Number of Subsequences

给定一个含有`abc?`的字符串,`?`可能是`abc`中的任意一个,求所有可能的无`?`字符串中,子序列`abc`出现的次数.

You are given a string $ s $ consisting of lowercase Latin letters "a", "b" and "c" and question marks "?". Let the number of question marks in the string $ s $ be $ k $ . Let's replace each question mark with one of the letters "a", "b" and "c". Here we can obtain all $ 3^{k} $ possible strings consisting only of letters "a", "b" and "c". For example, if $ s = $ "ac?b?c" then we can obtain the following strings: $ [ $ "acabac", "acabbc", "acabcc", "acbbac", "acbbbc", "acbbcc", "accbac", "accbbc", "accbcc" $ ] $ . Your task is to count the total number of subsequences "abc" in all resulting strings. Since the answer can be very large, print it modulo $ 10^{9} + 7 $ . A subsequence of the string $ t $ is such a sequence that can be derived from the string $ t $ after removing some (possibly, zero) number of letters without changing the order of remaining letters. For example, the string "baacbc" contains two subsequences "abc" — a subsequence consisting of letters at positions $ (2, 5, 6) $ and a subsequence consisting of letters at positions $ (3, 5, 6) $ .

The first line of the input contains one integer $ n $ $ (3 \le n \le 200\,000) $ — the length of $ s $ . The second line of the input contains the string $ s $ of length $ n $ consisting of lowercase Latin letters "a", "b" and "c" and question marks"?".

Print the total number of subsequences "abc" in all strings you can obtain if you replace all question marks with letters "a", "b" and "c", modulo $ 10^{9} + 7 $ .

6
ac?b?c

24

7
???????

2835

9
cccbbbaaa

0

5
a???c

46

In the first example, we can obtain $ 9 $ strings: - "acabac" — there are $ 2 $ subsequences "abc", - "acabbc" — there are $ 4 $ subsequences "abc", - "acabcc" — there are $ 4 $ subsequences "abc", - "acbbac" — there are $ 2 $ subsequences "abc", - "acbbbc" — there are $ 3 $ subsequences "abc", - "acbbcc" — there are $ 4 $ subsequences "abc", - "accbac" — there is $ 1 $ subsequence "abc", - "accbbc" — there are $ 2 $ subsequences "abc", - "accbcc" — there are $ 2 $ subsequences "abc". So, there are $ 2 + 4 + 4 + 2 + 3 + 4 + 1 + 2 + 2 = 24 $ subsequences "abc" in total.