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: Wrong Answer)

function main(input){
    var tmp = input.split("\n");
    var N = Number(tmp[0]);
    var a = tmp[1].split(" ");

    var num = N/2;
    var count_4 = 0;
    var count_odd = 0;

    for(var i=0; i<a.length; i++){
        if(a[i]%4==0){
            count_4++;
        }else if(a[i]%2==1){
            count_odd++;
        }
    }
    if(num<count_odd){
        if(count_odd-1<=count_4){
            console.log("Yes");
        }else{
            console.log("No");
        }
    }else{
        if(count_odd<=count_4){
            console.log("Yes");
        }else{
            console.log("no");
        }
    }
    //console.log(count_odd);
    //console.log(count_4);
}

main(require("fs").readFileSync("/dev/stdin", "utf8"));