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;
int main() {
        ios::sync_with_stdio(false);
        cin.tie(0);
        int n;
        while (cin >> n) {
                int a[100005], t1 = 0, t2 = 0;
                for (int i = 0; i < n; i++) {
                        cin >> a[i];
                        if (a[i] % 4 == 0) {
                                t1++;
                        }
                        if (a[i] % 2 == 0 && a[i] % 4 != 0) {
                                t2++;
                        }
                }
                int t = t1 * 2 + 1 + t2;
                if (t1 == 0) {
                        t--;
                }
                if (t2 % 2 == 1) {
                        t--;
                }
                if (t >= n) {
                        cout << "Yes" << endl;
                } else {
                        cout << "No" << endl;
                }
        }
        return 0;
}