<p>The <strong>n-queens</strong> puzzle is the problem of placing <code>n</code> queens on an <code>n x n</code> chessboard such that no two queens attack each other.</p>

<p>Given an integer <code>n</code>, return <em>the number of distinct solutions to the&nbsp;<strong>n-queens puzzle</strong></em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/13/queens.jpg" style="width: 600px; height: 268px;" />
<pre>
<strong>Input:</strong> n = 4
<strong>Output:</strong> 2
<strong>Explanation:</strong> There are two distinct solutions to the 4-queens puzzle as shown.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> 1
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 9</code></li>
</ul>

class Solution {
    private:
    vector<vector<string>> ans;
    int no;
    void combinations(int level, vector<pair<int, char>> risks, vector<string> possibility) {
        if(level == no) {
            ans.push_back(possibility);
            return;
        }
        vector<int> safe;
        for(int i = 0 ; i < no ; i++) {
            if(find_if(risks.begin(), risks.end(), [i](const pair<int, char>& p){return p.first == i;}) == risks.end()) {
               safe.push_back(i);
            }
        }
        for(int i = 0 ; i < risks.size() ; i++) {
            if(risks[i].second == 'l') {
                if(risks[i].first == 0) risks.erase(risks.begin() + i);
                else(risks[i].first--);
            }
            if(risks[i].second == 'r') {
                if(risks[i].first == no - 1) risks.erase(risks.begin() + i);
                else(risks[i].first++);
            }
        }
        for(auto &i : safe) {
            vector<pair<int, char>> risks2 = risks;
            risks2.push_back({i,'s'});
            if(i != 0) risks2.push_back({i - 1,'l'});
            if(i != no - 1) risks2.push_back({i + 1,'r'});
            string possible;
            for(int j = 0 ; j < no ; j++) {
                if(j == i) possible += 'Q';
                else possible += '.';
            }
            possibility.push_back(possible);
            combinations(level + 1, risks2, possibility);
            possibility.pop_back();
        }
    }
public:
    int totalNQueens(int n) {
        no = n;
        int level = 0;
        vector<pair<int, char>> risks;
        vector<string> possibility;
        combinations(level, risks, possibility);
        return ans.size();
    }
};
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