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<iostream>
#include<algorithm>
#include<queue>
#include<cmath>
#include<map>
#include<vector>
#include<iomanip>
using namespace std;
typedef long long ll;
ll inf = 100000000;
ll v[205];
ll x[20000005];
ll a[10000005];
ll dp[10005][10005];
int dx[4] = { 1,-1,0,0 };
int dy[4] = { 0,0,1,-1 };
typedef pair<ll, ll> P;


double q[200005];

int main() {
	int n;
	cin >> n;
	for (int i = 0; i < n; i++) {
		cin >> a[i];
	}
	sort(a, a + n);
	ll count = 0;
	ll count2 = 0;
	for (int i = 0; i < n; i++) {
		if (a[i] % 4 == 0) {
			count++;
		}
		if (a[i] == 2) {
			count2++;
		}
	}
	ll x = count2 % 2;
	ll y = count2 / 2;
	if (count+y >= n / 2 + x||count2==n) {
		cout << "Yes" << endl;
		return 0;
	}
	cout << "No" << endl;
	return 0;
}