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: Wrong Answer)

#include <bits/stdc++.h>

#define INF 1e9
using namespace std;
typedef long long ll;

int main() {

    int n; cin >> n;

    int a_1 = 0;
    int a_2 = 0;
    int a_4 = 0;

    for (int i = 0; i < n; ++i) {
        int a; cin >> a;

        if (a % 4 == 0) {
            ++a_4;
        } else if (a % 2 == 0) {
            ++a_2;
        } else {
            ++a_1;
        }
    }

    if (a_4 == a_1 || (a_4 + 1 == a_1 && a_2 == 0)) {
        puts("Yes");
    } else {
        puts("No");
    }
}