<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 {
public:
    map<string, int> mp;
    int nn;
    int rec(string &s) {
        if (s.size() == nn) {
            return 1;
        }
        if (mp.count(s) != 0) {
            return mp[s];
        }
        int ans = 0;
        set<int> na;
        for (int i = 0; i < s.size(); i++) {
            na.insert(s[i] - '0');
            int col = s[i] - '0';
            int dif = s.size() - i;
            na.insert(col + dif);
            na.insert(col - dif);
        }
        for (int i = 0; i < nn; i++) {
            if (na.count(i) != 0) {
                continue;
            }
            s += ('0' + i);
            ans += rec(s);
            s.pop_back();
        }
        return mp[s] = ans;
    }
    int totalNQueens(int n) {
        nn = n;
        string s = "";
        return rec(s);
    }
};
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