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)

#include<iostream>
#include<sstream>
#include<fstream>
#include<string>
#include<vector>
#include<deque>
#include<queue>
#include<stack>
#include<set>
#include<map>
#include<algorithm>
#include<functional>
#include<utility>
#include<bitset>
#include<cmath>
#include<cstdlib>
#include<ctime>
#include<cstdio>
#include<cstring>
#include<iomanip>
using namespace std;
int n,x,c2=0,c4=0;
bool flag=false;
int read(){
    int ans=0,f=1;
    char ch=getchar();
    while (ch<'0'||ch>'9') {if (ch=='-') f=-1;ch=getchar();}
    while (ch>='0'&&ch<='9'){ans=ans*10+ch-'0';ch=getchar();}
    return ans*f;
}
int main(){
	std::ios::sync_with_stdio(false);
	n=read();
	for (int i=0;i<n;i++){
		x=read();
		if (x%4==0)	c4++;
		else if (x%2==0) c2++;
	}
	if (c2==n) {cout<<"Yes";return 0;}	else if (!c4) {cout<<"No";return 0;}
	if (c2){n-=c2+1;c4-=1;flag=true;}
	if (c4>=(n/2)||((n<=1)&&flag)) cout<<"Yes";else cout<<"No";
	return 0;
}