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;

typedef long long int ll;
const ll N = 1000010;

ll a1[N], b1[N], c1[N];

int main()
{
    ll n; cin >> n;

    for (int i = 1; i <= n; i ++) cin >> a1[i];

    ll x = 0, f = 0, c = 0;
    for (int i = 1; i <= n; i ++) {
        if (a1[i] % 2 == 0 && a1[i] % 4){
            c ++;
            continue;
        }
        if (a1[i] % 4) b1[x++] = a1[i];
        else c1[f++] = a1[i];
    }
    if (x == f && c > 0 && x == 0) cout << "Yes\n";
    else if (x == f+1 && c == 0) cout << "Yes\n";
    else if (x <= f && c >= 0) cout << "Yes\n";
    else cout << "No\n";

    //main();

    return 0;
}