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 Rust (1.15.1) (judge verdict: Accepted)

use std::io::{BufRead, Write};
use std::io;

fn solve<R: BufRead, W: Write>(mut input: R, mut output: W) {
    let mut buf = String::new();
    input.read_line(&mut buf).unwrap();
    let s = buf.trim().as_bytes();
    let counts: Vec<usize> = (b'a'..b'z' + 1)
        .map(|x| s.iter().filter(|&&y| x == y).count())
        .collect();
    let result = s.len() * (s.len() - 1) / 2 -
        counts
            .iter()
            .map(|&x| if x == 0 { 0 } else { x * (x - 1) } / 2)
            .sum::<usize>() + 1;
    writeln!(output, "{}", result).unwrap();
}

fn main() {
    let stdin = io::stdin();
    let stdout = io::stdout();
    solve(stdin.lock(), stdout.lock());
}

#[cfg(test)]
mod tests {
    fn test(input: &str, output: &str) {
        let mut v: Vec<u8> = Vec::new();
        ::solve(input.as_bytes(), &mut v);
        assert_eq!(String::from_utf8(v).unwrap(), output);
    }

    #[test]
    fn case1() {
        test("aatt\n", "5\n");
    }
    #[test]
    fn case2() {
        test("xxxxxxxxxx\n", "1\n");
    }
    #[test]
    fn case3() {
        test("abracadabra\n", "44\n");
    }
}