Problem:
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.

Sample Input 1

4
abcd

Sample Output 1

15

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

Sample Input 2

3
baa

Sample Output 2

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.

Sample Input 3

5
abcab

Sample Output 3

17

Solution in PHP7 (7.0.15) (judge verdict: Wrong Answer)

<?php
fscanf(STDIN, "%d", $N);
fscanf(STDIN, "%s", $S);

$n = 0;
for($i=1, $i2 = 2**$N; $i<$i2; $i++) {
	$s = decbin($i);
	$s = str_pad($s, $N - strlen($s), '0', STR_PAD_LEFT) . $s;

	$sub = '';
	$ok = true;
	for($j=0; $j<$N && $ok; $j++) {
		if($s[$j] === 1) {
			if(strpos($str[$j]) !== false) {
				$ok = false;
			} else {
				$sub += $str[$j];
			}
		}
	}

	if($ok) {
		$n++;
	}

}

echo $n % (10**9+7);