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)

# import numpy as np
import math
N = int(input())
a = list(map(int, input().split()))

two_count = 0
four_count = 0
for i in a:
    if i >= 4 and i % 4 == 0:
        four_count += 1
    elif i >= 2 and i % 2 == 0:
        two_count += 1

if two_count <= 1:
    if len(a) == 2:
        print("Yes" if four_count >= 1 else "No")
    else:
        print("Yes" if four_count >= len(a)-2 else "No")
else:
    check = len(a) - two_count
    if check == 0:
        print("Yes")
    elif check <= 2:
        print("Yes" if four_count >= 1 else "No")
    else:
        print("Yes" if four_count >= check-2 else "No")