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.

ccb25ed6f1df9367829b68523e1deff4.png

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