<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) {
        // Each solution can be represented as a vector as follows:
        // sol[i] = j -> there is a queen on row i, col j
        vector<int> sol(n, 0);
        vector<vector<int>> allSolutions;
        vector<bool> visited(n, false);

        queens(0, n, sol, visited, allSolutions);

        return allSolutions.size();
    }

private:
    void queens(int step, int n, vector<int> &solution,
                vector<bool> &visited, vector<vector<int>> &allSolutions) {
        if (step == n) {
            // The checking was already done.
            allSolutions.push_back(solution);
            return;
        }

        for (int i = 0; i < n; i++) {
            // Try placing a queen on column i of row step.
            if (visited[i]) {
                continue;
            }

            visited[i] = true;

            solution[step] = i;

            // Check the current board before backtracking.
            if (!checkSolution(step, solution)) {
                visited[i] = false;
                continue;
            }

            queens(step + 1, n, solution, visited, allSolutions);

            visited[i] = false;
        }
    }

    bool checkSolution(int step, vector<int> &solution) {
        // Check if the queen from each row is attacked
        // by any queen from the following rows.
        for (int i = 0; i < step; i++) {
            for (int j = i + 1; j <= step; j++) {
                // Main diagonal.
                if (solution[i] - i == solution[j] - j) {
                    return false;
                }

                // Secondary diagonal.
                if (solution[i] + i == solution[j] + j) {
                    return false;
                }
            }
        }

        return true;
    }
};
8902