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 9.2.1) (judge verdict: Accepted)

#include <stdio.h>
int main(){
  long	n, a, div0=0, div1=0, div2=0;
  scanf("%ld", &n);
  
  for(int i=0; i<n; i++){
    scanf("%ld", &a);
    if	   ( a%4==0 ){ div2++; }
    else if( a%2==0 ){ div1++; }
  }
  div0 = n - (div1 + div2);
  
  if( div1 ){
    if( div0 <= div2   ){ printf("Yes\n"); return 0; }
  }else{
    if( div0 <= div2+1 ){ printf("Yes\n"); return 0; }
  }
  printf("No\n");
  return 0;
}