<p>You are given an <code>n x n</code> binary grid <code>board</code>. In each move, you can swap any two rows with each other, or any two columns with each other.</p>

<p>Return <em>the minimum number of moves to transform the board into a <strong>chessboard board</strong></em>. If the task is impossible, return <code>-1</code>.</p>

<p>A <strong>chessboard board</strong> is a board where no <code>0</code>&#39;s and no <code>1</code>&#39;s are 4-directionally adjacent.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/29/chessboard1-grid.jpg" style="width: 500px; height: 145px;" />
<pre>
<strong>Input:</strong> board = [[0,1,1,0],[0,1,1,0],[1,0,0,1],[1,0,0,1]]
<strong>Output:</strong> 2
<strong>Explanation:</strong> One potential sequence of moves is shown.
The first move swaps the first and second column.
The second move swaps the second and third row.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/29/chessboard2-grid.jpg" style="width: 164px; height: 165px;" />
<pre>
<strong>Input:</strong> board = [[0,1],[1,0]]
<strong>Output:</strong> 0
<strong>Explanation:</strong> Also note that the board with 0 in the top left corner, is also a valid chessboard.
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/29/chessboard3-grid.jpg" style="width: 164px; height: 165px;" />
<pre>
<strong>Input:</strong> board = [[1,0],[1,0]]
<strong>Output:</strong> -1
<strong>Explanation:</strong> No matter what sequence of moves you make, you cannot end with a valid chessboard.
</pre>

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

<ul>
	<li><code>n == board.length</code></li>
	<li><code>n == board[i].length</code></li>
	<li><code>2 &lt;= n &lt;= 30</code></li>
	<li><code>board[i][j]</code> is either&nbsp;<code>0</code> or <code>1</code>.</li>
</ul>

from typing import List

class Solution:
    def movesToChessboard(self, board: List[List[int]]) -> int:
        n = len(board)
        
        def pattern_count(line):
            ones = sum(line)
            if not (n // 2 <= ones <= (n + 1) // 2):
                return float('inf')
            pattern1 = sum(line[i] == i % 2 for i in range(n))
            pattern2 = sum(line[i] != i % 2 for i in range(n))
            if n % 2 == 0:
                return min(pattern1, pattern2) // 2
            else:
                if pattern1 % 2 == 0:
                    return pattern1 // 2
                else:
                    return pattern2 // 2
        
        # Check if board is valid
        if any(board[0][0] ^ board[i][0] ^ board[0][j] ^ board[i][j] for i in range(n) for j in range(n)):
            return -1
        
        row_swaps = pattern_count(board[0])
        col_swaps = pattern_count([board[i][0] for i in range(n)])
        
        if row_swaps == float('inf') or col_swaps == float('inf'):
            return -1
        
        return row_swaps + col_swaps

# Example usage:
# solution = Solution()
# print(solution.movesToChessboard([[0,1,1,0],[0,1,1,0],[1,0,0,1],[1,0,0,1]]))  # Output: 2
16500