hi(proizvod help)

hi i was trying to solve proizvod in C and it works only for 3 test cases. can someone check my noble code and tell me where is my mistake.
thanks

#include <stdio.h>
int last_two(long long int n);
int main(void)
{
  int n;
  long long int fak=1;
  scanf("%d",&n);

  while(n>0)
  {
    fak=fak*n;
    fak=last_two(fak);
    n--;
}

  printf("%lld\n",fak);
  return 0;
}
int last_two(long long int n)
{
  int i=0;
  int dig;
  int a[3];
  while(n>0&&i<3)
  {
    dig=n;
    if(dig!=0)
    a[i++]=dig;
    n/=10;
  }
  return a[1]*10+a[0];
}

You are remembering only the last two non-zero digits but in some cases more digits are relevant, for example 325*4 = 1300, and the last non-zero digit is 3, but your program remembers only 2 and 5; 25*4=100, and it would print 1.

if n is two-digit we remember the last two digit
if n is n-digit we remember the last n digits of fak
am i right?

my idea for the task is different, but i found out that a 5-digit memorization passes the tests

Yes, five digits are enough :)