Problem:
Score : 500 points

Problem Statement

You are given a string S consisting of 0 and 1.
Find the maximum integer K not greater than |S| such that we can turn all the characters of S into 0 by repeating the following operation some number of times.

Choose a contiguous segment [l,r] in S whose length is at least K (that is, r-l+1\geq K must be satisfied). For each integer i such that l\leq i\leq r, do the following: if S_i is 0, replace it with 1; if S_i is 1, replace it with 0.

Constraints

1\leq |S|\leq 10^5

S_i(1\leq i\leq N) is either 0 or 1.

Input

Input is given from Standard Input in the following format:

S

Output

Print the maximum integer K such that we can turn all the characters of S into 0 by repeating the operation some number of times.

Sample Input 1

010

Sample Output 1

2

We can turn all the characters of S into 0 by the following operations:

Perform the operation on the segment S[1,3] with length 3. S is now 101.

Perform the operation on the segment S[1,2] with length 2. S is now 011.

Perform the operation on the segment S[2,3] with length 2. S is now 000.

Sample Input 2

100000000

Sample Output 2

8

Sample Input 3

00001111

Sample Output 3

4

Solution in Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

import qualified Data.Vector as V


odd_solver::V.Vector Char->Int
odd_solver v = let m = div (V.length v) 2 in
               let s = div (V.length (last (filter same [V.slice (m-s) ((2*s)+1) v |s <- [0..m]]))) 2in
               m+s+1

even_solver::V.Vector Char->Int
even_solver v = let m = div (V.length v) 2 in
                let s = div (V.length (last (filter same [V.slice (m-s) (2*s) v | s <- [0..m]]))) 2 in
                m+s

same::V.Vector Char->Bool
same v        =if v == V.empty then True else V.foldl (\ b -> \ x -> ((V.head v)==x)&&b) True v

total_solver::String->Int
total_solver ls = let v = V.fromList ls in
                  if mod (V.length v) 2 == 1 then odd_solver v else even_solver v

main::IO()
main=do
  str<-getLine
  print (total_solver str)