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 Python (3.4.3) (judge verdict: Wrong Answer)

if __name__ == "__main__":
    N = int(input())
    a = list(map(int, input().split()))
    n1 = 0
    n2 = 0
    n4 = 0
    for i in a:
        if i % 4 == 0:
            n4 += 1
        elif i % 2 == 0:
            n2 += 1
        else:
            n1 += 1
    if n2 == 0 and n4 == 0 and n1 == 1:
        print("Yes")
    else:
        if n1 == n4:
            print("Yes")
        elif n1 == n4 + 1:
            if n2 == 0:
                print("Yes")
            else:
                print("No")
        else:
            print("No")