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: Accepted)

from copy import deepcopy

def main():
    n = int(input())
    a = list(map(int, input().split()))
    div2 = [0] * n
    div4 = deepcopy(div2)
    notdiv4 = deepcopy(div2)
    for i in range(n):
        if a[i] % 4 == 0:
            div4[i] = 1
        elif a[i] % 2 == 0:
            div2[i] = 1
        else:
            notdiv4[i] = 1
    num_notdiv4 = sum(notdiv4)
    num_notdiv4 += sum(div2) % 2
    if num_notdiv4 - 1 > sum(div4):
        print('No')
    else:
        print('Yes')

if __name__ == '__main__':
    main()