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: Wrong Answer)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text;

class TEST{
	static void Main(){
		Sol mySol =new Sol();
		mySol.Solve();
	}
}

class Sol{
	public void Solve(){
		
		List<char> L = new List<char>();
		List<int> Lidx = new List<int>();
		for(int i=0;i<N;i++) if(S[i] != 'x'){
			L.Add(S[i]);
			Lidx.Add(i);
		}
		
		if(L.Count == 0){
			Console.WriteLine(N % 2);
			return;
		}
		
		if(!IsPalindromic(L)){
			Console.WriteLine(-1);
			return;
		}
		
		int NN = L.Count;
		int l = NN/2;
		int r = NN/2;
		if(NN % 2 == 0) l--;
//		Console.WriteLine("{0} {1}",l,r);
		int ans = 0;
		while(l > 0){
			int cl = Lidx[l] - Lidx[l-1] - 1;
			int cr = Lidx[r+1] - Lidx[r] - 1;
			ans += Math.Abs(cl - cr);
			l--;
			r++;
		}
		int cl0 = Lidx[l];
		int cr0 = N - Lidx[r] - 1;
		ans += Math.Abs(cl0 - cr0);
		Console.WriteLine(ans);
	}
	
	bool IsPalindromic(List<char> L){
		int NN = L.Count;
		int l = NN/2;
		int r = NN/2;
		if(NN % 2 == 0) l--;
		while(l >= 0){
			if(L[l] != L[r]) return false;
			l--; r++;
		}
		return true;
	}
	
	int N;
	String S;
	public Sol(){
		S = rs();
		N = S.Length;
	}

	static String rs(){return Console.ReadLine();}
	static int ri(){return int.Parse(Console.ReadLine());}
	static long rl(){return long.Parse(Console.ReadLine());}
	static double rd(){return double.Parse(Console.ReadLine());}
	static String[] rsa(char sep=' '){return Console.ReadLine().Split(sep);}
	static int[] ria(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>int.Parse(e));}
	static long[] rla(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>long.Parse(e));}
	static double[] rda(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>double.Parse(e));}
}