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)

fun main(args: Array<String>) {
    val n = readLine()?.toInt() ?: return
    val aList = readLine()?.split(" ")?.map { it.toLong() } ?: return

    var by4 = 0
    var by2ButBy4 = 0

    for (a in aList) {
        if (a % 4 == 0L) {
            by4++
        } else if (a % 2 == 0L) {
            by2ButBy4++
        }
    }
    
    if (by2ButBy4 == n || by4 == n) {
        println("Yes")
        return
    }

    val requireBy4 = n - by4 - by2ButBy4 + if (by2ButBy4 != 0) 1 else 0
    val needBy4 = (requireBy4 / 2) + if (requireBy4 % 2 == 1) 1 else 0

    if (by4 >= needBy4) {
        println("Yes")
    } else {
        println("No")
    }
}