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 = scala.io.StdIn.readInt
	val a = scala.io.StdIn.readLine.split(" ").map(_.toLong)
	
	var count = 0
	var count1 = 0

	for(i<-a){
		if(i%4L == 0L) count = count + 1
		if(i%2L == 0L && i%4L != 0L) count1 = count1 + 1
	}

	if(count1%2 == 0){
		val A = N - count1
		if((A%2 == 0 && A/2 <= count)) print("YES")
		else if((A-1)%2 == 0 && (A-1)%2 <= count) print("YES")
		else print("NO")
	}else{
		val A = N - count1 + 1
		if((A%2 == 0 && A/2 <= count)) print("YES")
		else if((A-1)%2 == 0 && (A-1)%2 <= count) print("YES")
		else print("NO")
	}
}