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 C (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>

int main(){

  int a,n,s4=0,s2=0,s0=0;

  scanf("%d",&n);
  int i;
  for(i=0;i<n;i++){
    scanf("%d",&a);
    if(a%4==0)s4++;
    else if(a%2==0)s2++;
    else s0++;
  }

  int res=0;
  if(s2>0)s2=1;

  if(s0==0)res=1;
  else if(s0==0 && s4==0)res=1;
  else if(s4==n)res=1;
  else if(s2+s0-1<=s4)res=1;

  if(res>0)printf("Yes\n");
  else printf("No\n");

  return 0;

}