<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) {
        if (n <= 1)
            return n;

        vector<vector<bool>> board(n, vector<bool>(n, false));
        return placeQueens(n, 0, 0, board);
    }

    int placeQueens(int n, int queens, int row, vector<vector<bool>>& board) {
        if (n == queens)
            return 1;

        int count = 0;
        for (int col = 0; col < n; ++col) {
            if (!board[row][col]) {
                unordered_map<int, unordered_set<int>> hits;
                hitCells(n, row, col, board, hits);
                count += placeQueens(n, queens + 1, row + 1, board);
                unhitCells(hits, board);
            }
        }

        return count;
    }

    void hitCells(int n, int row, int col, vector<vector<bool>>& board, unordered_map<int, unordered_set<int>>& hits) {
        for (int i = 0; i < n; ++i) {
            hitCell(n, row, i, board, hits);
            hitCell(n, row + i, col, board, hits);
            hitCell(n, row + i, col - i, board, hits);
            hitCell(n, row + i, col + i, board, hits);
        }
    }

    void hitCell(int n, int row, int col, vector<vector<bool>>& board, unordered_map<int, unordered_set<int>>& hits) {
        if (row < 0 || row >= n || col < 0 || col >= n || board[row][col])
            return;

        board[row][col] = true;
        hits[row].insert(col);
    }

    void unhitCells(unordered_map<int, unordered_set<int>>& hits, vector<vector<bool>>& board) {
        for (auto& p : hits)
            for (int c : p.second)
                board[p.first][c] = false;
    }
};
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