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()!!
  var xs = readLine()!!.split(" ").map(String::toInt)

  val quads = xs.filter { it%4 == 0 }.size
  xs = xs.filter { it%4 != 0 } 

  val twices = xs.filter { it%2 == 0 }.size
  xs = xs.filter { it%2 != 0 } 

  val noks = xs.size

  when { 
    (noks - quads) <= 1 && twices%2 == 0 -> "Yes"
    else -> "No"
  }.run(::println)

  //println( noks -  quads )
}