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 n = 0, a = 0;
    int result = 0;
    int oddcnt = 0, e2cnt = 0, e4cnt = 0;
    
    scanf("%d", &n);
    while (n--) {
        scanf("%d", &a);
        if (a % 4 == 0) {
            e4cnt++;
        } else if (a % 2 == 0) {
            e2cnt++;
        } else {
            oddcnt++;
        }
    }
    
    if (e2cnt == 0) {
        if (oddcnt <= e4cnt + 1) {
            result = 1;
        }
    } else {
        if (oddcnt <= e4cnt) {
            result = 1;
        }
    }
    
    printf("%s\n", (result) ? "Yes" : "No");
    
    return 0;
}