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 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define rep(i,n) for(int i=0; i<(n); i++)
int main() {
  int n;
  cin >> n;
  vector<int> a(n);
  rep(i,n) cin >> a[i];
  int sum2 = 0;
  int sum4 = 0;
  for(int i=0; i<n; i++){
    if(a[i]%2==0 && a[i]%4!=0){
      sum2++;
    }
    if(a[i]%4==0) sum4++;
  }
  if(sum2>0){
    if((n-sum2+1)/2<=sum4) cout << "Yes" << endl;
    else cout << "No" << endl;
  }
  else{
    if(n/2<=sum4) cout << "Yes" << endl;
    else cout << "No" << endl;
  }
}