<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>all distinct solutions to the <strong>n-queens puzzle</strong></em>. You may return the answer in <strong>any order</strong>.</p>

<p>Each solution contains a distinct board configuration of the n-queens&#39; placement, where <code>&#39;Q&#39;</code> and <code>&#39;.&#39;</code> both indicate a queen and an empty space, respectively.</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> [[&quot;.Q..&quot;,&quot;...Q&quot;,&quot;Q...&quot;,&quot;..Q.&quot;],[&quot;..Q.&quot;,&quot;Q...&quot;,&quot;...Q&quot;,&quot;.Q..&quot;]]
<strong>Explanation:</strong> There exist two distinct solutions to the 4-queens puzzle as shown above
</pre>

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

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> [[&quot;Q&quot;]]
</pre>

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

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

class Solution {
   public:
    bool validIndex(int i, int j, int n) {
        return i >= 0 and i < n and j >= 0 and j < n;
    }
    bool safe(int i, int j, int cx, int cy, vector<vector<bool>>& vis) {
        int n = vis.size();
        if (i < 0 or i >= n or j < 0 or j >= n or vis[i][j])
            return false;
        while (validIndex(i, j, n)) {
            if (vis[i][j])
                return false;
            i += cx;
            j += cy;
        }
        return true;
    }
    bool isSafe(int i, int j, vector<vector<bool>>& vis) {
        if (vis[i][j])
            return false;
        return safe(i, j, -1, 0, vis) and safe(i, j, 1, 0, vis) and
               safe(i, j, 0, -1, vis) and safe(i, j, 0, 1, vis) and
               safe(i, j, 1, 1, vis) and safe(i, j, -1, 1, vis) and
               safe(i, j, -1, -1, vis) and safe(i, j, 1, -1, vis);
    }
    void solve(int i,
               int n,
               vector<vector<bool>>& vis,
               vector<vector<string>>& ans,
               vector<string> board) {
        // cout<<str<<" : "<<endl;
        if (i >= n) {
            ans.push_back(board);
            // tmp2
            return;
        }
        for (int j = 0; j < n; j++) {
            if (isSafe(i, j, vis)) {
                vis[i][j] = true;
                board[i][j] = 'Q';
                solve(i + 1, n, vis, ans, board);
                vis[i][j] = false;
            }
            board[i][j] = '.';
        }
    }
    vector<vector<string>> solveNQueens(int n) {
        vector<vector<bool>> vis(n, vector<bool>(n, false));
        string tmp(n, '.');
        vector<string> board(n, tmp);
        vector<vector<string>> ans;
        solve(0, n, vis, ans, board);
        return ans;
    }
};
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