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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

def inpl(): return list(map(int, input().split()))
H, W = inpl()
C = [input() for _ in range(H)]

def calc_cost(L, R):
    global C
    P = [[0]*(H+1) for _ in range(2*H + 1)]
    for l in range(H):
        for r in range(H):
            P[l-r+H][min(l, r)] = int(C[l][L] == C[r][R])

    S = [[0]*(H+1) for _ in range(2*H + 1)]
    for i in range(1, 2*H + 1):
        r = H - abs(H-i)
        for j in range(r):
            S[i][j+1] = S[i][j] + P[i][j]

    DP = [[100000]*(H+1) for _ in range(H+1)]
    DP[0][0] = 0
    
    for x in range(2*H+1):
        for y in range(max(0, x-H), min(x+1, H+1)):
            c = S[x-2*y+H][H-max(x-y, y)]
            if x-y < H:
                DP[x-y+1][y] = min(DP[x-y+1][y], DP[x-y][y] + c)
            if y < H:
                DP[x-y][y+1] = min(DP[x-y][y+1], DP[x-y][y] + c)

    return DP[-1][-1]

ans = 0
for i in range(W-1):
    ans += calc_cost(i, i+1)
print(ans)