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 scala.io.StdIn

object Main extends App {

  val n = StdIn.readInt
  val a = StdIn.readLine.split(" ").map(_.toLong)

  val (odd, even, mlt4) = a./:(0,0,0)((cnt,i) => {
    val odd = if((i&1) == 1) 1 else 0
    val even = if((i&1) == 0) 1 else 0
    val mlt4 = if((i&3) == 0) 1 else 0
    (cnt._1+odd, cnt._2+even, cnt._3+mlt4)
  })

  val ans = if(odd == mlt4+1) {
    if(even == mlt4) "Yes"
    else "No"
  }
  else if(odd <= mlt4) "Yes" else "No"

  println(ans)
}