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 rep(i,n) for(lint (i)=0;(i)<(n);(i)++)
#define repp(i,m,n) for(lint (i)=(m);(i)<(n);(i)++)
#define repm(i,n) for(lint (i)=(n);(i)>=0;(i)--)
#define INF (1ll<<60)
typedef long long lint;
const lint MOD =1000000007;
  int main(){
    lint N,count2=0,count4=0,counto=0;
    cin>>N;
    vector<lint> x;
    rep(i,N){
      lint v;
      cin>>v;
    x.push_back(v);
    if(x[i]%4==0)count4++;
    else if(x[i]%2==0)count2++;
    else counto++;
    }
    if(count2!=N&&count2!=0)counto++;
  if(counto>count4+1)cout<<"No";
  else cout<<"Yes";
  }