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 JavaScript (Node.js 12.16.1) (judge verdict: Wrong Answer)

function Main(input){
  input = input.split("\n");
   var arr = input[1].split(" ").map(Number);
  var t = 0;
  var f = 0;
  arr.forEach(function(val){
    if(val%4==0)f++;
    else if(val%2==0)t++;
  });
  t-=2;
  t = Math.max(t,0)
  var n = arr.length;
  console.log(f*3+t>=n?"Yes":"No")
}Main(require("fs").readFileSync("/dev/stdin", "utf8").trim());