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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using static System.Console;

namespace CF2016_D
{
    class Program
    {
        static int H, W;
        static void Main(string[] args)
        {
            var t = scan;
            H = t[0]; W = t[1];
            if (W != 3)
            {
                return;
            }
            var K = new string[H];
            for (int i = 0; i < H; i++)
            {
                K[i] = ReadLine();                
            }

            var cost = 0;
            for (int i = 0; i < H; i++)
            {
                for (int j = i; j < H ; j++)
                {
                    if (K[i][1] == K[j][0])
                    {
                        cost++;
                    }
                    if (K[i][1] == K[j][2])
                    {
                        cost++;
                    }
                }
            }
            int min = cost;

            cost = 0;
            for (int i = 0; i < H; i++)
            {
                for (int j = i; j < H; j++)
                {
                    if (K[i][0] == K[j][1])
                    {
                        cost++;
                    }
                }
            }
            for (int i = 0; i < H; i++)
            {
                for (int j = i; j < H; j++)
                {
                    if (K[i][1] == K[j][2])
                    {
                        cost++;
                    }
                }
            }
            min = Math.Min(min, cost);

            cost = 0;
            for (int i = 0; i < H; i++)
            {
                for (int j = i; j < H; j++)
                {
                    if (K[i][2] == K[j][1])
                    {
                        cost++;
                    }
                }
            }
            for (int i = 0; i < H; i++)
            {
                for (int j = i; j < H; j++)
                {
                    if (K[i][1] == K[j][0])
                    {
                        cost++;
                    }
                }
            }
            min = Math.Min(cost, min);
            Console.WriteLine(min);
        }

        static int[] scan { get { return Array.ConvertAll(Console.ReadLine().Split(), int.Parse); } }
    }
}