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 <bits/stdc++.h>
typedef long long ll;
using namespace std;

const int INF = 1e9;
const int MOD = 1e9+7;
const ll LINF = 1e18;

#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define REP(i,n) for(int i=0;i<(n);++i)
#define REPR(i,n) for(int i=n;i>=0;i--)
#define ALL(v) (v.begin(),v.end())
#define COUT(x) cout<<(x)<<endl

int main(){
    int n,c1=0,c2=0;
    cin >> n;
    bool flag = false;
    REP(i,n){
        int a;
        cin >> a;
        if(a%4==0)c1++;
        else if(a%2==0)flag = true;
        else c2++;
    }
    if(flag){
        if(c1>=c2)cout<<"Yes"<<endl;
        return 0;
    }
    else {
        if(c1>=c2-1)cout<<"Yes"<<endl;
        return 0;
    }
    cout << "No" << endl;
    return 0;
}