Try this
#include "iostream"
#include "vector"
int n,remainder,sum;
int main ()
{
std::vector <int> digits(5000);
std::cin>>n;
digits[0]=1;
digits[1]=1;
for (int k=2;k<n+1;k++) {
for (int i=1;i<=digits[0];i++) {
digits[i]=digits[i]*k+remainder;
remainder=0;
if (digits[i]>9) {
remainder=digits[i]/10;
digits[i]%=10;
if (i==digits[0])
digits[0]++;
}
}
}
for (int i=digits[0];i>=1;i--)
sum+=digits[i];
std::cout<<sum;
}