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.Linq;
using static System.Console;
using static System.Math;
class E { static void Main() => new K(); }
class K
{
	int[] G() => ReadLine().Split().Select(x => int.Parse(x)).ToArray();
	public K()
	{
		var I = G();
		int Y = I[0], X = I[1];
		var m = new char[X, Y];
		for (var y = 0; y < Y; y++)
		{
			var s = ReadLine();
			for (var x = 0; x < X; x++) m[x, y] = s[y];
		}
		var ans = 0L;
		for (var x = 0; x < X - 1; x++)
		{
			var p = new int[Y + 1, Y + 1];
			for (var i = 0; i < Y; i++) if (m[x, i] == m[x + 1, i]) p[0, 0]++;
			for (var a = 1; a <= Y; a++) for (var i = 0; i < Y - a; i++) if (m[x, i] == m[x + 1, i + a]) p[a, 0]++;
			for (var b = 1; b <= Y; b++) for (var i = 0; i < Y - b; i++) if (m[x, i + b] == m[x + 1, i]) p[0, b]++;
			for (var a = 1; a <= Y; a++) for (var b = 1; b <= Y; b++) p[a, b] = p[a - 1, b - 1] - (m[x, Y - a] == m[x + 1, Y - b] ? 1 : 0);
			var dp = new int[Y + 1, Y + 1];
			for (var a = Y - 1; a >= 0; a--) for (var b = Y - 1; b >= 0; b--) dp[a, b] = p[a, b] + Min(dp[a, b + 1], dp[a + 1, b]);
			ans += dp[0, 0];
		}
		Console.WriteLine(ans);
	}
}