i < n; i++) {
                if(!vis.contains(i)) {
                    int edge_cnt = 0;
                    int node_cnt = 0;
                    dfs(edge_cnt, node_cnt, vis, i, g);
                    group_cnt++;
                    free_edges_cnt += edge_cnt / 2 - node_cnt + 1;
                }
            }
            if(free_edges_cnt < group_cnt - 1) {
                return -1;
            }
            return group_cnt - 1;
        }
 
        void Solution::dfs(int &edge_cnt, int &node_cnt, unordered_set<int> &vis, int node, vector<unordered_set<int>> &g) {
            node_cnt++;
            edge_cnt += g[node].size();
            vis.insert(node);
            for(auto next: g[node]) {
                if(!vis.contains(next)) {
                    dfs(edge_cnt, node_cnt, vis, next, g);
                }
            }
        }
    }// namespace number_of_operations_to_make_network_connected
 
    namespace minimum_cost_to_make_at_least_one_valid_path_in_a_grid {
        int Solution::minCost(vector<vector<int>> &grid) {
            const int m = grid.size();
            const int n = grid[0].size();
            vector g(m, vector<Node *>(n, nullptr));
            for(int i = 0; i < m; i++) {
                for(int j = 0; j < n; j++) {
                    g[i][j] = new Node(i, j);
                }
            }
            for(int i = 0; i < m; i++) {
                for(int j = 0; j < n; j++) {
                    pair<int, int> nexts[4] = {{i + 1, j}, {i - 1, j}, {i, j + 1}, {i, j - 1}};
                    for(auto [x, y]: nexts) {
                        if(x >= 0 && x < m && y >= 0 && y < n) {
                            g[i][j]->siblings.insert(make_pair(g[x][y], 1));
                        }
                    }
                    int x = i;
                    int y = j;
                    switch(grid[i][j]) {
                        case 1:
                            y++;
                            break;
                        case 2:
                            y--;
                            break;
                        case 3:
                            x++;
                            break;
                        case 4:
                            x--;
                            break;
                    }
                    if(x >= 0 && x < m && y >= 0 && y < n) {
                        g[i][j]->siblings[g[x][y]] = 0;
                    }
                }
            }
            priority_queue<pair<int, Node *>, vector<pair<int, Node *>>, mycmp> pq;
            unordered_set<Node *> vis;
            pq.push({0, g[0][0]});
            while(!pq.empty()) {
                auto [cost, node] = pq.top();
                pq.pop();
                if(vis.contains(node)) {
                    continue;
                }
                vis.insert(node);
                if(node->x == m - 1 && node->y == n - 1) {
                    return cost;
                }
                for(auto [sibling, c]: node->siblings) {
                    if(!vis.contains(sibling)) {
                        pq.push({cost + c, sibling});
                    }
                }
            }
            return 0;
        }
 
        bool mycmp::operator()(const pair<int, Node *> &p1, const pair<int, Node *> &p2) const {
            if(p1.first != p2.first) {
                return p1.first > p2.first;
            }
            return p1.second->x + p1.second->y < p2.second->x + p2.second->y;
        }
    }// namespace minimum_cost_to_make_at_least_one_valid_path_in_a_grid
 
    namespace critical_connections_in_a_network {
        vector<vector<int>> Solution::criticalConnections(int n, vector<vector<int>> &connections) {
            vector<unordered_set<int>> g(n);
            for(auto &conn: connections) {
                g[conn[0]].insert(conn[1]);
                g[conn[1]].insert(conn[0]);
            }
            vector<vector<int>> ans;
            vector dfn(n, -1);
            vector low(n, -1);
            unordered_set<int> vis;
            int step = 0;
            for(int i = 0; i < n; i++) {
                if(dfn[i] == -1) {
                    step = 0;
                    tarjan(-1, step, dfn, i, g, low, ans);
                }
            }
            return ans;
        }
 
        void Solution::tarjan(int prev, int &step, vector<int> &dfn, int node, vector<unordered_set<int>> &g, vector<int> &low, vector<vector<int>> &ans) {
            dfn[node] = step;
            low[node] = step;
            for(const auto &next: g[node]) {
                if(dfn[next] == -1) {
                    tarjan(node, ++step, dfn, next, g, low, ans);
                }
                if(next != prev) {
                    low[node] = min(low[node], low[next]);
                }
                if(dfn[node] < low[next]) {
                    ans.push_back({node, next});
                }
            }
        }
    }// namespace critical_connections_in_a_network
 
    namespace factor_combinations {
        vector<vector<int>> Solution::getFactorsWithMin(int n, int minimum) {
            vector<vector<int>> ans;
            for(int i = minimum; i <= sqrt(n); i++) {
                if(n % i == 0) {
                    ans.push_back({i, n / i});
                    auto res = getFactorsWithMin(n / i, i);
                    for(auto &vec: res) {
                        ans.push_back({i});
                        ans.back().insert(ans.back().end(), vec.begin(), vec.end());
                    }
                }
            }
            return ans;
        }
 
        vector<vector<int>> Solution::getFactors(int n) { return getFactorsWithMin(n, 2); }
    }// namespace factor_combinations
 
    namespace decode_string {
        string Solution::decodeString(string s) {
            int i = 0;
            vector<int> cnt;
            vector<string> strs;
            while(i < s.length()) {
                if(isalpha(s[i]) != 0) {
                    cnt.emplace_back(1);
                    strs.emplace_back(string(1, s[i]));
                    i++;
                } else if(isdigit(s[i]) != 0) {
                    int j = i + 1;
                    while(j < s.length() && isdigit(s[j]) != 0) {
                        j++;
                    }
                    cnt.emplace_back(stoi(s.substr(i, j - i)));
                    i         = j;
                    int level = 1;
                    while(level > 0) {
                        j++;
                        if(s[j] == '[') {
                            level++;
                        } else if(s[j] == ']') {
                            level--;
                        }
                    }
                    strs.emplace_back(decodeString(s.substr(i + 1, j - i - 1)));
                    i = j + 1;
                }
            }
            ostringstream oss;
            for(i = 0; i < cnt.size(); i++) {
                for(int j = 0; j < cnt[i]; j++) {
                    oss << strs[i];
                }
            }
            return oss.str();
        }
    }// namespace decode_string
 
