F. Number of Subsequences
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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 $(3, 5, 6)$.

Input

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"?".

Output

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 $10^{9} + 7$.

Examples
Input
6
ac?b?c

Output
24

Input
7
???????

Output
2835

Input
9
cccbbbaaa

Output
0

Input
5
a???c

Output
46

Note

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.