output_description: 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.
  
  * * *
input_description: Input is given from Standard Input in the following format:
  
      
      
      S
attempt: #include <bits/stdc++.h>
  
  using namespace std;
  using ll = long long;
  using PII = std::pair<int, int>;
  using PLL = std::pair<ll, ll>;
  
  #define rep(i, n) for (int i = 0; i < (int)(n); i++)
  #define rep2(i, s, n) for (int i = (s); i < (int)(n); i++)
  
  bool k_flip(string s, int k)
  {
      int n = s.length();
  
      int status = 0;
      deque<int> endindex;
  
      rep(i, n - k + 1)
      {
          if (endindex.size() % 2 == 0 && s[i] == '1')
          {
              s[i] = '0';
              endindex.push_back(i + k - 1);
          }
          else if (endindex.size() % 2 == 1 && s[i] == '1')
          {
              s[i] = '0';
          }
          else if (endindex.size() % 2 == 1 && s[i] == '0')
          {
              endindex.push_back(i + k - 1);
          }
  
          if (endindex.front() == i)
              endindex.pop_front();
      }
  
      rep2(i, n - k + 1, n)
      {
          if (endindex.size() % 2 == 1)
          {
              if (s[i] == '0')
                  s[i] = '1';
              else
                  s[i] = '0';
          }
  
          if (endindex.front() == i)
              endindex.pop_front();
      }
  
      rep(i, k)
          if (s[i] == '1')
              status++;
  
      if (!status)
          return 1;
      else
          return 0;
  }
  
  int main()
  {
  
  #ifdef DEBUG
      cout << "DEBUG MODE" << endl;
      ifstream in("input.txt"); //for debug
      cin.rdbuf(in.rdbuf());    //for debug
  #endif
  
      string s;
      cin >> s;
      int ok, ng, mid;
  
      if (k_flip(s, s.length()))
          cout << s.length() << endl;
      else
      {
          ok = 0, ng = s.length();
          while (ng - ok> 1)
          {
              mid = (ok + ng) / 2;
              if (k_flip(s, mid))
                  ok = mid;
              else
                  ng = mid;
              
          }
          cout << ok << endl;
      }
  
      return 0;
  }
problem_description: 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`.
samples: [{"input": "010", "output": "2\n    \n\nWe can turn all the characters of S into `0` by the following operations:\n\n  * Perform the operation on the segment S[1,3] with length 3. S is now `101`.\n  * Perform the operation on the segment S[1,2] with length 2. S is now `011`.\n  * Perform the operation on the segment S[2,3] with length 2. S is now `000`.\n\n* * *"}, {"input": "100000000", "output": "8\n    \n\n* * *"}, {"input": "00001111", "output": "4"}]