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: Time Limit Exceeded)

int(input())
vals    = input()

vals    = vals.split()
#　数値変換
vals    = list(map(lambda v:int(v), vals))

def solve(remain, a):
    '''bは指定必須とする'''

    if len(remain) == 1:
        if (a*remain[0]) % 4 == 0:
            return True
        return False

    # len > 1の場合

    for i in range(len(remain)):
        if (a * remain[i]) % 4 == 0:
            res = solve(remain[0:i] + remain[i+1:], remain[i])
            if res == True:
                return True



for i in range(len(vals)):
    a   = vals[i]
    if solve(vals[0:i] + vals[i+1:], a) == True:
        print("Yes")
        break;
else:
    print("No")