Given an array A, we may rotate it by a non-negative integer K so that the array becomes A[K], A[K+1], A{K+2], ... A[A.length - 1], A[0], A[1], ..., A[K-1].  Afterward, any entries that are less than or equal to their index are worth 1 point. 
For example, if we have [2, 4, 1, 3, 0], and we rotate by K = 2, it becomes [1, 3, 0, 2, 4].  This is worth 3 points because 1 > 0 [no points], 3 > 1 [no points], 0 <= 2 [one point], 2 <= 3 [one point], 4 <= 4 [one point].
Over all possible rotations, return the rotation index K that corresponds to the highest score we could receive.  If there are multiple answers, return the smallest such index K.
Example 1:
Input: [2, 3, 1, 4, 0]
Output: 3
Explanation:  
Scores for each K are listed below: 
K = 0,  A = [2,3,1,4,0],    score 2
K = 1,  A = [3,1,4,0,2],    score 3
K = 2,  A = [1,4,0,2,3],    score 3
K = 3,  A = [4,0,2,3,1],    score 4
K = 4,  A = [0,2,3,1,4],    score 3
So we should choose K = 3, which has the highest score.
Example 2:
Input: [1, 3, 0, 2, 4]
Output: 0
Explanation:  A will always have 3 points no matter how it shifts.
So we will choose the smallest K, which is 0.
Note:
       A will have length at most 20000.
       A[i] will be in the range [0, A.length].
class Solution:
     def movesToChessboard(self, board):
         """
         :type board: List[List[int]]
         :rtype: int
         """
         n = len(board)
         for i in range(1, n):
             for j in range(1, n):
                 if (board[0][0] + board[0][j] + board[i][0] + board[i][j]) % 2 != 0:
                     return -1
         result = 0
         x = 0
         y = 0
         for i in range(0, n):
             if i % 2 == 0 and board[i][0] == 1:
                 x += 1
             elif i % 2 == 1 and board[i][0] == 0:
                 y += 1
         if n % 2 == 0:
             if x != y:
                 return -1
             result += min(x, n // 2 - x)
         else:
             if x == y:
                 result += x
             elif (n + 1) // 2 - x == (n - 1) // 2 - y:
                 result += (n + 1) // 2 - x
             else:
                 return -1
         x = 0
         y = 0
         for i in range(0, n):
             if i % 2 == 0 and board[0][i] == 1:
                 x += 1
             elif i % 2 == 1 and board[0][i] == 0:
                 y += 1
         if n % 2 == 0:
             if x != y:
                 return -1
             result += min(x, n // 2 - x)
         else:
             if x == y:
                 result += x
             elif (n + 1) // 2 - x == (n - 1) // 2 - y:
                 result += (n + 1) // 2 - x
             else:
                 return -1
         return result

class Solution:
     def movesToChessboard(self, board):
         """
         :type board: List[List[int]]
         :rtype: int
         """
         n = len(board)
         for i in range(1, n):
             for j in range(1, n):
                 if (board[0][0] + board[0][j] + board[i][0] + board[i][j]) % 2 != 0:
                     return -1
         result = 0
         x = 0
         y = 0
         for i in range(0, n):
             if i % 2 == 0 and board[i][0] == 1:
                 x += 1
             elif i % 2 == 1 and board[i][0] == 0:
                 y += 1
         if n % 2 == 0:
             if x != y:
                 return -1
             result += min(x, n // 2 - x)
         else:
             if x == y:
                 result += x
             elif (n + 1) // 2 - x == (n - 1) // 2 - y:
                 result += (n + 1) // 2 - x
             else:
                 return -1
         x = 0
         y = 0
         for i in range(0, n):
             if i % 2 == 0 and board[0][i] == 1:
                 x += 1
             elif i % 2 == 1 and board[0][i] == 0:
                 y += 1
         if n % 2 == 0:
             if x != y:
                 return -1
             result += min(x, n // 2 - x)
         else:
             if x == y:
                 result += x
             elif (n + 1) // 2 - x == (n - 1) // 2 - y:
                 result += (n + 1) // 2 - x
             else:
                 return -1
         return result
