<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 {
    string DOTS;
    vector<int> NUMS;
    int n;
public:
    vector<vector<string>> solveNQueens(int n) {
        this -> n = n;
        DOTS = string(n, '.');
        NUMS.resize(n);
        iota(NUMS.begin(), NUMS.end(), 0);
        vector<vector<string>> res {};
        helper(res, vector<int>{});
        return res;
    }

    void helper(vector<vector<string>>& res, vector<int> qs) {
        for (int q : qs) cout << q << ", ";
        cout << "\n";
        if (qs.size() == n) {
            vector<string> r {};
            for (int i = 0; i < qs.size(); i++) {
                string t {DOTS};
                t[qs[i]] = 'Q';
                r.emplace_back(t);
            }
            res.emplace_back(r);
            return;
        }
        int k = qs.size();
        vector<int> remainings {};
        set<int> qset {qs.begin(), qs.end()};
        set_difference(NUMS.begin(), NUMS.end(), qset.begin(), qset.end(), back_inserter(remainings));
        for (int r : remainings) cout << "Rem: " << r << ", ";
        cout << "\n";
        vector<int> p {}, m {};
        for (int i = 0; i < qs.size(); i++) {
            p.emplace_back(qs[i] + i);
            m.emplace_back(qs[i] - i);
        }
        for (int pp : p) cout << "p: " << pp << ", ";
        for (int mm : m) cout << "m: " << mm << ", ";
        cout << "\n";
        for (int r : remainings) {
            cout << "IF: " << (find(p.begin(), p.end(), r + k) == p.end() && find(m.begin(), m.end(), r - k) == p.end()) << "\n";
            cout << "rk: " << r << ", " << k << "\n";
            if (find(p.begin(), p.end(), r + k) == p.end() && find(m.begin(), m.end(), r - k) == m.end()) {
                qs.emplace_back(r);
                helper(res, qs);
                qs.pop_back();
            }
        }
        return;
    }
};
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