    namespace n_queens {
        vector<vector<string>> Solution::solveNQueens(int n) {
            vector<vector<string>> ans;
            const vector board(n, vector(n, false));
            dfs(board, 0, n, ans);
            return ans;
        }
 
        void Solution::dfs(const vector<vector<bool>> &board, int line, int n, vector<vector<string>> &ans) {
            if(line == n) {
                ans.emplace_back(toStringVec(board));
                return;
            }
            for(int i = 0; i < n; i++) {
                if(valid(board, n, line, i)) {
                    vector<vector<bool>> next = board;
                    next[line][i]             = true;
                    dfs(next, line + 1, n, ans);
                }
            }
        }
 
        bool Solution::valid(const vector<vector<bool>> &board, int n, int x, int y) {
            for(int i = 0; i < x; i++) {
                if(board[i][y]) {
                    return false;
                }
            }
            for(int i = x, j = y; i >= 0 && i < n && j >= 0 && j < n; i--, j--) {
                if(board[i][j]) {
                    return false;
                }
            }
            for(int i = x, j = y; i >= 0 && i < n && j >= 0 && j < n; i--, j++) {
                if(board[i][j]) {
                    return false;
                }
            }
            return true;
        }
 
        vector<string> Solution::toStringVec(const vector<vector<bool>> &board) {
            vector<string> ans(board.size());
            for(int i = 0; i < board.size(); i++) {
                ostringstream oss;
                for(int j = 0; j < board[i].size(); j++) {
                    oss << (board[i][j] ? 'Q' : '.');
                }
                ans[i] = oss.str();
            }
            return ans;
        }
    }// namespace n_queens
 
    namespace sudoku_solver {
        void Solution::solveSudoku(vector<vector<char>> &board) { dfs(board, board); }
 
        bool Solution::dfs(const vector<vector<char>> &board, vector<vector<char>> &ans) {
            for(int i = 0; i < 9; i++) {
                for(int j = 0; j < 9; j++) {
                    if(board[i][j] == '.') {
                        for(char c = '1'; c <= '9'; c++) {
                            if(valid(board, i, j, c)) {
                                bool haveValid            = true;
                                vector<vector<char>> next = board;
                                next[i][j]                = c;
                                if(dfs(next, ans)) {
                                    return true;
                                }
                            }
                        }
                        return false;
                    }
                }
            }
            ans = board;
            return true;
        }
 
        bool Solution::valid(const vector<vector<char>> &board, int x, int y, char num) {
            for(int i = 0; i < 9; i++) {
                if(board[i][y] == num) {
                    return false;
                }
            }
            for(int j = 0; j < 9; j++) {
                if(board[x][j] == num) {
                    return false;
                }
            }
            for(int i = 0; i < 3; i++) {
                for(int j = 0; j < 3; j++) {
                    if(board[x / 3 * 3 + i][y / 3 * 3 + j] == num) {
                        return false;
                    }
                }
            }
            return true;
        }
    }// namespace sudoku_solver
 
    namespace regular_expression_matching {
        bool Solution::isMatch(const string &s, const string &p) { return dfs(s, p, 0, 0); }
 
        bool Solution::dfs(const string &s, const string &p, int si, int pi) {
            if(pi == p.length() && si == s.length()) {
                return true;
            }
            if(pi == p.length()) {
                return false;
            }
            const char c  = p[pi++];
            bool multiple = false;
            if(pi < p.length() && p[pi] == '*') {
                multiple = true;
                pi++;
            }
            if(!multiple) {
                if(si == s.length()) {
                    return false;
                }
                if(c == '.' || s[si] == c) {
                    return dfs(s, p, si + 1, pi);
                }
                return false;
            }
            if(c == '.') {
                for(int i = si; i <= s.length(); i++) {
                    if(dfs(s, p, i, pi)) {
                        return true;
                    }
                }
                return false;
            }
            int i = si;
            while(s[i] == c) {
                if(dfs(s, p, ++i, pi)) {
                    return true;
                }
            }
            return dfs(s, p, si, pi);
        }
    }// namespace regular_expression_matching
 
    namespace different_ways_to_add_parentheses {
        vector<int> Solution::eval(const string &expr, int start, int end) {
            vector<int> ans;
            bool allDigit = true;
            for(int i = start; i <= end; i++) {
                if(!isdigit(expr[i])) {
                    allDigit     = false;
                    vector left  = eval(expr, start, i - 1);
                    vector right = eval(expr, i + 1, end);
                    for(const auto &l: left) {
                        for(const auto &r: right) {
                            switch(expr[i]) {
                                case '+':
                                    ans.emplace_back(l + r);
                                    break;
                                case '-':
                                    ans.emplace_back(l - r);
                                    break;
                                case '*':
                                    ans.emplace_back(l * r);
                                    break;
                            }
                        }
                    }
                }
            }
            if(allDigit) {
                int val = 0;
                for(int i = start; i <= end; i++) {
                    val *= 10;
                    val += expr[i] - '0';
                }
                ans.emplace_back(val);
            }
            return ans;
        }
 
        vector<int> Solution::diffWaysToCompute(const string &expression) {
            vector ans = eval(expression, 0, expression.length() - 1);
            sort(ans.begin(), ans.end());
            return ans;
        }
    }// namespace different_ways_to_add_parentheses
 
    namespace remove_invalid_parentheses {
        vector<string> Solution::removeInvalidParentheses(const string &s) {
            vector<string> ans;
            unordered_set<string> currSet;
 
