Score : $200$ points

Problem Statement

You are given a string $S$ of length $N$. Among its subsequences, count the ones such that all characters are different, modulo $10^9+7$. Two subsequences are considered different if their characters come from different positions in the string, even if they are the same as strings.

Here, a subsequence of a string is a concatenation of one or more characters from the string without changing the order.

Constraints

• $1 \leq N \leq 100000$
• $S$ consists of lowercase English letters.
• $|S|=N$

Input

Input is given from Standard Input in the following format:

$N$

$S$

Output

Print the number of the subsequences such that all characters are different, modulo $10^9+7$.

4
abcd

15

Since all characters in $S$ itself are different, all its subsequences satisfy the condition.

3
baa

5

The answer is five: b, two occurrences of a, two occurrences of ba. Note that we do not count baa, since it contains two as.

5
abcab

17