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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.IO;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace AtCoder.Contest.C
{
	static class Program
	{
		public static void Main(string[] args)
		{
			var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
			Console.SetOut(sw);

			Scanner cin = new Scanner();

			int n = cin.NextInt();
			string s = cin.Next();
			var a = new List<ModInt>();
			for (int i = 0; i < 26; i++)
			{
				a.Add(0);
			}
			foreach (var item in s)
			{
				a[item - 'a']++;
			}
			ModInt ans = 1;
			foreach (var item in a)
			{
				ans *= item + 1;
			}
			ans--;
			Console.WriteLine(ans);

			Console.Out.Flush();
		}
	}

	public struct ModInt : IComparable<ModInt>, IEquatable<ModInt>
	{
		public static long MOD = 1000000007;

		private readonly long num;

		public ModInt(long n) { num = n; }

		public override string ToString() => num.ToString();

		public static ModInt operator +(ModInt l, ModInt r)
		{
			long x = l.num + r.num;
			if (x >= MOD) x -= MOD;
			return new ModInt(x);
		}
		public static ModInt operator -(ModInt l, ModInt r)
		{
			long x = l.num - r.num;
			if (x < 0) x += MOD;
			return new ModInt(x);
		}
		public static ModInt operator *(ModInt l, ModInt r) => new ModInt((l.num * r.num) % MOD);
		public static ModInt operator /(ModInt l, ModInt r) => l * r.Inverse();

		public static ModInt operator ++(ModInt x)
		{
			var tmp = x + new ModInt(1);
			return tmp;
		}
		public static ModInt operator --(ModInt x)
		{
			var tmp = x - new ModInt(1);
			return tmp;
		}

		public static bool operator >(ModInt l, ModInt r) => l.CompareTo(r) > 0;
		public static bool operator <(ModInt l, ModInt r) => l.CompareTo(r) < 0;
		public static bool operator >=(ModInt l, ModInt r) => l.CompareTo(r) >= 0;
		public static bool operator <=(ModInt l, ModInt r) => l.CompareTo(r) <= 0;
		public static bool operator ==(ModInt l, ModInt r) => l.Equals(r);
		public static bool operator !=(ModInt l, ModInt r) => !l.Equals(r);

		public static implicit operator long(ModInt x) => x.num;
		public static implicit operator ModInt(long n)
		{
			n %= MOD;
			if (n < 0) n += MOD;
			return new ModInt(n);
		}

		public ModInt Inverse() => Inverse(this, MOD);
		public static ModInt Inverse(ModInt x) => Inverse(x.num, MOD);
		public static long Inverse(long x, long m)
		{
			if (x % m == 0) throw new DivideByZeroException();
			long a = x, b = m, u = 1, v = 0;
			while (b > 0)
			{
				long t = a / b;

				a -= t * b;
				long p = a; a = b; b = p;   // swap(a, b);

				u -= t * v;
				p = u; u = v; v = p;        // swap(u, v);
			}
			u %= m;
			if (u < 0) u += m;
			return u;
		}

		public static ModInt Pow(ModInt x, long n) => Pow(x.num, n);
		public static ModInt Pow(long x, long n)
		{
			if (n == 0) return x;
			long now = 1;
			for (n %= MOD - 1; n > 0; n /= 2, x = x * x % MOD)
			{
				if (n % 2 == 1) now = now * x % MOD;
			}
			return new ModInt(now);
		}

		public int CompareTo(ModInt x)
		{
			if (num == x.num) return 0;
			if (num > x.num) return 1;
			return -1;
		}

		public bool Equals(ModInt x) => num == x.num;

		// public override bool Equals(object obj) => obj is ModInt m && num == m.num;

		//public override int GetHashCode()
		//{
		//	return HashCode.Combine(num);
		//}

	}

	class Scanner
	{
		string[] s;
		int i;

		char[] cs = new char[] { ' ' };

		public Scanner()
		{
			s = new string[0];
			i = 0;
		}

		public string Next()
		{
			if (i < s.Length) return s[i++];
			string st = Console.ReadLine();
			while (st == "") st = Console.ReadLine();
			s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
			if (s.Length == 0) return Next();
			i = 0;
			return s[i++];
		}

		public int NextInt()
		{
			return int.Parse(Next());
		}

		public int[] ArrayInt(int N, int add = 0)
		{
			int[] Array = new int[N];
			for (int i = 0; i < N; i++)
			{
				Array[i] = NextInt() + add;
			}
			return Array;
		}

		public long NextLong()
		{
			return long.Parse(Next());
		}

		public long[] ArrayLong(int N, long add = 0)
		{
			long[] Array = new long[N];
			for (int i = 0; i < N; i++)
			{
				Array[i] = NextLong() + add;
			}
			return Array;
		}

		public double NextDouble()
		{
			return double.Parse(Next());
		}

		public double[] ArrayDouble(int N, double add = 0)
		{
			double[] Array = new double[N];
			for (int i = 0; i < N; i++)
			{
				Array[i] = NextDouble() + add;
			}
			return Array;
		}
	}
}