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)

#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")

#include <algorithm>
#include <climits>
#include <cmath>
#include <cstring>
#include <deque>
#include <forward_list>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <queue>
#include <set>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;
typedef long long ll;
typedef pair<int, int> P;

const ll MOD = 1E+09 + 7;
const ll INF = 1E18;
const int MAX_N = 1E+05;

int N;

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    cin >> N;

    int odd = 0;
    int four = 0;

    for (int i = 0; i < N; i++) {
        int a;
        cin >> a;
        if (a & 1) {
            odd++;
        } else if (a % 4 == 0) {
            four++;
        }
    }

    string ans;
    if (odd + four == N) {
        if (odd <= four + 1) {
            ans = "Yes";
        } else {
            ans = "No";
        }
    } else {
        if (odd <= four) {
            ans = "Yes";
        } else {
            ans = "No";
        }
    }

    cout << ans << "\n";

    return 0;
}