title: Count Digits Factorial Set 2
signature: int countDigitsFactorialSet2(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(56, 75); 
      cout << "TEST-" << 0 << "..."
           <<  result
           << "\n";
  
      result = driver(92, 143); 
      cout << "TEST-" << 1 << "..."
           <<  result
           << "\n";
  
      result = driver(52, 68); 
      cout << "TEST-" << 2 << "..."
           <<  result
           << "\n";
  
      result = driver(96, 150); 
      cout << "TEST-" << 3 << "..."
           <<  result
           << "\n";
  
      result = driver(96, 150); 
      cout << "TEST-" << 4 << "..."
           <<  result
           << "\n";
  
      result = driver(63, 88); 
      cout << "TEST-" << 5 << "..."
           <<  result
           << "\n";
  
      result = driver(51, 67); 
      cout << "TEST-" << 6 << "..."
           <<  result
           << "\n";
  
      result = driver(79, 117); 
      cout << "TEST-" << 7 << "..."
           <<  result
           << "\n";
  
      result = driver(70, 101); 
      cout << "TEST-" << 8 << "..."
           <<  result
           << "\n";
  
      result = driver(9, 6); 
      cout << "TEST-" << 9 << "..."
           <<  result
           << "\n";
  
      return 0;
  }
source_py: def count_digits_factorial_set_2(n):
      if (n < 0):
          return 0
      if (n <= 1):
          return 1
      x = ((n * math.log10((n / math.e))) + (math.log10(((2 * math.pi) * n)) / 2.0))
      return (math.floor(x) + 1)
source_cpp: long long count_digits_factorial_set_2(int n) {
    if ( n < 0 ) return 0;
    if ( n <= 1 ) return 1;
    double x = ( ( n * log10 ( n / M_E ) + log10 ( 2 * M_PI * n ) / 2.0 ) );
    return floor ( x ) + 1;
  }