CF1609E William The Oblivious

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.

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".

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.

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.