Paint House!

There are a row of N houses, each house can be painted with one of the three colors: red, blue or green.

The cost of painting each house with a certain color is different. You have to paint all the houses such that no two adjacent houses have the same color.

The cost of painting each house with a certain color is represented by a N x 3 cost matrix A.

For example, A[0][0] is the cost of painting house 0 with color red; A[1][2] is the cost of painting house 1 with color green, and so on.

Find the minimum total cost to paint all houses.

1 <= N <= 10⁵

1 <= A[i][j] <= 10³

First and only argument is an 2D integer matrix A of size N x 3 denoting the cost to paint the houses.

Return an integer denoting the minimum total cost to paint all houses.

Input 1:

 A = [  [1, 2, 3]
        [10, 11, 12]
     ]

Output 1:

 12

Explanation 1:

 Paint house 1 with red and house 2 with green i.e A[0][0] + A[1][1] = 1 + 11 = 12