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# (.NET Core 3.1.201) (judge verdict: Time Limit Exceeded)

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


class Program
{
    static void Main(string[] args)
    {
        // 入力
        var s = Console.ReadLine();
        var r = new string(s.Reverse().ToArray());
        var ans = 0;

        for (int i = 0; i < s.Length; i++)
        {
            if (s[i] != r[i])
            {
                if (s[i] != 'x' && r[i] != 'x')
                {
                    ans = -1;
                    break;
                }
                else if (s[i] == 'x')
                {
                    r = r.Insert(i, "x");
                    s = new string(r.Reverse().ToArray());
                    ans++;
                }
                else
                {
                    s = s.Insert(i, "x");
                    r = new string(s.Reverse().ToArray());
                    ans++;
                }
            }
        }


        // 出力
        Console.WriteLine(ans);
    }
}