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`.

Examples

Input

3
1 10 100


Output

Yes


Input

4
1 2 3 4


Output

No


Input

3
1 4 1


Output

Yes


Input

2
1 1


Output

No


Input

6
2 7 1 8 2 8


Output

Yes
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")
    }
}