<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) 
    {
        int sol = 0;
        unordered_set<int> rows;
        unordered_set<int> cols;
        unordered_set<int> diagonals;
        unordered_set<int> anti_diagonals;
        backtrack(sol, 0, n, rows, cols, diagonals, anti_diagonals);
        return sol;
    }

    void backtrack(int &sols, int currRow, int n, unordered_set<int> &attackedRows, unordered_set<int> &attackedCols, unordered_set<int> &attackedDiagonals, unordered_set<int> &attackedAntiDiagonals)
    {
        if (currRow >= n)
        {
            sols++;
            return;
        }

        for (int i = 0 ; i < n ; i++)
        {
            if (validSquare(currRow, i, attackedRows, attackedCols, attackedDiagonals, attackedAntiDiagonals))
            {
                attackedRows.insert(currRow);
                attackedCols.insert(i);
                attackedDiagonals.insert(currRow - i);
                attackedAntiDiagonals.insert(currRow + i);
                backtrack(sols, currRow + 1, n, attackedRows, attackedCols, attackedDiagonals, attackedAntiDiagonals);
                attackedRows.erase(currRow);
                attackedCols.erase(i);
                attackedDiagonals.erase(currRow - i);
                attackedAntiDiagonals.erase(currRow + i);
            }
        }

    }

    bool validSquare(int row, int col, unordered_set<int> &rows, unordered_set<int> &cols, unordered_set<int> &diagonals, unordered_set<int> &antidiagonals)
    {
        bool ret = true;
        ret &= (rows.find(row) == rows.end());
        ret &= (cols.find(col) == cols.end());
        ret &= (diagonals.find(row - col) == diagonals.end());
        ret &= (antidiagonals.find(row + col) == antidiagonals.end());
        return ret;
    }
};
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