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++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include<iostream>
#include<algorithm>
using namespace std;
int fun(int arr[],int n){
	do{
		int flag=1;
		int i;
		for(i=0;i<n-1&&flag==1;i++){
			if((arr[i]+arr[i+1])<2){
				flag=0;
			}
		}
		if(flag==1){
			return 1;
		}
	}while(next_permutation(arr,arr+n));
	return 0;
}
int main(){
	int n,i;
	int arr[100000];
	scanf("%d",&n);
	long long temp;
	
	for(i=0;i<n;i++){
		scanf("%lld",&temp);
		arr[i]=0;
		while(temp%2==0){
			arr[i]++;
			temp/=2;
		}
	}
	sort(arr,arr+n);
	if(fun(arr,n)==1){
		printf("Yes\n");
	}else{
		printf("No\n");
	}
	return 0;
}