Jack is a wise and miser man. Always tries to save his money.

One day, he wants to go from city A to city B. Between A and B, there are N number of cities(including B and excluding A) and in each city there are M buses numbered from 1 to M. And the fare of each bus is different. Means for all N*M busses, fare (K) may be different or same. Now Jack has to go from city A to city B following these conditions:

1. At every city, he has to change the bus.
2. And he can switch to only those buses which have number either equal or 1 less or 1 greater to the previous.

You are to help Jack to go from A to B by spending the minimum amount of money.

N, M, K <= 100.

Input

Line 1:    N M
Line 2-:    NxM Grid

Each row lists the fares the M busses to go form the current city to the next city.

Output

Single Line containing the minimum amount of fare that Jack has to give.

Example

Input:
5 5
1  3  1  2  6
10 2  5  4  15
10 9  6  7  1
2  7  1  5  3
8  2  6  1  9
Output:
10

Explanation

1 -> 4 -> 1 -> 3 -> 1: 10