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 <cstdio>
#include <cstdlib>
#include <iostream>
#include <algorithm>
#include <cstring>
#include <vector>
#include <map>
#include <cmath>
 
#define rep(i,n) for(int i = 0;i < (n);i++)
#define all(x) (x).begin(),(x).end()
#define pb(x) push_back(x)
#define mp(a,b) make_pair(a,b)

using namespace std;

typedef long long int ll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<pair<int, int> > vpi;
typedef vector<pair<ll, ll> > vpl;

int main(){
	cin.tie(0);
	ios::sync_with_stdio(false);
  int n;
  cin >> n;
  ll f, t, o;
  f = t = o = 0;
  rep(i, n){
    ll a;
    cin >> a;
    if(a%4 == 0) f++;
    else if(a%2 == 0) t++;
    else o++;
  }
  cout << f << t << o << endl;
  if(o <= f && t%2 == 0) cout << "Yes" << endl;
  else cout << "No" << endl;
	return 0;
}