E. William The Oblivious
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Before becoming a successful trader William got a university degree. During his education an interesting situation happened, after which William started to listen to homework assignments much more attentively. What follows is a formal description of the homework assignment as William heard it:

You are given a string $s$ of length $n$ only consisting of characters "a", "b" and "c". There are $q$ queries of format ($pos, c$), meaning replacing the element of string $s$ at position $pos$ with character $c$. After each query you must output the minimal number of characters in the string, which have to be replaced, so that the string doesn't contain string "abc" as a subsequence. A valid replacement of a character is replacing it with "a", "b" or "c".

A string $x$ is said to be a subsequence of string $y$ if $x$ can be obtained from $y$ by deleting some characters without changing the ordering of the remaining characters.

Input

The first line contains two integers $n$ and $q$ $(1 \le n, q \le 10^5)$, the length of the string and the number of queries, respectively.

The second line contains the string $s$, consisting of characters "a", "b" and "c".

Each of the next $q$ lines contains an integer $i$ and character $c$ $(1 \le i \le n)$, index and the value of the new item in the string, respectively. It is guaranteed that character's $c$ value is "a", "b" or "c".

Output

For each query output the minimal number of characters that would have to be replaced so that the string doesn't contain "abc" as a subsequence.

Example
Input
9 12
aaabccccc
4 a
4 b
2 b
5 a
1 b
6 b
5 c
2 a
1 a
5 a
6 b
7 b

Output
0
1
2
2
1
2
1
2
2
2
2
2

Note

Let's consider the state of the string after each query:

1. $s =$"aaaaccccc". In this case the string does not contain "abc" as a subsequence and no replacements are needed.
2. $s =$"aaabccccc". In this case 1 replacements can be performed to get, for instance, string $s =$"aaaaccccc". This string does not contain "abc" as a subsequence.
3. $s =$"ababccccc". In this case 2 replacements can be performed to get, for instance, string $s =$aaaaccccc". This string does not contain "abc" as a subsequence.
4. $s =$"ababacccc". In this case 2 replacements can be performed to get, for instance, string $s =$"aaaaacccc". This string does not contain "abc" as a subsequence.
5. $s =$"bbabacccc". In this case 1 replacements can be performed to get, for instance, string $s =$"bbacacccc". This string does not contain "abc" as a subsequence.
6. $s =$"bbababccc". In this case 2 replacements can be performed to get, for instance, string $s =$"bbacacccc". This string does not contain "abc" as a subsequence.
7. $s =$"bbabcbccc". In this case 1 replacements can be performed to get, for instance, string $s =$"bbcbcbccc". This string does not contain "abc" as a subsequence.
8. $s =$"baabcbccc". In this case 2 replacements can be performed to get, for instance, string $s =$"bbbbcbccc". This string does not contain "abc" as a subsequence.
9. $s =$"aaabcbccc". In this case 2 replacements can be performed to get, for instance, string $s =$"aaacccccc". This string does not contain "abc" as a subsequence.
10. $s =$"aaababccc". In this case 2 replacements can be performed to get, for instance, string $s =$"aaacacccc". This string does not contain "abc" as a subsequence.
11. $s =$"aaababccc". In this case 2 replacements can be performed to get, for instance, string $s =$"aaacacccc". This string does not contain "abc" as a subsequence.
12. $s =$"aaababbcc". In this case 2 replacements can be performed to get, for instance, string $s =$"aaababbbb". This string does not contain "abc" as a subsequence.