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 (void) {
    int i,N,b1 = 0, b2 = 0, b4 = 0;
    int a[100010];

    scanf("%d", &N);
    
    for(i = 0 ; i < N ; i ++) {
        scanf("%d", &a[i]);
        if (a[i] % 4 == 0) b4 ++;
        else if (a[i] % 2 == 0) b2++;
        else b1++;

     }

    if (b2 == 0) {
        if (b1 <= b4 + 1) printf("Yes\n");
        else printf("No\n");
    }else {
        if (b1 <= b4) printf("Yes\n");
        else printf("No\n");
    }
}