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++ (Clang 10.0.0) (judge verdict: Wrong Answer)

#include<iostream>
#include<string>
#include<algorithm>
using namespace std;
typedef long long ll;
const int Max = 1e6 + 5;
const int Mod = 1e9 + 7;
int lst[Max];
int ls[Max];

int main()
{
	int n;
	cin >> n;
	for (int i = 1;i <= n;i++)
	{
		scanf("%d", &lst[i]);
		if (lst[i] % 4 == 0)ls[4]++;
		else if (lst[i] % 2 == 0)ls[2]++;
		else ls[1]++;
	}
	int sum = ls[4] * 3 + ls[2];
	if (ls[2] == 1)sum--;
	if (sum > n)cout << "Yes" << endl;
	else cout << "No" << endl;


}