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 Ruby (2.3.3) (judge verdict: Runtime Error)

def palin?(t)
  n = t.size
  n.times{|i| return false if t[i] != t[n - i - 1]}
  true
end

s = gets.chomp
n = s.size

t = s.chars.zip(0...n).select{|x| x[0] != 'x'}

if not palin?(t.map{|x| x[0]})
  p -1
else
  i = (t.size - 1) / 2
  i = t[i][1]
  j = t.size / 2
  j = t[j][1]
  ans = 0
  while i >= 0 && j < n
    if s[i] == s[j]
      i -= 1
      j += 1
    elsif s[i] == 'x'
      ans += 1
      i -= 1
    elsif s[j] == 'x'
      ans += 1
      j += 1
    end
  end
  while j < n
    ans += 1
    j += 1
  end
  while i >= 0
    i -= 1
    ans += 1
  end
  p ans
end