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(){
	long long int b;
	int n,t,i,a2=0;
	scanf("%d",&n);
	t=n;
	
	if(n%2==0){
		for(i=0;i<n;i++){
			scanf("%lld",&b);
			if(b%4==0){
				t-=2;	
				if(t==0){
					printf("Yes\n");
					return 0;
				}
			}else if(b%2==0){
				a2++;
				if(a2%2==0){
					t-=2;
					a2=0;
				}
				if(t==0){
					printf("Yes\n");
					return 0;
				}
			}
		}
	}else if(n%2==1){
		for(i=0;i<n;i++){
			scanf("%lld",&b);
			if(b%4==0){
				t-=3;	
				if(t<0 || (t==0 && a2==1)|| n==3){
					printf("Yes\n");
					return 0;
				}
			}else if(b%2==0){
				a2++;
				if(a2%2==0){
					t-=2;
					a2=0;
				}
				if(t<0 ||(t==0 && a2==1)){
					printf("Yes\n");
					return 0;
				}
			}
		}
	}
		
	printf("No\n");
	
return 0;
}