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: Accepted)

using System;
using System.IO;
using System.Linq;
using System.Text;
using System.Text.RegularExpressions;
using System.Collections.Generic;
using System.Diagnostics;
using Enu = System.Linq.Enumerable;
using System.Numerics;

public class Program
{
    static readonly int INF = (int)1e9;

    public void Solve()
    {
        int H = Reader.Int();
        int W = Reader.Int();
        var rowBoard = Reader.StringArray(H);
        var cols = Enu.Range(0, W).Select(c => new char[H]).ToArray();
        for (int c = 0; c < W; c++)
            for (int r = 0; r < H; r++)
                cols[c][r] = rowBoard[r][c];

        int ans = 0;
        for (int c = 0; c + 1 < W; c++)
        {
            var A = cols[c];
            var B = cols[c + 1];
            var sameCount = new int[H + 1, H + 1];
            for (int ai = 1; ai <= H; ai++)
                for (int bi = 1; bi <= H; bi++)
                {
                    sameCount[ai, bi] = (A[ai - 1] == B[bi - 1] ? 1 : 0);
                    sameCount[ai, bi] += sameCount[ai - 1, bi - 1];
                }
            var dp = new int[H + 1, H + 1];
            Fill(dp, INF);
            dp[H, H] = 0;

            for (int ai = H; ai >= 0; ai--)
                for (int bi = H; bi >= 0; bi--)
                {
                    int cost = sameCount[ai, bi];
                    if (ai > 0)
                        CheckMin(ref dp[ai - 1, bi], dp[ai, bi] + cost);
                    if (bi > 0)
                        CheckMin(ref dp[ai, bi - 1], dp[ai, bi] + cost);
                }

            ans += dp[0, 0];
        }

        Console.WriteLine(ans);
    }

    bool CheckMin(ref int a, int b) { if (b < a) { a = b; return true; } return false; }

    void Fill<T>(T[,] A, T val)
    {
        for (int a = 0; a < A.GetLength(0); a++)
            for (int b = 0; b < A.GetLength(1); b++)
                A[a, b] = val;
    }
}


class Entry { static void Main() { new Program().Solve(); } }
class Reader
{
    static TextReader reader = Console.In;
    static readonly char[] separator = { ' ' };
    static readonly StringSplitOptions op = StringSplitOptions.RemoveEmptyEntries;
    static string[] A = new string[0];
    static int i;
    static void Init() { A = new string[0]; }
    public static void Set(TextReader r) { reader = r; Init(); }
    public static void Set(string file) { reader = new StreamReader(file); Init(); }
    public static bool HasNext() { return CheckNext(); }
    public static string String() { return Next(); }
    public static int Int() { return int.Parse(Next()); }
    public static long Long() { return long.Parse(Next()); }
    public static double Double() { return double.Parse(Next()); }
    public static int[] IntLine() { return Array.ConvertAll(Split(Line()), int.Parse); }
    public static int[] IntArray(int N) { return Range(N, Int); }
    public static int[][] IntTable(int H) { return Range(H, IntLine); }
    public static string[] StringArray(int N) { return Range(N, Next); }
    public static string[][] StringTable(int N) { return Range(N, () => Split(Line())); }
    public static string Line() { return reader.ReadLine().Trim(); }
    static string[] Split(string s) { return s.Split(separator, op); }
    static T[] Range<T>(int N, Func<T> f) { var r = new T[N]; for (int i = 0; i < N; r[i++] = f()) ; return r; }
    static string Next() { CheckNext(); return A[i++]; }
    static bool CheckNext()
    {
        if (i < A.Length) return true;
        string line = reader.ReadLine();
        if (line == null) return false;
        if (line == "") return CheckNext();
        A = Split(line);
        i = 0;
        return true;
    }
}