<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:
    vector<vector<string>> solveNQueens(int n) {
        vector<vector<string>> result;
        vector<bool> mask(3*n, true);
        for (auto tab: search(n, 0, mask)) {
            vector<string> board;
            for (auto col: tab) {
                string s = convert(col, n);
                board.push_back(s);
            }
            result.push_back(board);
        }
        return result;
    }
    string convert(int i, int n) {
        stringstream ss;
        for (int j = 0; j < n; ++j) {
            if (i != j) {
                ss << ".";
            } else {
                ss << "Q";
            }
        }
        return ss.str();
    }
    vector<vector<int>> search(int n, int row, vector<bool> mask) {
        if (row == n) { return vector(1, vector<int>()); }
        vector<vector<int>> result;
        for (int col = 0; col < n; ++col) {
            if (!mask[col + 0*n] || !mask[col + 1*n] || !mask[col + 2*n]) {
                continue;
            }
            mask[col + 0*n] = false;
            mask[col + 1*n] = false;
            mask[col + 2*n] = false;
            for (auto sub_result: search(n, row+1, next(n, mask))) {
                sub_result.push_back(col);
                result.push_back(std::move(sub_result));
            }
            mask[col + 0*n] = true;
            mask[col + 1*n] = true;
            mask[col + 2*n] = true;
        }
        return result;
    }
    vector<bool> next(int n, const vector<bool>& mask) {
        vector<bool> next_mask(mask.size(), true);
        for (int i = 0; i < n; ++i) {
            next_mask[i + 0*n] = mask[i + 0*n];
        }
        for (int i = 1; i < n; ++i) {
            next_mask[i + 1*n] = mask[i + 1*n - 1];
        }
        for (int i = 0; i < n-1; ++i) {
            next_mask[i + 2*n] = mask[i + 2*n + 1];
        }
        return next_mask;
    }
};
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