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 Lua (5.3.2) (judge verdict: Accepted)

local s = io.read()
local n = #s
local cnt = 0
local t = {}
for i = 1, n do
  local sstr = s:sub(i, i)
  if sstr == "x" then
    cnt = cnt + 1
  else
    local tmp = {}
    tmp.c = cnt
    tmp.s = sstr
    table.insert(t, tmp)
    cnt = 0
  end
end
local ret = 0
local mab = math.abs
local nt = #t
local isok = true

local half = nt // 2
for i = 1, half do
  if t[i].s ~= t[nt + 1 - i].s then
    isok = false
    break
  else
    if i == 1 then
      ret = ret + mab(t[i].c - cnt)
    else
      ret = ret + mab(t[i].c - t[nt + 2 - i].c)
    end
  end
end
if nt % 2 == 1 then
  if nt == 1 then
    ret = ret + mab(t[1].c - cnt)
  else
    ret = ret + mab(t[half + 1].c - t[half + 2].c)
  end
end
print(isok and ret or -1)