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.
Problem Constraints
1 <= N <= 105
1 <= A[i][j] <= 103
Input Format
First and only argument is an 2D integer matrix A of size N x 3 denoting the cost to paint the houses.
Output Format
Return an integer denoting the minimum total cost to paint all houses.
Example Input
Input 1:
A = [ [1, 2, 3]
[10, 11, 12]
]
Example Output
Output 1:
12
Example Explanation