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, $W = 3$.

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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.

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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.

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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.

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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.

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Sample Input 4

5 5
aaaaa
abbba
ababa
abbba
aaaaa

Sample Output 4

24

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Sample Input 5

7 10
xxxxxxxxxx
ccccxxffff
cxxcxxfxxx
cxxxxxffff
cxxcxxfxxx
ccccxxfxxx
xxxxxxxxxx

Sample Output 5

130