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 Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

--{-# LANGUAGE BangPatterns #-}
--{-# LANGUAGE ScopedTypeVariables #-}
--{-# LANGUAGE FlexibleContexts #-}
--{-# LANGUAGE ViewPatterns #-}
--{-# LANGUAGE OverloadedStrings #-}
--{-# LANGUAGE Strict #-}
--{-# LANGUAGE NumericUnderscores #-}
--{-# LANGUAGE BlockArguments #-}
{-# LANGUAGE MultiWayIf #-}

import qualified Data.Vector as V
import qualified Data.Vector.Unboxed as VU
import qualified Data.Vector.Unboxed.Mutable as VUM
import qualified Data.ByteString.Char8 as BC
import qualified Data.Map.Strict as MPS
import qualified Data.Map as MP
import qualified Data.Set as ST
import qualified Data.Sequence as SQ
import Data.Array
import Data.Array.Unboxed
import Data.Array.ST
import Data.Array.IO
import Data.Maybe
import Data.Ord
import Data.Ratio
import Data.Char
import Data.Bits
import Data.List
import Data.Tuple
import Data.Functor
import Data.IORef
import Data.STRef
import Control.Applicative
import Control.Monad
import Control.Monad.ST
import Control.Monad.State.Strict
import Debug.Trace
-- import qualified Data.Vector.Algorithms.Merge as VAM
-- import qualified Data.Heap as HP
-- import Numeric.Extra
-- import Data.Tuple.Extra
-- import Data.List.Extra

--------------------------------------------------------------------------
count sq
    | SQ.length sq < 2 = 0
    | otherwise =
        case SQ.viewl sq of
            l SQ.:< sq' ->
                case SQ.viewr sq' of
                    sq'' SQ.:> r ->
                        if  |   l==r -> count sq''
                            |   (l/='x') && (r/='x') && (l/=r) -> -1
                            |   (l/='x') -> 1 + count ('x' SQ.<| sq)
                            |   (r/='x') -> 1 + count (sq SQ.|> 'x')


solve xs = count xs'
    where
        xs' = SQ.fromList xs

main = do
    xs <- str
    print $ solve xs
--------------------------------------------------------------------------

-- Input Util
int :: IO Int
int = bsToInt <$> BC.getLine

double :: IO Double
double = bsToDouble <$> BC.getLine

str :: IO String
str = BC.unpack <$> BC.getLine

strBS :: IO BC.ByteString
strBS = BC.getLine

-- convert
bsToInt :: BC.ByteString -> Int
bsToInt = fst . fromJust . BC.readInt

bsToDouble :: BC.ByteString -> Double
bsToDouble = read . BC.unpack

bsToIntTuple :: BC.ByteString -> (Int, Int)
bsToIntTuple bs = (a,b)
    where
        Just (a,bs') = parseInt bs
        Just (b,_) = parseInt bs'

bsToIntTriple :: BC.ByteString -> (Int, Int, Int)
bsToIntTriple bs = (a,b,c)
    where
        Just (a,bs') = parseInt bs
        Just (b,bs'') = parseInt bs'
        Just (c,_) = parseInt bs''

parseInt :: BC.ByteString -> Maybe (Int, BC.ByteString)
parseInt = BC.readInt . BC.dropWhile isSpace

-- single line
fromSLineL :: (BC.ByteString -> a) -> IO [a]
fromSLineL f =  map f . BC.words <$> strBS

-- from single line to List / VU.Vector 
sLineToIntL :: IO [Int]
sLineToIntL = fromSLineL bsToInt

sLineToDoubleL :: IO [Double]
sLineToDoubleL = fromSLineL bsToDouble

sLineToStrL :: IO [String]
sLineToStrL = fromSLineL BC.unpack

sLineToStrBSL :: IO [BC.ByteString]
sLineToStrBSL = fromSLineL id 

sLineToIntV :: Int -> IO (VU.Vector Int)
sLineToIntV n = VU.unfoldrN n parseInt <$> BC.getLine

sLineToDoubleV :: IO (VU.Vector Double)
sLineToDoubleV = VU.fromList . map bsToDouble . BC.words <$> BC.getLine

-- multiple lines
fromMLinesL :: Int -> (BC.ByteString -> a) -> IO [a]
fromMLinesL n f = replicateM n (f <$> strBS)

fromMLinesV :: VU.Unbox a => Int -> (BC.ByteString -> a) -> IO (VU.Vector a)
fromMLinesV n f = VU.replicateM n (f <$> strBS)

-- from multiple lines to List / VU.Vector
mLinesToIntL :: Int -> IO [Int]
mLinesToIntL n = fromMLinesL n bsToInt

mLinesToDoubleL :: Int -> IO [Double]
mLinesToDoubleL n = fromMLinesL n bsToDouble

mLinesToStrL :: Int -> IO [String]
mLinesToStrL n = fromMLinesL n BC.unpack

mLinesToStrBSL :: Int -> IO [BC.ByteString]
mLinesToStrBSL n = fromMLinesL n id

mLinesToTupleL :: Int -> IO [(Int, Int)]
mLinesToTupleL n = fromMLinesL n bsToIntTuple

mLinesToTripleL :: Int -> IO [(Int, Int, Int)]
mLinesToTripleL n = fromMLinesL n bsToIntTriple

mLinesToIntV :: Int -> IO (VU.Vector Int)
mLinesToIntV n = fromMLinesV n bsToInt

mLinesToDoubleV :: Int -> IO (VU.Vector Double)
mLinesToDoubleV n = fromMLinesV n bsToDouble

mLinesToTupleV :: Int -> IO (VU.Vector (Int, Int))
mLinesToTupleV n = fromMLinesV n bsToIntTuple
    
mLinesToTripleV :: Int -> IO (VU.Vector (Int, Int, Int))
mLinesToTripleV n = fromMLinesV n bsToIntTriple

-- output
yesnoL :: Bool -> IO ()
yesnoL cond
    | cond = putStrLn "Yes"
    | otherwise = putStrLn "No"

yesnoU :: Bool -> IO ()
yesnoU cond
    | cond = putStrLn "YES"
    | otherwise = putStrLn "NO"

-- others
strToChr :: String -> Char
strToChr [x] = x

chrToStr :: Char -> String
chrToStr x = [x]

m1 :: Int -> Int
m1 = subtract 1

toDouble :: Int -> Double
toDouble = fromIntegral

toInt :: Double -> Int
toInt = floor

sqToList :: SQ.Seq a -> [a]
sqToList sq =
    case SQ.viewl sq of
        l SQ.:< sq' -> l : sqToList sq'
        SQ.EmptyL -> []