Connect

You are playing a solitaire puzzle called "Connect", which uses several letter tiles.

There are R × C empty cells. For each i (1 ≤ i ≤ R), you must put a string s_i (1 ≤ |s_i| ≤ C) in the i-th row of the table, without changing the letter order. In other words, you choose an integer sequence {a_j} such that 1 ≤ a₁ < a₂ < ... < a_|si| ≤ C , and put the j-th character of the string s_i in the a_j-th column (1 ≤ j ≤ |s_i|).

For example, when C = 8 and s_i = "ICPC", you can put s_i like followings.

I_C_P_C_
ICPC____
_IC___PC

'_' represents an empty cell.

For each non-empty cell x, you get a point equal to the number of adjacent cells which have the same character as x. Two cells are adjacent if they share an edge.

Calculate the maximum total point you can get.

Input

The first line contains two integers R and C (1 ≤ R ≤ 128, 1 ≤ C ≤ 16).

Then R lines follow, each of which contains s_i (1 ≤ |s_i| ≤ C). All characters of s_i are uppercase letters.

Output

Output the maximum total point in a line.

Sample Input 1

2 4
ACM
ICPC

Output for the Sample Input 1

2

Sample Input 2

2 9
PROBLEMF
CONNECT

Output for the Sample Input 2

6

Sample Input 3

4 16
INTERNATIONAL
COLLEGIATE
PROGRAMMING
CONTEST

Output for the Sample Input 3

18

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