            currSet.insert(s);
            while(true) {
                for(auto &str: currSet) {
                    if(isValid(str))
                        ans.emplace_back(str);
                }
                if(!ans.empty()) {
                    sort(ans.begin(), ans.end());
                    return ans;
                }
                unordered_set<string> nextSet;
                for(auto &str: currSet) {
                    for(int i = 0; i < str.size(); i++) {
                        if(i > 0 && str[i] == str[i - 1]) {
                            continue;
                        }
                        if(str[i] == '(' || str[i] == ')') {
                            nextSet.insert(str.substr(0, i) + str.substr(i + 1, str.size()));
                        }
                    }
                }
                currSet = nextSet;
            }
        }
 
        bool Solution::isValid(const string &str) {
            int count = 0;
 
            for(const char c: str) {
                if(c == '(') {
                    count++;
                } else if(c == ')') {
                    count--;
                    if(count < 0) {
                        return false;
                    }
                }
            }
 
            return count == 0;
        }
    }// namespace remove_invalid_parentheses
 
    namespace median_of_two_sorted_arrays {
        double Solution::findMedianSortedArrays(vector<int> &nums1, vector<int> &nums2) {
            if(nums1.size() > nums2.size()) {
                return findMedianSortedArrays(nums2, nums1);
            }
 
            const int m = nums1.size();
            const int n = nums2.size();
            int left = 0, right = m;
            // median1：前一部分的最大值
            // median2：后一部分的最小值
            int median1 = 0, median2 = 0;
 
            while(left <= right) {
                // 前一部分包含 nums1[0 .. i-1] 和 nums2[0 .. j-1]
                // 后一部分包含 nums1[i .. m-1] 和 nums2[j .. n-1]
                const int i = (left + right) / 2;
                const int j = (m + n + 1) / 2 - i;
 
                // nums_im1, nums_i, nums_jm1, nums_j 分别表示 nums1[i-1], nums1[i], nums2[j-1], nums2[j]
                int nums_im1 = i == 0 ? INT_MIN : nums1[i - 1];
                int nums_i   = i == m ? INT_MAX : nums1[i];
                int nums_jm1 = j == 0 ? INT_MIN : nums2[j - 1];
                int nums_j   = j == n ? INT_MAX : nums2[j];
 
                if(nums_im1 <= nums_j) {
                    median1 = max(nums_im1, nums_jm1);
                    median2 = min(nums_i, nums_j);
                    left    = i + 1;
                } else {
                    right = i - 1;
                }
            }
 
            return (m + n) % 2 == 0 ? (median1 + median2) / 2.0 : median1;
        }
    }// namespace median_of_two_sorted_arrays
 
    namespace count_of_smaller_numbers_after_self {
        vector<int> Solution::countSmaller(vector<int> &nums) {
            vector<int> resultList;
 
            Discretization(nums);
 
            Init(nums.size() + 5);
 
            for(int i = static_cast<int>(nums.size()) - 1; i >= 0; --i) {
                const int id = getId(nums[i]);
                resultList.push_back(Query(id - 1));
                Update(id);
            }
 
            reverse(resultList.begin(), resultList.end());
 
            return resultList;
        }
 
        void Solution::Init(int length) { c.resize(length, 0); }
 
        int Solution::LowBit(int x) { return x & -x; }
 
        void Solution::Update(int pos) {
            while(pos < c.size()) {
                c[pos] += 1;
                pos += LowBit(pos);
            }
        }
 
        int Solution::Query(int pos) const {
            int ret = 0;
 
            while(pos > 0) {
                ret += c[pos];
                pos -= LowBit(pos);
            }
 
            return ret;
        }
 
        void Solution::Discretization(vector<int> &nums) {
            a.assign(nums.begin(), nums.end());
            sort(a.begin(), a.end());
            a.erase(unique(a.begin(), a.end()), a.end());
        }
 
        int Solution::getId(int x) { return lower_bound(a.begin(), a.end(), x) - a.begin() + 1; }
    }// namespace count_of_smaller_numbers_after_self
 
    namespace best_time_to_buy_and_sell_stock_with_cooldown {
        int Solution::maxProfit(vector<int> &prices) {
            if(prices.empty()) {
                return 0;
            }
 
            const int n = prices.size();
            int f0      = -prices[0];
            int f1      = 0;
            int f2      = 0;
            for(int i = 1; i < n; ++i) {
                tie(f0, f1, f2) = make_tuple(max(f0, f2 - prices[i]), f0 + prices[i], max(f1, f2));
            }
 
            return max(f1, f2);
        }
    }// namespace best_time_to_buy_and_sell_stock_with_cooldown
 
    namespace best_time_to_buy_and_sell_stock_with_transaction_fee {
        int Solution::maxProfit(vector<int> &prices, int fee) {
            const int n = prices.size();
            vector<int> holding(n);
            vector<int> not_holding(n);
            not_holding[0] = 0;
            holding[0]     = -prices[0];
            for(int i = 1; i < n; i++) {
                not_holding[i] = max(not_holding[i - 1], holding[i - 1] + prices[i] - fee);
                holding[i]     = max(holding[i - 1], not_holding[i - 1] - prices[i]);
            }
            return max(not_holding.back(), holding.back());
        }
    }// namespace best_time_to_buy_and_sell_stock_with_transaction_fee
 
    namespace split_array_largest_sum {
        int Solution::splitArray(vector<int> &nums, int m) {
            int l = 0;
            int r = 0;
            for(auto num: nums) {
                r += num;
                l = max(l, num);
            }
            while(l < r) {
                const int mid = (l + r) / 2;
                const int cnt = get_m(nums, mid);
                if(cnt == m) {
                    r = mid;
                } else if(cnt > m) {
                    l = mid + 1;
                } else if(cnt < m) {
                    r = mid - 1;
                }
            }
            return l;
        }
 
