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 Scala (2.13.1) (judge verdict: Accepted)

import scala.collection.mutable

object Main extends App {
  val sc = new java.util.Scanner(System.in)
  val N = sc.nextInt()
  val hashMap = mutable.Map[Int, Int]()
  for (_ <- 1 to N) {
    val i = Integer.numberOfTrailingZeros(sc.nextInt()).min(2)
    hashMap.update(i, hashMap.getOrElse(i, 0) + 1)
  }
  val isSortable =
    hashMap.getOrElse(0, 0) + (if (hashMap.contains(1)) 1 else 0) <= hashMap.getOrElse(2, 0) + 1
  println(if (isSortable) "Yes" else "No")
}