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: Accepted)

#pragma GCC optimize("O2,unroll-loops")
#pragma GCC target("avx,popcnt")
#include<bits/stdc++.h>
#define all(x) x.begin(), x.end()
#define pb push_back
using namespace std;
using ll = long long;
using ld = long double;
const int maxn = 1<<20, mod = 1e9 + 7, i2 = (mod+1)/2;

int main() {
	cin.tie(0)->sync_with_stdio(0);
	int n, t, a = 0, b = 0, c = 0;
	cin >> n;
	for(int i = 0; i < n; i++) {
		cin >> t;
		if(t%4 == 0) a++;
		else if(t%2 == 0) b++;
		else c++;
	}
	int ok = (c <= (a + (b==0)));
	cout << (ok?"Yes\n":"No\n");
	return 0;
}