Problem:
Score : 400 points

Problem Statement

We have a sequence of length N, a = (a_1, a_2, ..., a_N).
Each a_i is a positive integer.

Snuke's objective is to permute the element in a so that the following condition is satisfied:

For each 1 ≤ i ≤ N - 1, the product of a_i and a_{i + 1} is a multiple of 4.

Determine whether Snuke can achieve his objective.

Constraints

2 ≤ N ≤ 10^5

a_i is an integer.

1 ≤ a_i ≤ 10^9

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

If Snuke can achieve his objective, print Yes; otherwise, print No.

Sample Input 1

3
1 10 100

Sample Output 1

Yes

One solution is (1, 100, 10).

Sample Input 2

4
1 2 3 4

Sample Output 2

No

It is impossible to permute a so that the condition is satisfied.

Sample Input 3

3
1 4 1

Sample Output 3

Yes

The condition is already satisfied initially.

Sample Input 4

2
1 1

Sample Output 4

No

Sample Input 5

6
2 7 1 8 2 8

Sample Output 5

Yes

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

open Str

let read_list f =
  split (regexp " +") (read_line ()) |> List.map f

let () =
  let _ = read_line () in
  let ls = read_list int_of_string in
  let (o, e, f) = List.fold_left (fun (o', e', f') x ->
                                  if x mod 4 = 0 then (o', e', f'+1)
                                  else if x mod 2 = 0 then (o', e'+1, f')
                                  else (o'+1, e', f')) (0,0,0) ls in
  (if e = 0 then
     if o - 1 <= f then "Yes" else "No"
   else
     if o <= f then "Yes" else "No") |> print_endline