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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

//「幾何、中央値など、最大値を求めるときは二分探索法」を考える。

using System;
using System.Linq;//リストの使用
using System.Collections.Generic;
class Program
{
static string s = Console.ReadLine();
static int n = s.Length;
static bool isChanging;

	static void Main()
	{
    Console.WriteLine(Search(1, n, 1));  
	}

  static long Search(long min, long max, int MinorMax)//二分探索法で最小値-1最大値1を求める
  {
    while (true)
    {
      long mid = min + (max - min) / 2;
      if(MinorMax == 1)
      {
        if(Check(mid)) min = mid;//さらに大きくても成り立つかも
        else max = mid;
      }else
      {
        if(Check(mid)) max = mid;//さらに小さくても成り立つかも
        else min = mid;
      }

      if(max - min <= 1)
      {
        if(MinorMax == 1)
        {
          if(Check(max)) return max;//最大値で成り立つかの確認を優先
          else return min;
        }else
        {
          if(Check(min)) return min;//最小値で成り立つかの確認を優先
          else return max;
        }

      break;
      }  
    }
  }

  static bool Check(long testNum)
  {//左から順に全て0にした時、左からtestNum個が全て0になれば良い。
    isChanging = false;

    for(int i = 0; i <= n-(int)testNum; i++)
    {
      if(s[i] == '0' && isChanging || s[i] == '1' && !isChanging)
      {
        isChanging = !isChanging;
      }
    }

    for(int i = n-(int)testNum+1; i < testNum; i++)
    {
      if(s[i] == '0' && isChanging || s[i] == '1' && !isChanging) return false;
    }

    return true;
  }  
}