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E. Stringforces

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given a string $$$s$$$ of length $$$n$$$. Each character is either one of the first $$$k$$$ lowercase Latin letters or a question mark.

You are asked to replace every question mark with one of the first $$$k$$$ lowercase Latin letters in such a way that the following value is maximized.

Let $$$f_i$$$ be the maximum length substring of string $$$s$$$, which consists entirely of the $$$i$$$-th Latin letter. A substring of a string is a contiguous subsequence of that string. If the $$$i$$$-th letter doesn't appear in a string, then $$$f_i$$$ is equal to $$$0$$$.

The value of a string $$$s$$$ is the minimum value among $$$f_i$$$ for all $$$i$$$ from $$$1$$$ to $$$k$$$.

What is the maximum value the string can have?

Input

The first line contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le n \le 2 \cdot 10^5$$$; $$$1 \le k \le 17$$$) — the length of the string and the number of first Latin letters used.

The second line contains a string $$$s$$$, consisting of $$$n$$$ characters. Each character is either one of the first $$$k$$$ lowercase Latin letters or a question mark.

Output

Print a single integer — the maximum value of the string after every question mark is replaced with one of the first $$$k$$$ lowercase Latin letters.

Examples

Input

10 2 a??ab????b

Output

4

Input

9 4 ?????????

Output

2

Input

2 3 ??

Output

0

Input

15 3 ??b?babbc??b?aa

Output

3

Input

4 4 cabd

Output

1

Note

In the first example the question marks can be replaced in the following way: "aaaababbbb". $$$f_1 = 4$$$, $$$f_2 = 4$$$, thus the answer is $$$4$$$. Replacing it like this is also possible: "aaaabbbbbb". That way $$$f_1 = 4$$$, $$$f_2 = 6$$$, however, the minimum of them is still $$$4$$$.

In the second example one of the possible strings is "aabbccdda".

In the third example at least one letter won't appear in the string, thus, the minimum of values $$$f_i$$$ is always $$$0$$$.

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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