Given a square grid of integers arr, a falling path with non-zero shifts is a choice of exactly one element from each row of arr, such that no two elements chosen in adjacent rows are in the same column.
Return the minimum sum of a falling path with non-zero shifts.
Example 1:
Input: arr = [[1,2,3],[4,5,6],[7,8,9]]
Output: 13
Explanation: 
The possible falling paths are:
[1,5,9], [1,5,7], [1,6,7], [1,6,8],
[2,4,8], [2,4,9], [2,6,7], [2,6,8],
[3,4,8], [3,4,9], [3,5,7], [3,5,9]
The falling path with the smallest sum is [1,5,7], so the answer is 13.
Constraints:
1 <= arr.length == arr[i].length <= 200
-99 <= arr[i][j] <= 99
class Solution:
    def minFallingPathSum(self, A: List[List[int]]) -> int:
        n = len(A)
        dp = [[0 for j in range(n)] for i in range(n)]
        for i in range(n):
            dp[-1][i] = A[-1][i]
        for i in range(n-2,-1,-1):
            for j in range(n):
                dp[i][j] = A[i][j] + min(dp[i+1][:j]+dp[i+1][j+1:])
        return min(dp[0])
class Solution:
    def minFallingPathSum(self, A: List[List[int]]) -> int:
        n = len(A)
        dp = [[0 for j in range(n)] for i in range(n)]
        for i in range(n):
            dp[-1][i] = A[-1][i]
        for i in range(n-2,-1,-1):
            for j in range(n):
                dp[i][j] = A[i][j] + min(dp[i+1][:j]+dp[i+1][j+1:])
        return min(dp[0])