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 (2.11.7) (judge verdict: Wrong Answer)

object Main{
  def main(args:Array[String]) = {
    val tmp = scala.io.StdIn.readLine
    val list = scala.io.StdIn.readLine.split(" ").map(_.toInt).toList
    var four = List.empty[Int]
    var two = List.empty[Int]
    var oth = List.empty[Int]
    for(s <- list){
      if(s % 4 == 0)
        four = s :: four
      else if(s % 2 == 0)
        two = s :: two
      else
        oth = s :: oth
    }
    if(four.size >= oth.size - 1)
      println("Yes")
    else
      println("No")
  }
}