        int Solution::get_m(const vector<int> &nums, int msum) {
            int ans = 0;
            int c   = 0;
            for(const auto num: nums) {
                if(c + num > msum) {
                    ans++;
                    c = 0;
                }
                c += num;
            }
            if(c > 0) {
                ans++;
            }
            return ans;
        }
    }// namespace split_array_largest_sum
 
    namespace house_robber_iii {
        int Solution::rob(TreeNode *root) {
            int ans = 0;
            return max(dfs(true, root), dfs(false, root));
        }
 
        int Solution::dfs(bool steal, TreeNode *node) {
            if(um.contains({node, steal})) {
                return um[{node, steal}];
            }
            int ans = steal ? node->val : 0;
            if(node->left != nullptr) {
                const int ns = dfs(!steal, node->left);
                const int s  = !steal ? dfs(steal, node->left) : 0;
                ans += max(s, ns);
            }
            if(node->right != nullptr) {
                const int ns = dfs(!steal, node->right);
                const int s  = !steal ? dfs(steal, node->right) : 0;
                ans += max(s, ns);
            }
            um[{node, steal}] = ans;
            return ans;
        }
 
        size_t myhash::operator()(const pair<TreeNode *, bool> &p) const { return (uint64_t) p.first * 2 + (p.second ? 1 : 0); }
 
        bool myeq::operator()(const pair<TreeNode *, bool> &p1, const pair<TreeNode *, bool> &p2) const { return p1.first == p2.first && p1.second == p2.second; }
    }// namespace house_robber_iii
 
    namespace maximal_square {
        int Solution::maximalSquare(vector<vector<char>> &matrix) {
            const int m = matrix.size();
            const int n = matrix[0].size();
            vector horizontal_next_1s(m, vector(n, 0));
            vector vertical_next_1s(m, vector(n, 0));
            vector dp(m + 1, vector(n + 1, 0));
            for(int i = 0; i < m; i++) {
                int cnt = 0;
                for(int j = n - 1; j >= 0; j--) {
                    if(matrix[i][j] == '1') {
                        cnt++;
                    } else {
                        cnt = 0;
                    }
                    horizontal_next_1s[i][j] = cnt;
                }
            }
            for(int j = 0; j < n; j++) {
                int cnt = 0;
                for(int i = m - 1; i >= 0; i--) {
                    if(matrix[i][j] == '1') {
                        cnt++;
                    } else {
                        cnt = 0;
                    }
                    vertical_next_1s[i][j] = cnt;
                }
            }
            int ans = 0;
            for(int i = m - 1; i >= 0; i--) {
                for(int j = n - 1; j >= 0; j--) {
                    if(matrix[i][j] == '1') {
                        dp[i][j] = min(min(vertical_next_1s[i][j], horizontal_next_1s[i][j]), 1 + dp[i + 1][j + 1]);
                        ans      = max(ans, dp[i][j]);
                    }
                }
            }
            return ans * ans;
        }
    }// namespace maximal_square
 
    namespace maximal_rectangle {
        int Solution::maximalRectangle(vector<vector<char>> &matrix) {
            const int m = matrix.size();
            if(m == 0) {
                return 0;
            }
            const int n = matrix[0].size();
            vector left(m, vector(n, 0));
 
            for(int i = 0; i < m; i++) {
                for(int j = 0; j < n; j++) {
                    if(matrix[i][j] == '1') {
                        left[i][j] = (j == 0 ? 0 : left[i][j - 1]) + 1;
                    }
                }
            }
 
            int ret = 0;
            for(int j = 0; j < n; j++) {
                // 对于每一列，使用基于柱状图的方法
                vector<int> up(m, 0), down(m, 0);
 
                stack<int> stk;
                for(int i = 0; i < m; i++) {
                    while(!stk.empty() && left[stk.top()][j] >= left[i][j]) {
                        stk.pop();
                    }
                    up[i] = stk.empty() ? -1 : stk.top();
                    stk.push(i);
                }
                stk = stack<int>();
                for(int i = m - 1; i >= 0; i--) {
                    while(!stk.empty() && left[stk.top()][j] >= left[i][j]) {
                        stk.pop();
                    }
                    down[i] = stk.empty() ? m : stk.top();
                    stk.push(i);
                }
 
                for(int i = 0; i < m; i++) {
                    const int height = down[i] - up[i] - 1;
                    int area         = height * left[i][j];
                    ret              = max(ret, area);
                }
            }
            return ret;
        }
    }// namespace maximal_rectangle
 
    namespace predict_the_winner {
        bool Solution::PredictTheWinner(vector<int> &nums) {
            const int length = nums.size();
            auto dp          = vector<int>(length);
            for(int i = 0; i < length; i++) {
                dp[i] = nums[i];
            }
            for(int i = length - 2; i >= 0; i--) {
                for(int j = i + 1; j < length; j++) {
                    dp[j] = max(nums[i] - dp[j], nums[j] - dp[j - 1]);
                }
            }
            return dp[length - 1] >= 0;
        }
    }// namespace predict_the_winner
 
    namespace palindrome_partitioning {
 
        vector<vector<string>> Solution::partition(const string &s) {
            const vector<string> vec;
            vector<vector<string>> ans;
            dfs(vec, s, ans, 0, 0);
            return ans;
        }
 
        bool Solution::is_palindromic(const string &s, int start, int end) {
            for(int i = start, j = end; i < j; i++, j--) {
                if(s[i] != s[j]) {
                    return false;
                }
            }
            return true;
        }
 
        void Solution::dfs(const vector<string> &current, const string &s, vector<vector<string>> &ans, int start, int cursor) {
            if(cursor == s.length() - 1 && is_palindromic(s, start, cursor)) {
                ans.emplace_back(current);
                ans.back().emplace_back(s.substr(start, cursor - start + 1));
                return;
            }
            if(cursor >= s.length() - 1 || start >= s.length()) {
                return;
            }
            if(is_palindromic(s, start, cursor)) {
                vector next = current;
                next.emplace_back(s.substr(start, cursor - start + 1));
                dfs(next, s, ans, cursor + 1, cursor + 1);
            }
            dfs(current, s, ans, start, cursor + 1);
        }
    }// namespace palindrome_partitioning
 
