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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

s = input()
s2= list(s)
if s2==s2[::-1]:
  print(0)
  exit()
s1 = []
le = []
lex = []
cnt= 0
for i in list(s):
  if i!="x":
    le.append(cnt)
    s1.append(i)
  else:
    lex.append(cnt)
  cnt+=1
if s1!=s1[::-1]:
  print(-1)
  exit()
ans = []
res=0
if len(le)%2==1:
  midlle=le[len(le)//2]
  for i in lex:
    if not i-midlle in ans:
      res+=1
      ans.append(abs(i-midlle))
    else:
      res-=1
  print(res)
else:
  midlle=(le[len(le)//2]+le[len(le)//2-1])//2
  for i in lex:
    if not i-midlle in ans:
      if i-midlle==0:
        continue
      res+=1
      ans.append(abs(i-midlle))
    else:
      res-=1
  print(res)