Problem:
Score : 800 points

Problem Statement

Mr. Takahashi has in his room an art object with H rows and W columns, made up of H \times W blocks.
Each block has a color represented by a lowercase English letter (a-z).
The color of the block at the i-th row and j-th column is c_{i,j}.

Mr. Takahashi would like to dismantle the object, finding it a bit kitschy for his tastes.
The dismantling is processed by repeating the following operation:

Choose one of the W columns and push down that column one row.
The block at the bottom of that column disappears.

Each time the operation is performed, a cost is incurred.
Since blocks of the same color have a property to draw each other together, the cost of the operation is the number of the pairs of blocks (p, q) such that:

The block p is in the selected column.

The two blocks p and q are horizontally adjacent (before pushing down the column).

The two blocks p and q have the same color.

Mr. Takahashi dismantles the object by repeating the operation H \times W times to get rid of all the blocks.
Compute the minimum total cost to dismantle the object.

Constraints

1 ≤ H ≤ 300

2 ≤ W ≤ 300

All characters c_{i,j} are lowercase English letters (a-z).

Partial Score

In test cases worth 300 points, W = 3.

Input

The input is given from Standard Input in the following format:

H W
c_{1,1}c_{1,2}..c_{1,W}
c_{2,1}c_{2,2}..c_{2,W}
:
c_{H,1}c_{H,2}..c_{H,W}

Output

Print the minimum total cost to dismantle the object.

Sample Input 1

2 3
rrr
brg

Sample Output 1

2

For example, the total cost of 2 can be achieved by performing the operation as follows and this is the minimum value.

Sample Input 2

6 3
xya
xya
ayz
ayz
xaz
xaz

Sample Output 2

0

The total cost of 0 can be achieved by first pushing down all blocks of the middle column, then all of the left column, and all of the right column.

Sample Input 3

4 2
ay
xa
xy
ay

Sample Output 3

0

The total cost of 0 can be achieved by the following operations:

pushing down the right column one row;

pushing down the left column one row;

pushing down all of the right column;

and pushing down all of the left column.

Sample Input 4

5 5
aaaaa
abbba
ababa
abbba
aaaaa

Sample Output 4

24

Sample Input 5

7 10
xxxxxxxxxx
ccccxxffff
cxxcxxfxxx
cxxxxxffff
cxxcxxfxxx
ccccxxfxxx
xxxxxxxxxx

Sample Output 5

130

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;

int H,W;
char C[400][400];
int mem[400][400][400];

int saiki(int a,int b,int c){
    if(a==H&&b==H&&c==H)return 0;
    if(mem[a][b][c]!=-1)return mem[a][b][c];
    int ans=100000000;

    //ひだり
    int cost=0;
    if(a!=H){
        if(b<=a)if(C[a][1]==C[0][0])cost++;        
        ans=min(ans,saiki(a+1,b,c)+cost);
    }
    //まんなか
    cost=0;
    if(b!=H){
        if(a<=b)if(C[b][0]==C[0][1])cost++;
        if(c<=b)if(C[b][2]==C[0][1])cost++;
        ans=min(ans,saiki(a,b+1,c)+cost);
    }
    
    //みぎ
    cost=0;
    if(c!=H){
        if(b<=c)if(C[c][1]==C[0][2])cost++;
        ans=min(ans,saiki(a,b,c+1)+cost);
    }
        
    return mem[a][b][c]=ans;
}

int main(){
    cin>>H>>W;
    for(int i=0;i<H;i++)for(int j=0;j<W;j++)cin>>C[i][j];
    if(W>3)return 0;
    memset(mem,-1,sizeof(mem));
    cout<<saiki(0,0,0)<<endl;
    return 0;
}