Problem:
Score : 500 points

Problem Statement

You have a string A = A_1 A_2 ... A_n consisting of lowercase English letters.

You can choose any two indices i and j such that 1 \leq i \leq j \leq n and reverse substring A_i A_{i+1} ... A_j.

You can perform this operation at most once.

How many different strings can you obtain?

Constraints

1 \leq |A| \leq 200,000

A consists of lowercase English letters.

Input

Input is given from Standard Input in the following format:

A

Output

Print the number of different strings you can obtain by reversing any substring in A at most once.

Sample Input 1

aatt

Sample Output 1

5

You can obtain aatt (don't do anything), atat (reverse A[2..3]), atta (reverse A[2..4]), ttaa (reverse A[1..4]) and taat (reverse A[1..3]).

Sample Input 2

xxxxxxxxxx

Sample Output 2

1

Whatever substring you reverse, you'll always get xxxxxxxxxx.

Sample Input 3

abracadabra

Sample Output 3

44

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;

class Program
{
    static void Main(string[] args)
    {
        string s = Console.ReadLine();

        int[] charCounts = new int[256];
        foreach (char c in s)
        {
            int index = c - 'a';
            charCounts[index] += 1;
        }

        ulong pairs = 0;
        foreach (int x in charCounts)
        {
            if (x > 1)
            {
                pairs += (ulong)x * (ulong)(x - 1) / 2;
                Console.Error.WriteLine("Pairs is now {0} after x = {1}", pairs, x);
            }
        }

        ulong max = (ulong)s.Length * (ulong)(s.Length - 1) / 2;
        ulong answer = max - pairs + 1;

        Console.Error.WriteLine("max: {0}, pairs: {1}", max, pairs);

        Console.WriteLine(answer);
        Console.ReadLine();
    }
}