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<cstring>
#include<string>
#include<algorithm>
#include<cmath>
#include<vector>
using namespace std;
#define rep(i,s,n) for(int i = s;i<n;i++)
#define repe(i,s,n) for(int i = s;i<=n;i++)
#define pb push_back
#define fi first
#define se second
typedef long long ll;
typedef pair<int,int>pint;
typedef vector<int>vint;
typedef vector<pint>vpint;
static const ll maxLL = (ll)1 << 62;
const int mod=1e9+7;

int main(){
    int n;
    cin>>n;
    int a[100101];
    int cnt2=0;int cnt4=0;
    rep(i,0,n){
        cin>>a[i];
        if(a[i]%4==0)cnt4++;
        else if(a[i]%2==0)cnt2++;
    }
    int x=n-2*cnt4-1;
    bool can=false;
    if(n/2<=cnt4)can=true;
    else if(x<=cnt2 && cnt2<=2)can=true;
    if(can)cout<<"Yes"<<endl;
    else cout<<"No"<<endl;
    return 0;
}