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: Time Limit Exceeded)

#include <stdio.h>
#include <stdlib.h>
int mark=0;
void perm(long int a[],int k,int n){
    int i,c=0;
    long int temp;
    if(k==n-1){
        for(i=1;i<n;i++){
            if(a[i-1]*a[i]%4==0)
                c++;
        }
        if(c==n-1)
            mark=1;
    }else{
    for(i=k;i<n;i++){
      temp=a[k];a[k]=a[i];a[i]=temp;
      perm(a,k+1,n);
      temp=a[k];a[k]=a[i];a[i]=temp;
    }
    }
}

int main()
{
    long int n;
    scanf("%ld",&n);
    long int a[n];
    int i=0;
    for(i=0;i<n;i++){
        scanf("%ld",&a[i]);
    }
    perm(a,0,n);
    if(mark)
        printf("Yes");
    else
        printf("No");
}