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E. Keyboard Purchase

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou have a password which you often type — a string $$$s$$$ of length $$$n$$$. Every character of this string is one of the first $$$m$$$ lowercase Latin letters.

Since you spend a lot of time typing it, you want to buy a new keyboard.

A keyboard is a permutation of the first $$$m$$$ Latin letters. For example, if $$$m = 3$$$, then there are six possible keyboards: abc, acb, bac, bca, cab and cba.

Since you type your password with one finger, you need to spend time moving your finger from one password character to the next. The time to move from character $$$s_i$$$ to character $$$s_{i+1}$$$ is equal to the distance between these characters on keyboard. The total time you have to spend typing the password with a keyboard is called the slowness of this keyboard.

More formaly, the slowness of keyboard is equal to $$$\sum\limits_{i=2}^{n} |pos_{s_{i-1}} - pos_{s_i} |$$$, where $$$pos_x$$$ is position of letter $$$x$$$ in keyboard.

For example, if $$$s$$$ is aacabc and the keyboard is bac, then the total time of typing this password is $$$|pos_a - pos_a| + |pos_a - pos_c| + |pos_c - pos_a| + |pos_a - pos_b| + |pos_b - pos_c|$$$ = $$$|2 - 2| + |2 - 3| + |3 - 2| + |2 - 1| + |1 - 3|$$$ = $$$0 + 1 + 1 + 1 + 2 = 5$$$.

Before buying a new keyboard you want to know the minimum possible slowness that the keyboard can have.

Input

The first line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \le n \le 10^5, 1 \le m \le 20$$$).

The second line contains the string $$$s$$$ consisting of $$$n$$$ characters. Each character is one of the first $$$m$$$ Latin letters (lowercase).

Output

Print one integer – the minimum slowness a keyboard can have.

Examples

Input

6 3 aacabc

Output

5

Input

6 4 aaaaaa

Output

0

Input

15 4 abacabadabacaba

Output

16

Note

The first test case is considered in the statement.

In the second test case the slowness of any keyboard is $$$0$$$.

In the third test case one of the most suitable keyboards is bacd.

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

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