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: Wrong Answer)

#include<stdio.h>

int main(void){
  int n,i,a,b[3],cnt;
  scanf("%d",&n);
  for(i=0;i<3;i++) b[i]=0;
  for(i=0;i<n;i++){
    scanf("%d",&a);
    cnt=0;
    while(a/=2) cnt++;
    if(cnt==0) b[0]++;
    else if(cnt==1) b[1]++;
    else b[2]++;
  }
  printf("%d %d %d\n",b[0],b[1],b[2]);
  if((b[0]<=b[2]+1) && (b[1]==0)) printf("Yes\n");
  else if((b[0]<b[2]) && (b[1]!=0)) printf("Yes\n");
  else printf("No\n");
  return 0;
}