    namespace palindrome_partitioning_ii {
        int Solution::minCut(string s) {
            vector is_palindromic(s.length(), vector(s.length(), false));
            for(int i = 0; i < s.length(); i++) {
                for(int j = 0; i - j >= 0 && i + j < s.length() && s[i - j] == s[i + j]; j++) {
                    is_palindromic[i - j][i + j] = true;
                }
            }
            for(int i = 0; i < s.length() - 1; i++) {
                if(s[i] == s[i + 1]) {
                    for(int j = 0; i - j >= 0 && i + 1 + j < s.length() && s[i - j] == s[i + 1 + j]; j++) {
                        is_palindromic[i - j][i + 1 + j] = true;
                    }
                }
            }
            vector dp(s.length(), 2000);
            dp[0] = 0;
            for(int j = 1; j < dp.size(); j++) {
                if(is_palindromic[0][j]) {
                    dp[j] = 0;
                    continue;
                }
                for(int i = j; i >= 0; i--) {
                    if(is_palindromic[i][j]) {
                        dp[j] = min(dp[j], dp[i - 1] + 1);
                    }
                }
            }
            return dp.back();
        }
    }// namespace palindrome_partitioning_ii
 
    namespace partition_equal_subset_sum {
        bool Solution::canPartition(vector<int> &nums) {
            const int n = nums.size();
            if(n < 2) {
                return false;
            }
            const int sum    = accumulate(nums.begin(), nums.end(), 0);
            const int maxNum = *max_element(nums.begin(), nums.end());
            if(sum & 1) {
                return false;
            }
            const int target = sum / 2;
            if(maxNum > target) {
                return false;
            }
            vector dp(n, vector(target + 1, 0));
            for(int i = 0; i < n; i++) {
                dp[i][0] = true;
            }
            dp[0][nums[0]] = true;
            for(int i = 1; i < n; i++) {
                const int num = nums[i];
                for(int j = 1; j <= target; j++) {
                    if(j >= num) {
                        dp[i][j] = dp[i - 1][j] | dp[i - 1][j - num];
                    } else {
                        dp[i][j] = dp[i - 1][j];
                    }
                }
            }
            return dp[n - 1][target];
        }
    }// namespace partition_equal_subset_sum
 
    namespace minimum_cost_for_tickets {
        int Solution::mincostTickets(vector<int> &days, vector<int> &costs) {
            unordered_set<int> us;
            int end = 0;
            for(const auto &day: days) {
                us.insert(day);
                end = max(end, day);
            }
            vector dp(end + 1, 0);
            for(int i = 1; i <= end; i++) {
                dp[i] = i - 1 >= 0 ? dp[i - 1] : 0;
                if(us.contains(i)) {
                    dp[i] += costs[0];
                    dp[i] = min(dp[i], (i - 7 >= 0 ? dp[i - 7] : 0) + costs[1]);
                    dp[i] = min(dp[i], (i - 30 >= 0 ? dp[i - 30] : 0) + costs[2]);
                }
            }
            return dp.back();
        }
    }// namespace minimum_cost_for_tickets
 
    namespace best_time_to_buy_and_sell_stock_iii {
        int Solution::maxProfit(vector<int> &prices) {
            vector dp(5, vector<long>(prices.size(), -10000000000));
            // 0 - 不持有
            // 1 - 第一次持有
            // 2 - 第一次卖出
            // 3 - 第二次持有
            // 4 - 第二次卖出
            dp[0][0] = 0;
            dp[1][0] = -prices[0];
            for(int i = 1; i < prices.size(); i++) {
                dp[0][i] = dp[0][i - 1];
                dp[1][i] = max(dp[1][i - 1], dp[0][i - 1] - prices[i]);
                dp[2][i] = max(dp[2][i - 1], dp[1][i - 1] + prices[i]);
                dp[3][i] = max(dp[3][i - 1], dp[2][i - 1] - prices[i]);
                dp[4][i] = max(dp[4][i - 1], dp[3][i - 1] + prices[i]);
            }
            long ans = dp[0].back();
            for(int i = 1; i <= 4; i++) {
                ans = max(ans, dp[i].back());
            }
            return ans;
        }
    }// namespace best_time_to_buy_and_sell_stock_iii
 
    namespace dungeon_game {
        int Solution::calculateMinimumHP(vector<vector<int>> &dungeon) {
            const int n = dungeon.size(), m = dungeon[0].size();
            vector dp(n + 1, vector(m + 1, INT_MAX));
            dp[n][m - 1] = dp[n - 1][m] = 1;
            for(int i = n - 1; i >= 0; --i) {
                for(int j = m - 1; j >= 0; --j) {
                    const int minn = min(dp[i + 1][j], dp[i][j + 1]);
                    dp[i][j]       = max(minn - dungeon[i][j], 1);
                }
            }
            return dp[0][0];
        }
    }// namespace dungeon_game
 
    namespace course_schedule {
        bool Solution::canFinish(int numCourses, vector<vector<int>> &prerequisites) {
            vector<int> in(numCourses);
            vector<unordered_set<int>> out(numCourses);
            unordered_set<int> learned;
            for(auto &prerequisite: prerequisites) {
                in[prerequisite[1]]++;
                out[prerequisite[0]].insert(prerequisite[1]);
            }
            bool hasChange = true;
            while(hasChange) {
                hasChange = false;
                for(int i = 0; i < numCourses; i++) {
                    if(in[i] == 0 && !learned.contains(i)) {
                        hasChange = true;
                        learned.insert(i);
                        for(auto &next: out[i]) {
                            in[next]--;
                        }
                    }
                }
            }
            for(int i = 0; i < numCourses; i++) {
                if(in[i] != 0) {
                    return false;
                }
            }
            return true;
        }
    }// namespace course_schedule
 
