<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:
    //diagonal
    //antidiagonal
    //column
    vector<vector<string>> solveNQueens(int n) {
        queue<set<pair<int,int>>> q;
        q.push({});
        vector<vector<string>> ans;
        while (q.size()) {
            set<pair<int,int>> cur = q.front(); q.pop();
            int l = cur.size();
            if (l == n) {
                vector<string> works(l, string(l, '.'));
                for (auto [x,y] : cur) {
                    works[x][y] = 'Q';
                }
                ans.push_back(works);
                continue;
            }
            for (int i = 0; i < n; i++) {
                pair<int,int> candidate = {l,i};
                bool works = true;
                for (auto [x,y] : cur) {
                    if (y == i) {
                        works = false;
                        break;
                    }
                    if (x + y == l + i) {
                        works = false;
                        break;
                    }
                    if (x - y == l - i) {
                        works = false;
                        break;
                    }
                }
                if (works) {
                    auto next = cur;
                    next.insert(candidate);
                    q.push(next);
                }
            }
        }
        return ans;
    }
};
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