Problem:
Score : 400 points

Problem Statement

We have a string s consisting of lowercase English letters.
Snuke can perform the following operation repeatedly:

Insert a letter x to any position in s of his choice, including the beginning and end of s.

Snuke's objective is to turn s into a palindrome.
Determine whether the objective is achievable. If it is achievable, find the minimum number of operations required.

Notes

A palindrome is a string that reads the same forward and backward.
For example, a, aa, abba and abcba are palindromes, while ab, abab and abcda are not.

Constraints

1 \leq |s| \leq 10^5

s consists of lowercase English letters.

Input

Input is given from Standard Input in the following format:

s

Output

If the objective is achievable, print the number of operations required.
If it is not, print -1 instead.

Sample Input 1

xabxa

Sample Output 1

2

One solution is as follows (newly inserted x are shown in bold):

xabxa → xaxbxa → xaxbxax

Sample Input 2

ab

Sample Output 2

-1

No sequence of operations can turn s into a palindrome.

Sample Input 3

a

Sample Output 3

0

s is a palindrome already at the beginning.

Sample Input 4

oxxx

Sample Output 4

3

One solution is as follows:

oxxx → xoxxx → xxoxxx → xxxoxxx

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

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Globalization;
using System.Diagnostics;
using static System.Console;
//using System.Numerics;
//using static System.Math;
using System.Text;

class Program
{
    static void Main()
    {
        //SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
        new Program().solve();
        Out.Flush();
    }
    Scanner cin = new Scanner();
    readonly int[] dd = { 0, 1, 0, -1, 0 }; //→↓←↑
    readonly int mod = 1000000007;

    string S;
    int N;
    void solve()
    {
        S = cin.next;
        N = S.Length;
        int xcnt = 0;
        var L = new StringBuilder();
        for (int i = 0; i < N; i++)
        {
            if (S[i] != 'x')
            {
                L.Append(S[i]);
            }
        }
        var M = L.Length;
        //WriteLine(L);
        for (int i = 0; i < M / 2; i++)
        {
            if (L[i] != L[M - 1 - i])
            {
                WriteLine(-1);
                return;
            }
        }

        int idx = -1;

        if (M == 0)
        {
            WriteLine(0);
        }
        else if (M % 2 == 1)
        {
            int cnt = 0;
            var A = new int[M / 2 + 1];
            var B = new int[M / 2 + 1];
            for (int i = 0; i < N; i++)
            {
                if (S[i] != 'x')
                {
                    cnt++;
                }
                else
                {
                    if (cnt <= M / 2)
                    {
                        A[M / 2 - cnt]++;
                    }
                    else
                    {
                        B[cnt - M / 2 - 1]++;
                    }
                }


            }
            long sum = 0;
            //WriteLine(string.Join(" ", A));
            //WriteLine(string.Join(" ", B));
            for (int i = 0; i < M / 2 + 1; i++)
            {
                sum += Math.Abs(A[i] - B[i]);
            }
            WriteLine(sum);


        }
        else
        {
            int cnt = 0;
            var A = new int[M / 2];
            var B = new int[M / 2];
            for (int i = 0; i < N; i++)
            {
                if (S[i] != 'x')
                {
                    cnt++;
                }
                else
                {
                    if (cnt <= M / 2 - 1)
                    {
                        A[M / 2 - cnt - 1]++;
                    }
                    else if (cnt >= M / 2 + 1)
                    {
                        B[cnt - M / 2 - 1]++;
                    }
                }


            }
            long sum = 0;
            //WriteLine(string.Join(" ", A));
            //WriteLine(string.Join(" ", B));
            for (int i = 0; i < M / 2; i++)
            {
                sum += Math.Abs(A[i] - B[i]);
            }
            WriteLine(sum);
        }
    }

}

class Scanner
{
    string[] s; int i;
    char[] cs = new char[] { ' ' };
    public Scanner() { s = new string[0]; i = 0; }
    public string[] scan { get { return ReadLine().Split(); } }
    public int[] scanint { get { return Array.ConvertAll(scan, int.Parse); } }
    public long[] scanlong { get { return Array.ConvertAll(scan, long.Parse); } }
    public double[] scandouble { get { return Array.ConvertAll(scan, double.Parse); } }
    public string next
    {
        get
        {
            if (i < s.Length) return s[i++];
            string st = ReadLine();
            while (st == "") st = ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            i = 0;
            return next;
        }
    }
    public int nextint { get { return int.Parse(next); } }
    public long nextlong { get { return long.Parse(next); } }
    public double nextdouble { get { return double.Parse(next); } }
}