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 Kotlin (1.0.0) (judge verdict: Time Limit Exceeded)

import java.util.*

fun main(args: Array<String>) {

    val sc = Scanner(System.`in`)
    val N = sc.nextInt()
    val S = sc.next()
    val map = mutableMapOf<Char,Int>()
    for (c in S)
        map[c] = (map[c] ?: 0) +1
    var ans = 0L

    fun calc(c:Char, n:Int) :Long{
        //println("$n $c:${map[c]}")
        if (n == 1) {
            return map[c]?.toLong()?:0
        } else {
            var res = 0L
            if (!map.any { it.key.toChar() in c+1 .. 'z'}) return 0L
            for (ci in c+1..'z') {
                if (ci !in map.keys) continue
                res += map[c]!!*calc(ci,n-1)
            }
            //println("return$res")
            return res
        }
    }

    for (n in 1 .. map.size) {
        for (c in 'a'..'z') {
            if (c !in map.keys) continue
            ans += calc(c,n)
            //println("$n $ans")
        }
    }
    println(ans%(1000000007L))
}