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>

using namespace std;

int a[1000001];

int main() {
    ios_base::sync_with_stdio(false);
    int n;
    cin >> n;
    int cnt0 = 0, cnt1 = 0, cnt2 = 0;
    for (int i = 0; i < n; ++i) {
        cin >> a[i];
        if (a[i] == 2 || a[i] * 2 % 4 == 0) {
            cnt2++;
        } else {
        if (a[i] % 4 == 0) {
            cnt0++;
        } else {
            cnt1++;
        }
        }
    }
    if (cnt2 % 2 != 0) {
        cnt1++;
    }
    if (cnt0 + (cnt2 / 2) >= cnt1 - 1) {
        cout << "Yes" << endl;
    } else {
        cout << "No" << endl;
    }
    return 0;
}