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 OCaml (4.02.3) (judge verdict: Accepted)

let pr x = print_endline @@ string_of_int x

let max (a : int) (b : int) =
  if a > b then a else b

let min (a : int) (b : int) =
  if a < b then a else b

let fold f init s =
  let rec iter i res =
    if i < 0 then res else iter (i - 1) (f res s.[i]) in
  iter (String.length s - 1) init

let solve seq =
  let len = String.length seq in
  let (_,_,res) = fold
                    (fun (cnt,pre,mv) x ->
                      if x != pre then
                        (cnt+1,x,min mv (max cnt (len - cnt)))
                      else (cnt+1,x,mv))
                    (0,seq.[0],len) seq in res

let () = input_line stdin
         |> solve
         |> pr