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 <iostream>
#include <algorithm>
#include <cmath>
#include <vector>
#include <stack>
#include <queue>
#include <deque>
#include <cstdlib>
#include <cstdio>
#include <string>
#include <cstring>
#include <climits>
#include <map>
using namespace std;

#define MAX 100001

int n;
int A[MAX];

int main() {
    cin >> n;
    
    int num_two = 0;
    int seki = 1;
    int num_four = 0;
    int num_eight = 0;
    int num;
    
    int c;
    for ( int i = 1; i <= n; i++ ) {
        cin >> c;
        if ( c == 2 ) {
            num_two += 1;
            seki *= c;
        }
        if ( c % 4 == 0 ) {
            num_four += 1;
            seki *= c;
        }
        if ( c % 8 == 0 ) {
            num_eight += 1;
        }
    }
    
    if ( n % 2 == 1 ) {
        num = 2 * (num_four) + 1;
    } else {
        num = 2 * (num_four);
    }
    
    if ( num >= n || (seki >= pow(4, n / 2) && ( num_eight - num_two >= 0) && 2 * (num_eight + num_two) + 1 >= n) ) {
        cout << "Yes" << endl;
    } else {
        cout << "No" << endl;
    }
    
    return 0;
}