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 C++14 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <iostream>
using namespace std;
int a,arr[100000],brr[100000],tmp1,tmp2,tmp3;
void input(){
    cin>>a;
    for (int i=0;i<a;i++){
        cin>>arr[i];
        if (arr[i]%4==0)
            tmp1++;
        if (arr[i]%2==1)
            tmp2++;
        if (arr[i]%2==0)
            tmp3++;
    }
}
void solve(){
    tmp3-=tmp1;
    if (tmp2-tmp1<=1&&tmp3%2==0)
        cout<<"Yes";
    else if ((tmp2+tmp3)-tmp1<=1)
        cout<<"Yes";
    else
        cout<<"No";
}
int main(){
    input(),solve();
}