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: Time Limit Exceeded)

import java.io.*;
import java.util.*;

public class Main {
  private static Integer ZERO = Integer.valueOf(0);
  private static int ALPHABET_SIZE = 26;

  private static UpdateRangeGetRangeSegmentTree.Operator<Integer, Integer> OPERATOR = new UpdateRangeGetRangeSegmentTree.Operator<Integer, Integer>() {
    public Integer multiplyLazyValue(Integer lazy, int count) {
      return lazy;
    }
    public Integer getUnitLazy() {
      return ZERO;
    }
    public Integer mergeLazyValue(Integer lazy1, Integer lazy2) {
      return lazy1 + lazy2;
    }
    public Integer apply(Integer value, Integer lazy) {
      return value + lazy;
    }
    public Integer mergeValue(Integer smallValue, Integer largeValue) {
      return smallValue + largeValue;
    }
    public Integer getUnitValue() {
      return ZERO;
    }
  };

  private static long solve(char[] cs) {
    List<Deque<Integer>> dequeList = new ArrayList<>();
    for (int i = 0; i < ALPHABET_SIZE; i++) {
      dequeList.add(new ArrayDeque<>());
    }
    for (int i = 0; i < cs.length; i++) {
      dequeList.get(cs[i] - 'a').add(i);
    }

    int numOddQueueCount = 0;
    for (Deque<Integer> deque : dequeList) {
      if (deque.size() % 2 == 1) {
        numOddQueueCount++;
      }
    }
    if (numOddQueueCount > 1) {
      return -1;
    }

    Integer[] initialValues = new Integer[cs.length];
    for (int i = 0; i < cs.length; i++) {
      initialValues[i] = i;
    }
    UpdateRangeGetRangeSegmentTree<Integer, Integer> segmentTree = new UpdateRangeGetRangeSegmentTree<>(OPERATOR, initialValues);
    long answer = 0;
    for (int i = 0; i < cs.length / 2; i++) {
      int minCost = Integer.MAX_VALUE;
      int minCostIndex = -1;
      for (int j = 0; j < ALPHABET_SIZE; j++) {
        Deque<Integer> deque = dequeList.get(j);
        if (deque.size() < 2) {
          continue;
        }
        int leftIndex = segmentTree.get(deque.peekFirst());
        int rightIndex = segmentTree.get(deque.peekLast());
        int cost = Math.abs(leftIndex - i) + Math.abs(cs.length - 1 - i - rightIndex);
        if (minCost > cost) {
          minCost = cost;
          minCostIndex = j;
        }
      }
      answer += minCost;

      segmentTree.update(0, dequeList.get(minCostIndex).pollFirst(), 1);
      segmentTree.update(dequeList.get(minCostIndex).pollLast() + 1, cs.length, -1);
    }

    return answer;
  }

  private static void execute(ContestReader reader, ContestWriter out) {
    char[] cs = reader.nextCharArray();
    out.println(solve(cs));
  }
  
  public static void main(String[] args) {
    ContestReader reader = new ContestReader(System.in);
    ContestWriter out = new ContestWriter(System.out);
    execute(reader, out);
    out.flush();
  }
}

// Verify CODE FESTIVAL 2015 final D
// https://atcoder.jp/contests/code-festival-2015-final-open/tasks/codefestival_2015_final_d

class UpdateRangeGetRangeSegmentTree<T, S> {
  public interface Operator<T, S> {
    T multiplyLazyValue(T lazy, int count);
    T getUnitLazy();
    T mergeLazyValue(T lazy1, T lazy2);
    S apply(S value, T lazy);
    S mergeValue(S smallValue, S largeValue);
    S getUnitValue();
  }
  
  private final Operator<T, S> operator;
  private final int n;
  private final List<T> lazies;
  private final List<S> values;
  
  public UpdateRangeGetRangeSegmentTree(Operator<T, S> operator, S[] initialValues) {
    this.operator = operator;
    
    int tempN = 1;
    while (tempN < initialValues.length) {
      tempN *= 2;
    }
    n = tempN;
    lazies = new ArrayList<>();
    values = new ArrayList<>();
    for (int i = 0; i < 2 * n - 1; i++) {
      lazies.add(this.operator.getUnitLazy());
      values.add(null);
    }
    for (int i = 0; i < initialValues.length; i++) {
      values.set(i + n - 1, initialValues[i]);
    }
    for (int i = initialValues.length; i < n; i++) {
      values.set(i + n - 1, this.operator.getUnitValue());
    }
    for (int i = n - 2; i >= 0; i--) {
      values.set(i, this.operator.mergeValue(values.get(2 * i + 1), values.get(2 * i + 2)));
    }
  }
  
