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 Kotlin (1.0.0) (judge verdict: Wrong Answer)

import java.lang.Math

val MOD: Int = 1000000000 + 7
val MODL: Long = MOD.toLong()

fun main(args: Array<String>)
{
    val n = readLine()!!.toInt()
    val a = readLine()!!.split(" ").map{it.toInt()}.toIntArray()

    var cnt2 = 0
    var cnt4 = 0
    for (i in 0 until n) {
        cnt2 += if (a[i] % 2 == 0) 1 else 0
        cnt4 += if (a[i] % 4 == 0) 1 else 0
    }

    if (cnt2 == n || cnt4 * 2 >= (n - cnt2)) println("Yes")
    else println("No")
}