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 repr(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define rep(i,n) repr(i,0,n)
#define reprrev(i,a,b) for(int i=(int)(b)-1;i>=(int)(a);i--)
#define reprev(i,n) reprrev(i,0,n)
#define all(a) (a).begin(),(a).end()
#define rall(a) (a).rbegin(),(a).rend()
#define mp make_pair
#define mt make_tuple
#define MOD 1000000007
#define PI 3.1415926535
typedef long long ll;
typedef pair<int, int> Pi;
typedef pair<ll, ll> Pll;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef vector<bool> vb;
typedef vector<char> vc;
typedef vector<string> vs;
typedef vector<double> vd;
typedef vector<Pi> vPi;
typedef vector<Pll> vPll;
typedef vector<vector<int>> vvi;
typedef vector<vector<bool>> vvb;
typedef vector<vector<ll>> vvll;
typedef vector<vector<char>> vvc;
typedef vector<vector<string>> vvs;
typedef vector<vector<double>> vvd;
typedef vector<vector<Pi>> vvPi;
typedef priority_queue<int, vector<int>, greater<int> > pqli;
typedef priority_queue<ll, vector<ll>, greater<ll> > pqlll;
typedef priority_queue<Pi, vector<Pi>, greater<Pi> > pqlP;
string YN(bool y) { return (y?"YES":"NO"); }
string yn(bool y) { return (y?"Yes":"No"); }
string ON(bool y) { return (y?"OK":"NG"); }
int main(void)
{
	int n, d0=0, d1=0, d2=0;

	cin>>n;

	vi a(n), d(n);

	rep(i, n){
		cin>>a[i];
		d[i]=a[i]%4;
		if(d[i]==0){
			d0++;
		}else if(d[i]==1||d[i]==3){
			d1++;
		}else{
			d2++;
		}
	}
	if(d0+1<d1){
		cout<<"No"<<endl;
	}else if(d0+1==d1){
		if(d2==0){
			cout<<"Yes"<<endl;
		}else{
			cout<<"No"<<endl;
		}
	}else{
		cout<<"Yes"<<endl;
	}
}