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: Accepted)

import java.util.Scanner

object Main extends App {
  val sc = new Scanner(System.in)

  val n = sc.nextInt

  val al = Seq.fill(n)(sc.nextInt)

  val div2 = al.filter(_ % 2 == 0)
  val (divOnly2, divOver4) = div2.partition(_ % 4 != 0)

  val oddCon      = n - div2.size
  val divOnly2Con = divOnly2.size
  val divOver4Con = divOver4.size

  val res =
    if(divOnly2Con >= 1) if( divOver4Con >= oddCon ) "Yes" else "No"
    else if(  divOver4Con + 1 >= oddCon ) "Yes" else "No"

  println(res)
}

/*
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*
*
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* */