(*
n! means n × (n ? 1) × ... × 3 × 2 × 1

Find the sum of the digits in the number 100!
*)

open Big_int;;

let b0 = big_int_of_int 0;;
let b1 = big_int_of_int 1;;
let b10 = big_int_of_int 10;;
let b100 = big_int_of_int 100;;

let rec fact i bf =
  if (i >= 100) then bf else
  fact (i+1) (mult_int_big_int i bf)
;;

let bn = fact 1 b1;;

let rec sumup bn s = 
  if(eq_big_int bn b0) then s else
  sumup (div_big_int bn b10) ( (int_of_big_int (mod_big_int bn b10))+s )
;;

Printf.printf "%s\n" (string_of_big_int bn);;
Printf.printf "%d\n" (sumup bn 0);;