    namespace course_schedule_ii {
        vector<int> Solution::findOrder(int numCourses, vector<vector<int>> &prerequisites) {
            vector<int> ans;
            vector<int> in(numCourses);
            vector<unordered_set<int>> out(numCourses);
            unordered_set<int> learned;
            for(auto &prerequisite: prerequisites) {
                in[prerequisite[0]]++;
                out[prerequisite[1]].insert(prerequisite[0]);
            }
            bool hasChange = true;
            while(hasChange) {
                hasChange = false;
                for(int i = 0; i < numCourses; i++) {
                    if(in[i] == 0 && !learned.contains(i)) {
                        hasChange = true;
                        learned.insert(i);
                        ans.emplace_back(i);
                        for(auto &next: out[i]) {
                            in[next]--;
                        }
                    }
                }
            }
            if(ans.size() == numCourses) {
                return ans;
            }
            return {};
        }
    }// namespace course_schedule_ii
 
    namespace longest_increasing_path_in_a_matrix {
        int Solution::longestIncreasingPath(vector<vector<int>> &matrix) {
            if(matrix.empty() || matrix[0].empty()) {
                return 0;
            }
            rows            = matrix.size();
            columns         = matrix[0].size();
            auto outdegrees = vector(rows, vector<int>(columns));
            for(int i = 0; i < rows; ++i) {
                for(int j = 0; j < columns; ++j) {
                    for(int k = 0; k < 4; ++k) {
                        const int newRow = i + dirs[k][0], newColumn = j + dirs[k][1];
                        if(newRow >= 0 && newRow < rows && newColumn >= 0 && newColumn < columns && matrix[newRow][newColumn] > matrix[i][j]) {
                            ++outdegrees[i][j];
                        }
                    }
                }
            }
            queue<pair<int, int>> q;
            for(int i = 0; i < rows; ++i) {
                for(int j = 0; j < columns; ++j) {
                    if(outdegrees[i][j] == 0) {
                        q.push({i, j});
                    }
                }
            }
            int ans = 0;
            while(!q.empty()) {
                ++ans;
                const int size = q.size();
                for(int i = 0; i < size; ++i) {
                    const auto cell = q.front();
                    q.pop();
                    const int row = cell.first, column = cell.second;
                    for(int k = 0; k < 4; ++k) {
                        int newRow = row + dirs[k][0], newColumn = column + dirs[k][1];
                        if(newRow >= 0 && newRow < rows && newColumn >= 0 && newColumn < columns && matrix[newRow][newColumn] < matrix[row][column]) {
                            --outdegrees[newRow][newColumn];
                            if(outdegrees[newRow][newColumn] == 0) {
                                q.push({newRow, newColumn});
                            }
                        }
                    }
                }
            }
            return ans;
        }
    }// namespace longest_increasing_path_in_a_matrix
 
    namespace parallel_courses {
        int Solution::minimumSemesters(int n, vector<vector<int>> &relations) {
            vector<node *> nodes(n);
            for(int i = 1; i <= n; i++) {
                nodes[i - 1] = new node(i, 0);
            }
            for(const auto &relation: relations) {
                nodes[relation[1] - 1]->pred.insert(nodes[relation[0] - 1]);
                nodes[relation[0] - 1]->out++;
            }
            bool flag = true;
            unordered_set<int> vis;
            while(flag) {
                flag = false;
                for(int i = 0; i < n; i++) {
                    if(nodes[i]->out == 0) {
                        if(vis.contains(i)) {
                            continue;
                        }
                        vis.insert(i);
                        flag = true;
                        for(node *next: nodes[i]->pred) {
                            next->out--;
                            next->len = max(next->len, nodes[i]->len + 1);
                        }
                    }
                }
            }
            int ans = 0;
            for(int i = 0; i < n; i++) {
                if(nodes[i]->out != 0) {
                    return -1;
                }
                ans = max(ans, nodes[i]->len);
            }
            return ans;
        }
    }// namespace parallel_courses
 
    namespace alien_dictionary {
        string Solution::alienOrder(vector<string> &words) {
            unordered_map<char, unordered_set<char>> g;
            unordered_map<char, int> in;
            ostringstream oss;
            unordered_set<char> charset;
            for(const auto &word: words) {
                for(const auto &ch: word) {
                    charset.insert(ch);
                }
            }
            for(const auto &ch: charset) {
                g[ch]  = unordered_set<char>();
                in[ch] = 0;
            }
            int max_len = 0;
            for(const auto &word: words) {
                max_len = max(max_len, static_cast<int>(word.length()));
            }
            for(int i = 0; i < max_len; i++) {
                unordered_map<string, vector<string>> um;
                for(const auto &word: words) {
                    if(word.length() >= i) {
                        um[i > 0 ? word.substr(0, i) : ""].emplace_back(word);
                    }
                }
                for(const auto &[pred, section]: um) {
                    for(int j = 0, k = 1; k < section.size(); j++, k++) {
                        if(i < section[j].length() && i < section[k].length()) {
                            if(section[j][i] != section[k][i]) {
                                g[section[j][i]].insert(section[k][i]);
                            }
                        } else if(i < section[j].length()) {
                            return "";
                        }
                    }
                }
            }
            for(const auto &[k, section]: g) {
                for(const auto &n: section) {
                    in[n]++;
                }
            }
            bool flag = true;
            unordered_set<char> vis;
            while(flag) {
                flag = false;
                for(const auto &[ch, n]: in) {
                    if(n == 0 && !vis.contains(ch)) {
                        flag = true;
                        vis.insert(ch);
                        oss << ch;
                        for(const auto &nc: g[ch]) {
                            in[nc]--;
                        }
                    }
                }
            }
            for(const auto &[ch, n]: in) {
                if(n != 0) {
                    return "";
                }
            }
            return oss.str();
        }
    }// namespace alien_dictionary
 
