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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<cstdio>
#include<algorithm>
#include<cstring>
#define ll long long
using namespace std;
const ll MOD=1e9+7;
char s[100005];
int n,num[26];
ll ans,sum,inv[100005];
ll quick_pow(ll x,ll a)
{
	ll ans=1;
	while(a)
	{
		if(a&1)ans=ans*x%MOD;
		x=x*x%MOD;
		a>>=1;
	}
	return ans;
}
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++)inv[i]=quick_pow(i,MOD-2);
	inv[0]=1;
	scanf("%s",s+1);
	sum=1;
	for(int i=1;i<=n;i++)
	{
		num[s[i]-'a']++;
		ans+=sum*inv[num[s[i]-'a']]%MOD;
		sum=sum*inv[num[s[i]-'a']]%MOD*(num[s[i]-'a']+1)%MOD;
	}
	printf("%lld\n",ans);
	return 0;
}