  private void eval(int k, int l, int r) {
    if (lazies.get(k).equals(operator.getUnitLazy())) {
      return;
    }
    values.set(k, operator.apply(values.get(k), operator.multiplyLazyValue(lazies.get(k), r - l)));
    if (r - l > 1) {
      lazies.set(2 * k + 1, operator.mergeLazyValue(lazies.get(2 * k + 1), lazies.get(k)));
      lazies.set(2 * k + 2, operator.mergeLazyValue(lazies.get(2 * k + 2), lazies.get(k)));
    }
    lazies.set(k, operator.getUnitLazy());
  }
  
  private void update(int a, int b, T lazy, int k, int l, int r) {
    eval(k, l, r);
    if (b <= l || r <= a) {
      return;
    }
    if (a <= l && r <= b) {
      lazies.set(k, operator.mergeLazyValue(lazies.get(k), lazy));
      eval(k, l, r);
    } else {
      update(a, b, lazy, 2 * k + 1, l, (l + r) / 2);
      update(a, b, lazy, 2 * k + 2, (l + r) / 2, r);
      values.set(k, operator.mergeValue(values.get(2 * k + 1), values.get(2 * k + 2)));
    }
  }
  
  public void update(int a, int b, T lazy) {
    update(a, b, lazy, 0, 0, n);
  }
  
  private S getRange(int a, int b, int k, int l, int r) {
    if (b <= l || r <= a) {
      return operator.getUnitValue();
    }
    eval(k, l, r);
    if (a <= l && r <= b) {
      return values.get(k);
    }
    S vl = getRange(a, b, 2 * k + 1, l, (l + r) / 2);
    S vr = getRange(a, b, 2 * k + 2, (l + r) / 2, r);
    return operator.mergeValue(vl, vr);
  }
  
  public S getRange(int a, int b) {
    return getRange(a, b, 0, 0, n);
  }
  
  public S get(int a) {
    return getRange(a, a + 1);
  }

  private void dump(List list) {
    int sum = 0;
    for (int i = 0; sum + (1 << i) <= 2 * n - 1; sum += 1 << i, i++) {
      for (int j = sum; j < sum + (1 << i); j++) {
        System.err.print(list.get(j));
        System.err.print(" ");
      }
      System.err.println();
    }
    System.err.println();
  }
  
  public void dump() {
    System.err.println("values: ");
    dump(values);
    System.err.println("lazies: ");
    dump(lazies);
  }
}

class ContestWriter extends PrintWriter {
  ContestWriter(PrintStream printeStream) {
    super(printeStream);
  }

  public void printList(List<? extends Object> list) {
    for (Object object : list) {
      println(object);
    }
  }

  public void printListOneLine(List<? extends Object> list) {
    List<String> stringList = new ArrayList<>();
    for (Object object : list) {
      stringList.add(object.toString());
    }
    println(String.join(" ", stringList));
  }
}

class ContestReader {
  private static final int BUFFER_SIZE = 1024;
  
  private final InputStream stream;
  private final byte[] buffer;
  private int pointer;
  private int bufferLength;
  
  ContestReader(InputStream stream) {
    this.stream = stream;
    this.buffer = new byte[BUFFER_SIZE];
    this.pointer = 0;
    this.bufferLength = 0;
  }
  
  private boolean hasNextByte() {
    if (pointer < bufferLength) {
      return true;
    }
    
    pointer = 0;
    try {
      bufferLength = stream.read(buffer);
    } catch (IOException e) {
      throw new RuntimeException(e);
    }
    return bufferLength > 0;
  }
  
  private int readByte() {
    if (hasNextByte()) {
      return buffer[pointer++];
    } else {
      return -1;
    }
  }
  
  private static boolean isPrintableChar(int c) {
    return 33 <= c && c <= 126;
  }
  
  public boolean hasNext() {
    while (hasNextByte() && !isPrintableChar(buffer[pointer])) {
      pointer++;
    }
    return hasNextByte();
  }
  
