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)

let () =
  let n = Scanf.scanf "%d\n" (fun n -> n) in
  let as_ = Array.to_list @@ Array.init n (fun _ -> Scanf.scanf "%d " (fun a -> a)) in
  let n_odd = List.length @@ List.filter (fun n -> n mod 2 = 1) as_ in
  let n_4n2 = List.length @@ List.filter (fun n -> n mod 2 = 0 && n mod 4 <> 0) as_ in
  let n_4n = List.length @@ List.filter (fun n -> n mod 4 = 0) as_ in
  print_endline @@ if n_odd <= n_4n || n_4n2 = 0 && n_odd <= n_4n + 1 then "Yes" else "No"