title: Maximum Games Played Winner
signature: int maximumGamesPlayedWinner(int n) {
test_code: #include <algorithm>
  #include <assert.h>
  #include <cstdlib>
  #include <iostream>
  #include <map>
  #include <set>
  #include <string>
  #include <tuple> 
  #include <unordered_map>
  #include <vector>
  #include <math.h>
  #include <cmath>
  #include <bits/stdc++.h>
  #include <numeric>
  #include <functional>
  
  using namespace std;
  
  // SOLUTION CODE
  // ============================================
  PLACEHOLDER_CODE_BODY
  
  // TESTING CODE 
  // ============================================
  bool validateSolution(int actual, int expected){
      return actual == expected;
  }
  
  string driver(int n, int expected){
      try
      {
          if (validateSolution(PLACEHOLDER_FN_NAME(n), expected)){
              return "PASSED";
          }
          return "FAILED";
      }
      catch (const std::overflow_error& exception_obj)
      {
          return typeid(exception_obj).name();
      }
      catch (const std::runtime_error& exception_obj)
      {
          return typeid(exception_obj).name();
      }
      catch (const std::exception& exception_obj)
      {
          return typeid(exception_obj).name();
      }
      catch (...)
      {
          return "UNK_ERROR";
      }
  }
  
  int main() {
      string result = "";
  
      result = driver(73, 8); 
      cout << "TEST-" << 0 << "..."
           <<  result
           << "\n";
  
      result = driver(28, 6); 
      cout << "TEST-" << 1 << "..."
           <<  result
           << "\n";
  
      result = driver(33, 6); 
      cout << "TEST-" << 2 << "..."
           <<  result
           << "\n";
  
      result = driver(23, 6); 
      cout << "TEST-" << 3 << "..."
           <<  result
           << "\n";
  
      result = driver(84, 8); 
      cout << "TEST-" << 4 << "..."
           <<  result
           << "\n";
  
      result = driver(31, 6); 
      cout << "TEST-" << 5 << "..."
           <<  result
           << "\n";
  
      result = driver(48, 7); 
      cout << "TEST-" << 6 << "..."
           <<  result
           << "\n";
  
      result = driver(46, 7); 
      cout << "TEST-" << 7 << "..."
           <<  result
           << "\n";
  
      result = driver(45, 7); 
      cout << "TEST-" << 8 << "..."
           <<  result
           << "\n";
  
      result = driver(90, 9); 
      cout << "TEST-" << 9 << "..."
           <<  result
           << "\n";
  
      return 0;
  }
source_py: def maximum_games_played_winner(N):
      dp = [0 for i in range(N)]
      dp[0] = 1
      dp[1] = 2
      i = 1
      while (dp[i] <= N):
          i = (i + 1)
          dp[i] = (dp[(i - 1)] + dp[(i - 2)])
      return (i - 1)
source_cpp: int maximum_games_played_winner(int N) {
    int dp [ N ];
    dp [ 0 ] = 1;
    dp [ 1 ] = 2;
    int i = 2;
    do {
      dp [ i ] = dp [ i - 1 ] + dp [ i - 2 ];
    }
    while ( dp [ i ++ ] <= N );
    return ( i - 2 );
  }