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 v5.12) (judge verdict: Accepted)

function Main(input) {
  input = input.split("\n");
  var n = parseInt(input[0]);
  tmp = input[1].split(" ");
  a=new Array(n).fill(0);
  for(i=0;i<n;i++){
    a[i]=parseInt(tmp[i]);
  }
  var odd=0;
  var four=0;
  for(i=0;i<n;i++){
    if(a[i]%2==1){
      odd++;
    }else if(a[i]%4==0){
      four++;
    }
  }
  var ans="No";
  if(odd==0){
    ans="Yes";
  }else if(odd-four<=0){
    ans="Yes";
  }else if(n==3&&odd-four<=1&&four>0){
    ans="Yes";
  }else if(n%2==1&&odd-four<=1){
    ans="Yes";
  }
  console.log('%s', ans);
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));