Problem:
Score : 800 points

Problem Statement

You are given a string S consisting of lowercase English letters.
Determine whether we can turn S into a palindrome by repeating the operation of swapping two adjacent characters. If it is possible, find the minimum required number of operations.

Constraints

1 \leq |S| \leq 2 × 10^5

S consists of lowercase English letters.

Input

Input is given from Standard Input in the following format:

S

Output

If we cannot turn S into a palindrome, print -1. Otherwise, print the minimum required number of operations.

Sample Input 1

eel

Sample Output 1

1

We can turn S into a palindrome by the following operation:

Swap the 2-nd and 3-rd characters. S is now ele.

Sample Input 2

ataatmma

Sample Output 2

4

We can turn S into a palindrome by the following operation:

Swap the 5-th and 6-th characters. S is now ataamtma.

Swap the 4-th and 5-th characters. S is now atamatma.

Swap the 3-rd and 4-th characters. S is now atmaatma.

Swap the 2-nd and 3-rd characters. S is now amtaatma.

Sample Input 3

snuke

Sample Output 3

-1

We cannot turn S into a palindrome.

Solution in Rust (1.15.1) (judge verdict: Accepted)

// https://atcoder.jp/contests/arc088/tasks/arc088_c
//
#![allow(unused_imports)]
use std::io::*;
use std::fmt::*;
use std::str::*;
use std::cmp::*;
use std::collections::*;

macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };

    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };

    ($iter:expr, [ next / $t:tt ]) => {
        {
            let len = read_value!($iter, usize);
            (0..len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
        }
    };

    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };

    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };

    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

#[allow(unused_macros)]
macro_rules! dvec {
    ($t:expr ; $len:expr) => {
        vec![$t; $len]
    };

    ($t:expr ; $len:expr, $($rest:expr),*) => {
        vec![dvec!($t; $($rest),*); $len]
    };
}

#[allow(unused_macros)]
macro_rules! ifv {
    ($t:expr, $a:expr, $b: expr) => {
        if $t { $a } else { $b }
    }
}

#[allow(unused_macros)]
macro_rules! fill {
    ($t:expr, $v:expr) => {
        for i in 0..$t.len() {
            $t[i] = $v;
        }
    };
}

#[allow(unused_macros)]
macro_rules! join {
    ($t:expr, $glue:expr) => {
        $t.into_iter().map(|w| w.to_string()).collect::<Vec<_>>().join($glue)
    };
}

#[allow(unused_macros)]
macro_rules! debug {
    ($($a:expr),*) => {
        println!(concat!($(stringify!($a), " = {:?}, "),*), $($a),*);
    }
}

// ====

struct FenwickTree<T> {
    data: Vec<T>
}

impl<T: Copy + Default + std::ops::Add + std::ops::AddAssign + std::ops::Sub> FenwickTree<T> {
    fn new(n: usize, initial: T) -> Self {
        FenwickTree { data: vec![initial; n+1] }
    }

    /// Computes sum value of ([0, i)).
    fn sum(&self, i: usize) -> T {
        let mut idx = i as i64;
        let mut ret = T::default();
        while idx > 0 {
            ret += self.data[idx as usize];
            idx -= idx & (-idx);
        }
        ret
    }

    /// Adds value x into i-th position.
    fn add(&mut self, i: usize, x: T) {
        let mut idx = (i + 1) as i64;
        while idx < self.data.len() as i64 {
            self.data[idx as usize] += x;
            idx += idx & (-idx);
        }
    }

    fn range(&self, r: std::ops::Range<usize>) -> <T as std::ops::Sub>::Output {
        self.sum(r.end) - self.sum(r.start)
    }
}

// ====


fn doit(p: Vec<usize>) -> i64 {
    let n = p.len();
    let mut count = 0i64;
    let mut bit = FenwickTree::new(n, 0i64);
    for i in 0..n {
        count += bit.range(p[i]+1..n);
        bit.add(p[i], 1);
    }
    count
}

fn main() {
    input! {
        s: chars
    };
    let s = s.into_iter().map(|c| ((c as u8) - ('a' as u8)) as usize).collect::<Vec<_>>();
    let n = s.len();
    let mut count = vec![0; 26];
    for i in 0..n {
        count[s[i]] += 1;
    }

    let mut odd = 26;
    for i in 0..26 {
        if count[i] % 2 == 1 {
            if odd == 26 {
                odd = i;
            } else {
                println!("-1");
                return;
            }
        }
    }
    let mut ws = vec![0; n];
    let mut cnt = vec![0; 26];
    {
        let mut pre = 0;
        let mut hal = (n+1)/2;
        for i in 0..n {
            if cnt[s[i]] < count[s[i]] / 2 {
                ws[pre] = s[i];
                pre += 1;
            } else if s[i] == odd && cnt[s[i]] + 1 == (count[s[i]] + 1) / 2 {
                ws[n/2] = s[i];
            } else {
                ws[hal] = s[i];
                hal += 1;
            }
            cnt[s[i]] += 1;
        }
    }
    for i in 0..n/2 {
        ws[n-1-i] = ws[i];
    }
    let mut idxmap = vec![vec![]; 26];
    for i in 0..n {
        idxmap[ws[i]].push(i);
    }
    let mut perm = vec![0; n];
    let mut cnt = vec![0; 26];
    for i in 0..n {
        perm[i] = idxmap[s[i]][cnt[s[i]]];
        cnt[s[i]] += 1;
    }

    println!("{}", doit(perm));
}