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 Pascal (FPC 2.6.2) (judge verdict: Accepted)

program V1003;
 var
  a:array[1..3] of longint;
  i,n,x:longint;
 begin
  readln(n);
  fillchar(a,sizeof(a),0);
  for i:=1 to n do
   begin
    read(x);
    if x mod 4=0 then inc(a[3])
                 else if x mod 2=0 then inc(a[2])
                                   else inc(a[1]);
   end;
  readln;
  if a[2]>0 then a[2]:=1;
  if a[2]+a[1]>a[3]+1 then writeln('No')
                      else writeln('Yes');
 end.