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 <bits/stdc++.h>
using namespace std;
#define MOD 1000000007
#define pb push_back
#define xx first
#define yy second
#define sz(x) ((int)x.size())
#define all(x) x.begin(),x.end()
#define rep(i,n) for(int i=0;i<n;i++)
#define repp(i,k,n) for(int i=k;i<n;i++)
typedef long long ll;
typedef unsigned long long ull;
typedef vector<int> iv;
typedef pair<int,int> iip;
typedef map<int,int> mii;
template <typename T>
void dbg(T t){cerr<<t<<endl ;}
template<typename T, typename... Args>
void dbg(T t, Args... args) {cerr << t <<" ";dbg(args...) ;}

int main(){
	int n,a;
	int t[3]={0,0,0};
	cin>>n;
	rep(i,n){
		cin>>a;
		if(a%4==0)t[2]++;
		else if(a%2==0)t[1]++;
		else t[0]++;
	}
	if(t[1]!=0)t[0]++;
		if(t[0]>t[2]+1)cout<<"No"<<endl;
		else cout<<"Yes"<<endl;

	return 0;
 }