<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 {
private:
    int trueN;
    int result = 0;
    void backtracking(int row, unordered_map<int, bool> badCol, unordered_map<int, bool> posDiag, unordered_map<int, bool> negDiag) {
        if (row == trueN) {
            result++;
            return;
        }

        for (int i = 0; i < trueN; i++) {
            // If this position (row,col) is in badCols, posDiag, OR negDiag we can't place a Queen
            if (badCol[i] == true || posDiag[row+i] == true || negDiag[row-i] == true) {
                continue;
            }
            //place Queen on current row + column
            badCol[i] = true;
            posDiag[row+i] = true;
            negDiag[row-i] = true;

            backtracking(row+1, badCol, posDiag, negDiag);

            //remove queen from this position and continue
            badCol[i] = false;
            posDiag[row+i] = false;
            negDiag[row-i] = false;
        }
    }
public:
    int totalNQueens(int n) {
        trueN = n;
        unordered_map<int, bool> badCol;
        unordered_map<int, bool> posDiag;
        unordered_map<int, bool> negDiag;
        backtracking(0, badCol, posDiag, negDiag);

        return result;
    }
};
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