    namespace single_number_iii {
        vector<int> Solution::singleNumber(vector<int> &nums) {
            int xorsum = 0;
            for(const int num: nums) {
                xorsum ^= num;
            }
            // 防止溢出
            const int lsb = xorsum == INT_MIN ? xorsum : xorsum & -xorsum;
            int type1 = 0, type2 = 0;
            for(const int num: nums) {
                if(num & lsb) {
                    type1 ^= num;
                } else {
                    type2 ^= num;
                }
            }
            return {type1, type2};
        }
    }// namespace single_number_iii
 
    namespace shortest_path_to_get_all_keys {
        int Solution::shortestPathAllKeys(vector<string> &grid) {
            priority_queue<frame> pq;
            int m        = grid.size();
            int n        = grid[0].size();
            int start_x  = 0;
            int start_y  = 0;
            int lock_cnt = 0;
            unordered_map<unsigned, vector<vector<int>>> min_step;
            for(int i = 0; i < m; i++) {
                for(int j = 0; j < n; j++) {
                    if(grid[i][j] == START) {
                        start_x = i;
                        start_y = j;
                    } else if(isupper(grid[i][j])) {
                        lock_cnt++;
                    }
                }
            }
            frame start(start_x, start_y, lock_cnt);
            pq.push(start);
            while(!pq.empty()) {
                frame f = pq.top();
                pq.pop();
                if(f.keys.size() == lock_cnt) {
                    return f.step;
                }
                if(!min_step.contains(f.get_mask())) {
                    min_step[f.get_mask()] = vector(m, vector(n, INT_MAX));
                }
                if(min_step[f.get_mask()][f.x][f.y] <= f.step) {
                    continue;
                }
                min_step[f.get_mask()][f.x][f.y] = f.step;
                const pair<int, int> nexts[4]    = {{f.x + 1, f.y}, {f.x - 1, f.y}, {f.x, f.y + 1}, {f.x, f.y - 1}};
                for(const auto &[n_x, n_y]: nexts) {
                    if(n_x >= 0 && n_x < m && n_y >= 0 && n_y < n && grid[n_x][n_y] != WALL) {
                        if(islower(grid[n_x][n_y])) {
                            frame next = f;
                            next.x     = n_x;
                            next.y     = n_y;
                            next.step++;
                            next.keys.insert(grid[n_x][n_y]);
                            if(!min_step.contains(next.get_mask())) {
                                min_step[next.get_mask()] = vector(m, vector(n, INT_MAX));
                            }
                            if(min_step[next.get_mask()][n_x][n_y] > next.step) {
                                pq.push(next);
                            }
                        } else if(isupper(grid[n_x][n_y])) {
                            if(f.keys.contains(static_cast<char>(tolower(grid[n_x][n_y])))) {
                                frame next = f;
                                next.x     = n_x;
                                next.y     = n_y;
                                next.step++;
                                if(!min_step.contains(next.get_mask())) {
                                    min_step[next.get_mask()] = vector(m, vector(n, INT_MAX));
                                }
                                if(min_step[next.get_mask()][n_x][n_y] > next.step) {
                                    pq.push(next);
                                }
                            }
                        } else {
                            frame next = f;
                            next.x     = n_x;
                            next.y     = n_y;
                            next.step++;
                            if(!min_step.contains(next.get_mask())) {
                                min_step[next.get_mask()] = vector(m, vector(n, INT_MAX));
                            }
                            if(min_step[next.get_mask()][n_x][n_y] > next.step) {
                                pq.push(next);
                            }
                        }
                    }
                }
            }
            return -1;
        }
 
        bool frame::operator<(const frame &f) const {
            if(step != f.step) {
                return step > f.step;
            }
            return keys.size() < f.keys.size();
        }
 
        unsigned frame::get_mask() const {
            unsigned mask = 0;
            for(const auto &key: keys) {
                mask |= 1 << key - 'a';
            }
            return mask;
        }
    }// namespace shortest_path_to_get_all_keys
 
    namespace minimum_number_of_k_consecutive_bit_flips {
        int Solution::minKBitFlips(vector<int> &nums, int k) {
            const int n = nums.size();
            int ans = 0, revCnt = 0;
            for(int i = 0; i < n; ++i) {
                if(i >= k && nums[i - k] > 1) {
                    revCnt ^= 1;
                    nums[i - k] -= 2;// 复原数组元素，若允许修改数组 nums，则可以省略
                }
                if(nums[i] == revCnt) {
                    if(i + k > n) {
                        return -1;
                    }
                    ++ans;
                    revCnt ^= 1;
                    nums[i] += 2;
                }
            }
            return ans;
        }
    }// namespace minimum_number_of_k_consecutive_bit_flips
 
    namespace design_underground_system {
        void UndergroundSystem::checkIn(int id, const string &stationName, int t) { records[id] = {stationName, t}; }
        void UndergroundSystem::checkOut(int id, const string &stationName, int t) { um[records[id].first][stationName].emplace_back(t - records[id].second); }
 
        double UndergroundSystem::getAverageTime(const string &startStation, const string &endStation) {
            int total = 0;
            for(const auto t: um[startStation][endStation]) {
                total += t;
            }
            return static_cast<double>(total) / um[startStation][endStation].size();
        }
    }// namespace design_underground_system
 
    namespace lru_cache {
        LRUCache::LRUCache(int capacity)
            : capacity(capacity) {}
 
        int LRUCache::get(int key) {
            if(um.contains(key)) {
                if(key != keys.back()) {
                    keys.erase(find(keys.begin(), keys.end(), key));
                    keys.emplace_back(key);
                }
                return um[key];
            }
            return -1;
        }
 
