I understand that the problem is in the fact function, as I can't print the input at some point, but how can I fix it?

function factDigits(n) {
  let factorial = fact(BigInt(n));
          
  return digits_count(factorial);
}
        
function fact(input) {
  if(input === 0n) {
    return 1n;
  }
          
  return input * fact(input-1n);
}
        
function digits_count(n) {
  let count = 0;
  if (n >= 1n) ++count;
        
  while (n / 10n >= 1n) {
   n /= 10n;
   ++count;
  }
        
  return count;
}