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>
using namespace std;

#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define REP(i,n)   FOR(i,0,n)
#define ALL(a)     (a).begin(),(a).end()
#define MOD 1000000007

typedef long long int ll;

const ll INF=(ll)1e18;
//const int INF=(1<<30);


int main(){
  int N;
  cin >> N;
  int cnt_2 = 0;
  int cnt_4 = 0;
  int cnt_other = 0;
  REP(i,N){
    ll a;
    cin >> a;
    if(a%4==0){
      cnt_2++;
    }else if(a%2==0){
      cnt_2++;
    }else{
      cnt_other++;
    }

  }

  if(cnt_2==0){
    if(cnt_4+1>cnt_other){
      cout << "Yes" << endl;
    }else{
      cout << "No" << endl;
    }
  }else{
    if(cnt_4>cnt_other){
      cout << "Yes" << endl;
    }else{
      cout << "No" << endl;
    }
  }
}