MISERMAN - Wise And Miser

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 buses, 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: N×M 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


Added by:The quick brown fox jumps over the lazy dog
Date:2010-10-18
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64 NODEJS OBJC VB.NET
Resource:Udit Agarwal

hide comments
2011-10-30 12:27:50 Kumar Harsh
@Luka : It is written that Line 2 will have a NxM GRID, which should be sufficient, although still the author could have been more explicit.

And for those who dont understand the question, see it like this :

Start from any column in the first row, and work your way downwards summing up all the cells you encounter.

The rule is :
You have to move to the next row by taking only 1 step either straight down, or diagonally left-down or right-down.

(think of all the possible moves of a pawn in a chess game)
2010-10-19 09:59:58 Luka Kalinovcic
Input section states that there are 2 lines. Input example has more. Even an empty line. Also, explanation is wrong.

Please put a little more effort in the text to keep the level of problems high.

Last edit: 2010-10-18 20:09:06
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