ODD_BITS = 0b0101_0101_0101_0101_0101_0101_0101_0101
EVEN_BITS = ODD_BITS * 2

class Solution:
    def movesToChessboard(self, board: List[List[int]]) -> int:
        W = len(board)
        H = len(board[0])

        def _to_bits(arr) -> int:
            ans = 0
            for a in arr:
                ans = ans * 2 + a
            return ans

        def _count_bits(i) -> int:
            return bin(i).count("1")

        rows = list(map(_to_bits, board))
        cols = [_to_bits(board[x][y] for x in range(W)) for y in range(H)]

        def _check_valid(lines: List[int], line_len: int) -> bool:
            c = Counter(lines)
            if len(c) != 2:
                return False

            a, b = tuple(c.keys())
            if abs(c[a] - c[b]) > 1:
                return False
            if a & b != 0:
                return False
            if _count_bits(a | b) != line_len:
                return False

            return True

        if not _check_valid(rows, W) or not _check_valid(cols, H):
            return -1

        def _min_swaps(lines: List[int], line_len: int) -> int:
            cnt = _count_bits((lines[0] ^ ODD_BITS) & ((1 << line_len) - 1))
            ans_cands = [cnt, line_len - cnt]
            ans_cands = [ans for ans in ans_cands if ans % 2 == 0]
            assert ans_cands, "Should have at least one candidate"
            return min(ans_cands) // 2

        return _min_swaps(rows, W) + _min_swaps(cols, H)