100692: [AtCoder]ABC069 C - 4-adjacent

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