<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>all distinct solutions to the <strong>n-queens puzzle</strong></em>. You may return the answer in <strong>any order</strong>.</p>

<p>Each solution contains a distinct board configuration of the n-queens&#39; placement, where <code>&#39;Q&#39;</code> and <code>&#39;.&#39;</code> both indicate a queen and an empty space, respectively.</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> [[&quot;.Q..&quot;,&quot;...Q&quot;,&quot;Q...&quot;,&quot;..Q.&quot;],[&quot;..Q.&quot;,&quot;Q...&quot;,&quot;...Q&quot;,&quot;.Q..&quot;]]
<strong>Explanation:</strong> There exist two distinct solutions to the 4-queens puzzle as shown above
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> [[&quot;Q&quot;]]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 9</code></li>
</ul>

class Solution {
public:
using vs = vector<string>;  // Alias for vector<string>

vector<vector<string>> boards;
bool isIdxAvail(const vs &board, int row, int col)
{
    return row >= 0 && col >= 0 && row < board.size() && col < board.front().size();
}
bool isQueen(const char &ch)
{
    return ch == 'Q';
}
bool isValidPos(const vs &board, int row, int col)
{
    if (!isIdxAvail(board, row, col))
        return false;

    int col_size = board.front().size();
    int row_size = board.size();

    for (int c = 0; c < col_size; ++c) // check cols
    {
        if (isQueen(board[row][c]))
            return false;
    }
    for (int r = 0; r < row_size; ++r) // check rows
    {
        if (isQueen(board[r][col]))
            return false;
    }

    for (int i = row, j = col; isIdxAvail(board, i, j); --i, --j) // to upper left diag
    {
        if (isQueen(board[i][j]))
            return false;
    }
    for (int i = row, j = col; isIdxAvail(board, i, j); --i, ++j) // to upper right diag
    {
        if (isQueen(board[i][j]))
            return false;
    }
    for (int i = row, j = col; isIdxAvail(board, i, j); ++i, --j) // to left bottom diag
    {
        if (isQueen(board[i][j]))
            return false;
    }
    for (int i = row, j = col; isIdxAvail(board, i, j); ++i, ++j) // to left bottom diag
    {
        if (isQueen(board[i][j]))
            return false;
    }
    return true;
}

void solve(int row, vector<string> board) {
if(row == board.size()) {
boards.push_back(board);
return;
}
for(int col = 0; col < board[0].size(); ++col) {
    if(isValidPos(board, row, col)) {
        board[row][col] = 'Q';
        solve(row+1, board);
        board[row][col] = '.';
    }
}
}
    vector<vector<string>> solveNQueens(int n) {
        boards.clear();
        solve(0, vector<string>(n, string(n, '.')));
        return boards;

    }
};
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