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 extends App {
  val n = io.StdIn.readLine().toLong
  val limit = if (n % 3L == 0L) n / 3L else n / 3L + 1L
  val seq = io.StdIn.readLine().split(" ").map(_.toLong)
  val cnt4 = seq.count(_ % 4L == 0L)
  val cnt2 = seq.count(_ % 2L == 0L) - cnt4
  if (cnt4 > 0L && cnt4 >= limit) {
    println("Yes")
  } else if (n - cnt4 * 3 <= cnt2) {
    println("Yes")
  } else {
    println("No")
  }
}