Problem:
Score : 200 points

Problem Statement

There are N positive integers written on a blackboard: A_1, ..., A_N.

Snuke can perform the following operation when all integers on the blackboard are even:

Replace each integer X on the blackboard by X divided by 2.

Find the maximum possible number of operations that Snuke can perform.

Constraints

1 \leq N \leq 200

1 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the maximum possible number of operations that Snuke can perform.

Sample Input 1

3
8 12 40

Sample Output 1

2

Initially, [8, 12, 40] are written on the blackboard.
Since all those integers are even, Snuke can perform the operation.

After the operation is performed once, [4, 6, 20] are written on the blackboard.
Since all those integers are again even, he can perform the operation.

After the operation is performed twice, [2, 3, 10] are written on the blackboard.
Now, there is an odd number 3 on the blackboard, so he cannot perform the operation any more.

Thus, Snuke can perform the operation at most twice.

Sample Input 2

4
5 6 8 10

Sample Output 2

0

Since there is an odd number 5 on the blackboard already in the beginning, Snuke cannot perform the operation at all.

Sample Input 3

6
382253568 723152896 37802240 379425024 404894720 471526144

Sample Output 3

8

Solution in OCaml (4.02.3) (judge verdict: Accepted)

open Batteries

module IntSet = Set.Make (struct
  let compare = Pervasives.compare

  type t = int
end)

let read_two () = Scanf.sscanf (read_line ()) "%d %d" (fun a b -> (a, b))

let read_three () =
  Scanf.sscanf (read_line ()) "%d %d %d" (fun a b c -> (a, b, c))

let read_four () =
  Scanf.sscanf (read_line ()) "%d %d %d" (fun a b c d -> (a, b, c, d))

let read_list () =
  read_line () |> String.split_on_char ' '
  |> List.map (fun s -> int_of_string s)

let rec read_list_nl n =
  if n = 0 then [] else (read_line () |> int_of_string) :: read_list_nl (n - 1)

(* a**x *)
let pow a x =
  let rec aux acc = function 0 -> acc | n -> aux (acc * a) (n - 1) in
  aux 1 x

let rec pow2 n = if n mod 2 = 0 then 1 + pow2 (n / 2) else 0

let rec f d a n = if n > d then 0 else 1 + f d a (n + a)

let rec total acc = function [] -> acc | x :: rest -> total (acc + x) rest

let () =
  let _ = read_int () in
  let ans =
    read_list () |> List.map pow2
    |> List.fold_left (fun x acc -> if acc > x then x else acc) 32
  in
  print_int ans;
  print_newline ()