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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.*;
import java.util.*;
import java.math.*;
// import java.awt.Point;
 
public class Main {
    InputStream is;
    PrintWriter out;
    String INPUT = "";
 
    static int mod = 1_000_000_007;
    // int mod = 998244353;
    long inf = Long.MAX_VALUE/2;

    void solve(){
        char[] s = ns().toCharArray();
        int n = s.length;
        long ans1 = func(s);
        char[] s2 = new char[n];
        for(int i = 0; i < n; i++){
            s2[i] = s[n-1-i];
        }
        long ans2 = func(s2);
        out.println(Math.min(ans1, ans2));
    }

    long func(char[] s){
        int n = s.length;
        int[] num = new int[26];
        int[][] list = new int[26][n];
        int[] idx = new int[26];
        for(int i = 0; i < n; i++){
            num[s[i]-'a']++;
            list[s[i]-'a'][idx[s[i]-'a']++] = i;
        }
        int odd = 0;
        for(int i = 0; i < 26; i++){
            if(num[i]%2==1) odd++;
        }
        if(odd>=2){
            return -1;
        }
        int[] target = new int[n];
        int[] count = new int[26];
        int p = 0;
        for(int i = 0; i < n; i++){
            if(count[s[i]-'a']<num[s[i]-'a']/2){
                target[p] = s[i]-'a';
                p++;
                count[s[i]-'a']++;
            }
            if(num[s[i]-'a']%2==1){
                target[(n-1)/2] = s[i]-'a';
            }
        }
        for(int i = 0; i < n; i++){
            target[n-1-i] = target[i];
        }
        // for(int i = 0; i < n; i++){
        //     out.print(target[i]+" ");
        // }
        // out.println();
        // idx = new int[26];
        // for(int i = 0; i < n; i++){
        //     out.print(list[target[i]][idx[target[i]]++]+" ");
        // }
        // out.println();
        idx = new int[26];
        BIT bit = new BIT(n);
        long sum = 0;
        for(int i = 0; i < n; i++){
            bit.accumlate(list[target[i]][idx[target[i]]++],1);
            sum += bit.sum(i+1,n);
        }
        return sum;
        // out.println(sum);
    }

    class BIT {
    private int n;
    private long[] bit;
    public BIT(int n) {
        this.n = n;
        bit = new long[n+1];
    }

    public void accumlate(int index,long num) {
        index++;
        while(index<=n) {
            bit[index] += num;
            index+=index&-index;
        }
    }

    /* [begin , end) */
    public long sum(int begin,int end) {
        return sum(end) - sum(begin);
    }

    private long sum(int i) {
        long s = 0;
        while(i>0) {
            s+=bit[i];
            i-=i&-i;
        }
        return s;
    }

    public long get(int index) {
        return sum(index,index+1);
    }

    // public void set(int index,long num) {
    //     accumlate(index,num-(sum(index)-sum(index-1)));
    // }

    public String toString() {
        long[] value = new long[n];
        for(int i=0;i<n;i++) {
            value[i] = get(i);
        }
        return Arrays.toString(value);
    }
}
   
    void run() throws Exception
    {
        is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        out = new PrintWriter(System.out);
        long s = System.currentTimeMillis();
        solve();
        out.flush();
        if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
    }
    
    public static void main(String[] args) throws Exception { new Main().run(); }
    
    private byte[] inbuf = new byte[1024];
    private int lenbuf = 0, ptrbuf = 0;
    
    private int readByte()
    {
        if(lenbuf == -1)throw new InputMismatchException();
        if(ptrbuf >= lenbuf){
            ptrbuf = 0;
            try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
            if(lenbuf <= 0)return -1;
        }
        return inbuf[ptrbuf++];
    }
    
    private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
    private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
    
    private double nd() { return Double.parseDouble(ns()); }
    private char nc() { return (char)skip(); }
    
    private String ns()
    {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while(!(isSpaceChar(b) && b != ' ')){
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    
    private char[] ns(int n)
    {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while(p < n && !(isSpaceChar(b))){
            buf[p++] = (char)b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }
    
    private char[][] nm(int n, int m)
    {
        char[][] map = new char[n][];
        for(int i = 0;i < n;i++)map[i] = ns(m);
        return map;
    }
    
    private int[] na(int n)
    {
        int[] a = new int[n];
        for(int i = 0;i < n;i++)a[i] = ni();
        return a;
    }
    
    private int ni()
    {
        int num = 0, b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private long nl()
    {
        long num = 0;
        int b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); }
 
}