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`.

Examples

Input

3
1 10 100


Output

Yes


Input

4
1 2 3 4


Output

No


Input

3
1 4 1


Output

Yes


Input

2
1 1


Output

No


Input

6
2 7 1 8 2 8


Output

Yes
#!/usr/bin/python

import sys

def main(argv):
    line = sys.stdin.readline()
    while line:
        N = int(line)
        a = map(lambda x: int(x), sys.stdin.readline().split(" "))

        counters = [0, 0 ,0]
        for i in a:
            if i % 4 == 0:
                counters[2] += 1
            elif i % 2 == 0:
                counters[1] += 1
            else:
                counters[0] += 1

        if counters[0] > (counters[2] + 1):
            print("No")
        elif counters[0] == (counters[2] + 1):
            if counters[1] > 0:
                print("No")
            else:
                print("Yes")
        else:
            print("Yes")
            
        line = sys.stdin.readline()

if __name__ == "__main__":
    main(sys.argv)