<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:
    int totalNQueens(int n) {
        vector<vector<int>> locs;
        cout << " start " << endl;
        return recurser(n, locs, 0, n);
    }

    int recurser(int n, vector<vector<int>>& locs, int row, int len) {
        if (n == 0) {
            return 1;
        }
        int soln = 0;
        for (int i = 0; i < len; i++) {
            if (collision(locs, row, i)) {
                continue;
            } else {
                // cout << "n. " << n << "  row. " << row << "  col. "  << i << endl;
                locs.push_back({row, i});
                soln += recurser(n - 1, locs, row + 1, len);
                locs.pop_back();
            }
        }

        return soln;
    }

    bool collision(vector<vector<int>>& locs, int row, int col) {
        for (vector<int> loc : locs) {
            int rowp = loc[0];
            int colp = loc[1];

            if (row == rowp || col == colp) {
                return true;
            }

            if (abs(row - rowp) == abs(col - colp)) {
                return true;
            }
        }

        return false;
    }
};
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