Transform to Chessboard
<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://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0700-0799/0782.Transform%20to%20Chessboard/images/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://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0700-0799/0782.Transform%20to%20Chessboard/images/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://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/0700-0799/0782.Transform%20to%20Chessboard/images/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>
Bit Manipulation; Array; Math; Matrix
class Solution:
    def movesToChessboard(self, board: List[List[int]]) -> int:
        def f(mask, cnt):
            ones = mask.bit_count()
            if n & 1:
                if abs(n - 2 * ones) != 1 or abs(n - 2 * cnt) != 1:
                    return -1
                if ones == n // 2:
                    return n // 2 - (mask & 0xAAAAAAAA).bit_count()
                return (n + 1) // 2 - (mask & 0x55555555).bit_count()
            else:
                if ones != n // 2 or cnt != n // 2:
                    return -1
                cnt0 = n // 2 - (mask & 0xAAAAAAAA).bit_count()
                cnt1 = n // 2 - (mask & 0x55555555).bit_count()
                return min(cnt0, cnt1)

        n = len(board)
        mask = (1 << n) - 1
        rowMask = colMask = 0
        for i in range(n):
            rowMask |= board[0][i] << i
            colMask |= board[i][0] << i
        revRowMask = mask ^ rowMask
        revColMask = mask ^ colMask
        sameRow = sameCol = 0
        for i in range(n):
            curRowMask = curColMask = 0
            for j in range(n):
                curRowMask |= board[i][j] << j
                curColMask |= board[j][i] << j
            if curRowMask not in (rowMask, revRowMask) or curColMask not in (
                colMask,
                revColMask,
            ):
                return -1
            sameRow += curRowMask == rowMask
            sameCol += curColMask == colMask
        t1 = f(rowMask, sameRow)
        t2 = f(colMask, sameCol)
        return -1 if t1 == -1 or t2 == -1 else t1 + t2