  public String next() {
    if (!hasNext()) {
      throw new NoSuchElementException();
    }
    StringBuilder sb = new StringBuilder();
    while(true) {
      int b = readByte();
      if (!isPrintableChar(b)) {
        break;
      }
      sb.appendCodePoint(b);
    }
    return sb.toString();
  }
  
  public String nextLine() {
    if (!hasNext()) {
      throw new NoSuchElementException();
    }
    StringBuilder sb = new StringBuilder();
    while(true) {
      int b = readByte();
      if (!isPrintableChar(b) && b != 0x20) {
        break;
      }
      sb.appendCodePoint(b);
    }
    return sb.toString();
  }
  
  public char nextChar() {
    return next().charAt(0);
  }
  
  public int nextInt() {
    if (!hasNext()) {
      throw new NoSuchElementException();
    }
    
    int n = 0;
    boolean minus = false;
    
    {
      int b = readByte();
      if (b == '-') {
        minus = true;
      } else if ('0' <= b && b <= '9') {
        n = b - '0';
      } else {
        throw new NumberFormatException();
      }
    }
    
    while(true){
      int b = readByte();
      if ('0' <= b && b <= '9') {
        n *= 10;
        n += b - '0';
      } else if (b == -1 || !isPrintableChar(b)) {
        return minus ? -n : n;
      } else {
        throw new NumberFormatException();
      }
    }
  }
  
  public long nextLong() {
    if (!hasNext()) {
      throw new NoSuchElementException();
    }
    
    long n = 0;
    boolean minus = false;
    
    {
      int b = readByte();
      if (b == '-') {
        minus = true;
      } else if ('0' <= b && b <= '9') {
        n = b - '0';
      } else {
        throw new NumberFormatException();
      }
    }
    
    while(true){
      int b = readByte();
      if ('0' <= b && b <= '9') {
        n *= 10;
        n += b - '0';
      } else if (b == -1 || !isPrintableChar(b)) {
        return minus ? -n : n;
      } else {
        throw new NumberFormatException();
      }
    }
  }
  
  public double nextDouble() {
    return Double.parseDouble(next());
  }
  
  public String[] next(int n) {
    String[] array = new String[n];
    for (int i = 0; i < n; i++) {
      array[i] = next();
    }
    return array;
  }
  
  public String[] nextLine(int n) {
    String[] array = new String[n];
    for (int i = 0; i < n; i++) {
      array[i] = nextLine();
    }
    return array;
  }
  
  public char[] nextChar(int n) {
    char[] array = new char[n];
    for (int i = 0; i < n; i++) {
      array[i] = nextChar();
    }
    return array;
  }
  
  public int[] nextInt(int n) {
    int[] array = new int[n];
    for (int i = 0; i < n; i++) {
      array[i] = nextInt();
    }
    return array;
  }
  
  public long[] nextLong(int n) {
    long[] array = new long[n];
    for (int i = 0; i < n; i++) {
      array[i] = nextLong();
    }
    return array;
  }
  
  public double[] nextDouble(int n) {
    double[] array = new double[n];
    for (int i = 0; i < n; i++) {
      array[i] = nextDouble();
    }
    return array;
  }
  
  public char[] nextCharArray() {
    return next().toCharArray();
  }
  
  public String[][] next(int n, int m) {
    String[][] matrix = new String[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        matrix[i][j] = next();
      }
    }
    return matrix;
  }
  
  public int[][] nextInt(int n, int m) {
    int[][] matrix = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        matrix[i][j] = nextInt();
      }
    }
    return matrix;
  }
  
  public char[][] nextChar(int n, int m) {
    char[][] matrix = new char[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        matrix[i][j] = nextChar();
      }
    }
    return matrix;
  }
  
  public long[][] nextLong(int n, int m) {
    long[][] matrix = new long[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        matrix[i][j] = nextLong();
      }
    }
    return matrix;
  }
  
  public double[][] nextDouble(int n, int m) {
    double[][] matrix = new double[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        matrix[i][j] = nextDouble();
      }
    }
    return matrix;
  }
  
  public char[][] nextCharArray(int n) {
    char[][] matrix = new char[n][];
    for (int i = 0; i < n; i++) {
      matrix[i] = next().toCharArray();
    }
    return matrix;
  }
}