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()
{
 int N;
 int a[100005];
 int div2=0;
 int div4=0;
 int i;
 int inc=0;

 scanf("%d",&N);
 for(i=0;i<N;i++) 
 { 
  scanf("%d",&a[i]);
  if ((a[i]%2 == 0)&&(a[i]%4 != 0)) div2++;
  if (a[i]%4 == 0) div4++;
 }
 if (div4>0) inc=1;

 if((2*div4 + inc + 2*(div2/2)) >= N)
 {
  printf("Yes\n");
 }else{
  printf("No\n");
 }

 return 0;
}