<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 {
    int N;
    vector<vector<string>> ans;
    vector<string> grid;

    void makeGrid(int n)
    {
        this->N = n;
        grid.clear();
        string t = "";
        for (int i = 0; i < n; i++)
            t += ".";
        for (int i = 0; i < n; i++)
            grid.push_back(t);
    }

    bool attacks(int x, int y)
    {
        for (size_t i = 0; i < N; i++)
        {
            if (grid[i][y] == 'Q' and i!=x)return true;
            if (grid[x][i] == 'Q' and i!=y)return true;
        }
        for (size_t i = 0; i < N; i++)
        {
            for (size_t j = 0; j < N; j++)
            {
                if(grid[i][j]=='Q' and i+j==x+y and x!=i and y!=j)return true;
                if(grid[i][j]=='Q' and i-j==x-y and x!=i and y!=j)return true;
            }
        }
        return false;
    }

    bool isCandidate()
    {
        for (size_t i = 0; i < N; i++)
            for (size_t j = 0; j < N; j++)
                if (grid[i][j] == 'Q' and attacks(i, j))
                    return false;
        return true;
    }

    void solve(int row)
    {
        if(row==N){
            ans.push_back(grid);
            return;
        }
        for(int i=0;i<N;i++){
            grid[i][row]='Q';
            if(isCandidate()){
                solve(row+1);
            }
            grid[i][row]='.';
        }
    }
public:
    int totalNQueens(int n) {
        makeGrid(n);
        solve(0);
        return ans.size();
    }
};
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