problem 20

/*n! means n × (n − 1) × ... × 3 × 2 × 1

For example, 10! = 10 × 9 × ... × 3 × 2 × 1 = 3628800,
and the sum of the digits in the number 10! is 3 + 6 + 2 + 8 + 8 + 0 + 0 = 27.

Find the sum of the digits in the number 100!
*/
#include<iostream> 
#include<string>
#include<sstream>
#include<vector>
#include<math.h>
#include <bits/stdc++.h> 
#include <boost/multiprecision/cpp_int.hpp> 
#include<boost/lexical_cast.hpp>
using namespace std;

using boost::multiprecision::cpp_int; 
cpp_int Factorial(int number) 
{ 
    cpp_int num = 1; 
    for (int i = 1; i <= number; i++) 
        num = num * i; 
    return num; 
} 
  
int main() 
{   int result = 0;
    int number = 100; 
    cpp_int fact = Factorial(number); 
    string  factorial = boost::lexical_cast<string>(fact);
    //cout << factorial + 1 <<endl;
    for(char x : factorial){
      result += stoi(&x); 
    } 
    cout << result <<endl;
    return 0; 
}