You are given a two-dimensional list of integers matrix. Return the minimum sum you can get by taking a number in each row with the constraint that any row-adjacent numbers cannot be in the same column.
Constraints
1 ≤ n ≤ 250 where n is the number of rows in matrix
2 ≤ m ≤ 250 where m is the number of columns in matrix
Example 1
Input
matrix = [
[4, 5, -2],
[2, 6, 1],
[3, 1, 2]
]
Output
1
Explanation
We can take -2 from the first row, 2 from the second row, and 1 from the last row.
Example 2
Input
matrix = [
[3, 0, 3],
[2, 1, 3],
[-2, 3, 0]
]
Output
1
Explanation
We can take 0 from the first row, 3 from the second row, and -2 from the last row.