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 dump(x) cout << (x) << endl
typedef long long ll;
typedef pair<int, int> pi;
typedef vector<int> V;

int main() {
  int n;
  cin >> n;
  vector<ll> a(n);
  int x, y, z;
  x = y = z = 0;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    int cnt = 0;
    while (a[i]%2 == 0) {
      a[i] /= 2;
      cnt++;
    }
    if (cnt == 0) x++;
    else if (cnt == 1) z++;
    else if (cnt > 1) y++;
  }
  if (z == 1) x += z;
  x <= y*2 ? dump("Yes") : dump("No");
  return 0;
}