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++ (GCC 9.2.1) (judge verdict: Accepted)

#include "bits/stdc++.h"

using namespace std;

void Main() {
    int N;
    cin >> N;
    vector<int> a(N, 0);
    for (int i = 0; i < N; ++i) {
        cin >> a[i];
    }

    int nodd = 0;
    int n4 = 0;
    int n2 = 0;
    for (int i = 0; i < N; ++i) {
        if (a[i] % 2 == 1) {
            ++nodd;
            continue;
        }
        if (a[i] % 4 == 0) {
            ++n4;
            continue;
        }
        ++n2;
    }

    bool ok = false;
    if (n2 == 0) {
        if (nodd - 1 <= n4) {
            ok = true;
        }
        else {
            ok = false;
        }
    }
    else {
        if (nodd <= n4) {
            ok = true;
        }
        else {
            ok = false;
        }
    }
    cout << (ok ? "Yes" : "No") << endl;
}

int main() {
    std::cout << std::fixed << std::setprecision(15);
    Main();
    return 0;
}