        void LRUCache::put(int key, int value) {
            if(um.size() == capacity) {
                if(um.contains(key)) {
                    //满 含
                    if(key != keys.back()) {
                        keys.erase(find(keys.begin(), keys.end(), key));
                        keys.emplace_back(key);
                    }
                } else {
                    //满 不含
                    um.erase(*keys.begin());
                    keys.erase(keys.begin());
                    keys.emplace_back(key);
                }
            } else {
                if(um.contains(key)) {
                    //未满 含
                    if(key != keys.back()) {
                        keys.erase(find(keys.begin(), keys.end(), key));
                        keys.emplace_back(key);
                    }
                } else {
                    //未满 不含
                    keys.emplace_back(key);
                }
            }
            um[key] = value;
        }
    }// namespace lru_cache
 
    namespace time_based_key_value_store {
        void TimeMap::set(const string &key, string value, int timestamp) { um[key][timestamp] = std::move(value); }
 
        string TimeMap::get(const string &key, int timestamp) {
            const auto it = um[key].lower_bound(timestamp);
            return it == um[key].end() ? "" : it->second;
        }
    }// namespace time_based_key_value_store
 
    namespace range_module {
        void RangeModule::addRange(int left, int right) { tree.assign(left, right - 1, true); }
 
        bool RangeModule::queryRange(int left, int right) { return tree.check(left, right - 1); }
 
        void RangeModule::removeRange(int left, int right) { tree.assign(left, right - 1); }
    }// namespace range_module
 
    namespace lfu_cache {
        int LFUCache::get(int key) {
            if(capacity == 0) {
                return -1;
            }
            int ans = -1;
            if(um.contains(key)) {
                // 如果存在
                ans = um[key];
                cnt[key]++;                                                                   //增加计数
                const auto it = find(tnc[cnt[key] - 1].begin(), tnc[cnt[key] - 1].end(), key);//
                if(it != tnc[cnt[key] - 1].end()) {
                    tnc[cnt[key] - 1].erase(it);
                    if(tnc[cnt[key] - 1].empty()) {
                        tnc.erase(cnt[key] - 1);
                    }
                }
                tnc[cnt[key]].emplace_back(key);
            }
            return ans;
        }
 
        void LFUCache::put(int key, int value) {
            if(capacity == 0) {
                return;
            }
            cnt[key]++;
            if(um.size() == capacity) {
                //满
                if(um.contains(key)) {
                    //已存在
                    tnc[cnt[key] - 1].erase(find(tnc[cnt[key] - 1].begin(), tnc[cnt[key] - 1].end(), key));
                    if(tnc[cnt[key] - 1].empty()) {
                        tnc.erase(cnt[key] - 1);
                    }
                } else {
                    //不存在
                    while(tnc.begin()->second.empty()) {
                        tnc.erase(tnc.begin());
                    }
                    const auto evicted = tnc.begin()->second.begin();
                    const int val      = *evicted;
                    tnc.begin()->second.erase(evicted);
                    cnt.erase(val);
                    um.erase(val);
                }
            } else {
                //未满
                if(um.contains(key)) {
                    //已存在
                    tnc[cnt[key] - 1].erase(find(tnc[cnt[key] - 1].begin(), tnc[cnt[key] - 1].end(), key));
                    if(tnc[cnt[key] - 1].empty()) {
                        tnc.erase(cnt[key] - 1);
                    }
                } else {
                    //不存在
                }
            }
            tnc[cnt[key]].emplace_back(key);
            um[key] = value;
        }
    }// namespace lfu_cache
 
    namespace leetcode454_4sum_ii {
        int Solution::sumCount(int sum, int i) {
            if(mem[i].contains(sum)) {
                return mem[i][sum];
            }
            if(i == vec.size() - 1) {
                return vec[i][sum];
            }
            int ans = 0;
            for(const auto &[k, v]: vec[i]) {
                ans += v * sumCount(sum - k, i + 1);
            }
            mem[i][sum] = ans;
            return ans;
        }
 
        int Solution::fourSumCount(vector<int> &nums1, vector<int> &nums2, vector<int> &nums3, vector<int> &nums4) {
            mem = vector<unordered_map<int, int>>(4);
            vec = vector<unordered_map<int, int>>(4);
            for(const auto &num: nums1) {
                vec[0][num]++;
            }
            for(const auto &num: nums2) {
                vec[1][num]++;
            }
            for(const auto &num: nums3) {
                vec[2][num]++;
            }
            for(const auto &num: nums4) {
                vec[3][num]++;
            }
            return sumCount(0, 0);
        }
    }// namespace leetcode454_4sum_ii
 
    namespace maximum_size_subarray_sum_equals_k {
        int Solution::maxSubArrayLen(vector<int> &nums, int k) {
            auto pref_sum = vector(nums.size(), 0);
            pref_sum[0]   = nums[0];
            unordered_map<int, set<int>> um;
            um[0].insert(-1);
            um[nums[0]].insert(0);
            for(int i = 1; i < nums.size(); i++) {
                pref_sum[i] += nums[i] + pref_sum[i - 1];
                um[pref_sum[i]].insert(i);
            }
            int ans = 0;
            for(int i = nums.size() - 1; i >= 0; i--) {
                const int r = pref_sum[i];
                int l       = r - k;
                if(!um[l].empty()) {
                    ans = max(ans, i - *um[l].begin());
                }
            }
            return ans;
        }
    }// namespace maximum_size_subarray_sum_equals_k
 
    namespace minimum_swaps_to_group_all_1s_together {
        int Solution::minSwaps(vector<int> &data) {
            auto one_count = vector(data.size(), 0);
            int cnt1       = 0;
            for(int i = 0; i < one_count.size(); i++) {
                one_count[i] = cnt1 + data[i];
                cnt1         = one_count[i];
            }
            if(cnt1 == 0) {
                return 0;
            }
            int ans = cnt1 - one_count[cnt1 - 1];
            for(int i = 0; i + cnt1 < one_count.size(); i++) {
                ans = min(ans, cnt1 - (one_count[i + cnt1] - one_count[i]));
            }
            return ans;
        }
    }// namespace minimum_swaps_to_group_all_1s_together
}// namespace leetcode