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 <math.h>
#include <ctype.h>
#include <bits/stdc++.h>
using namespace std;
#define FOR(i, a, n) for (int i = a; i < n; i++)
#define REP(i, n) for(int i = 0; i < n; i++)

int main(){
    int n;
    cin >> n;
    
    int t_cnt = 0, f_cnt = 0, o_cnt = 0, tmp;
    REP(i, n){
        cin >> tmp;
        if(tmp % 4 == 0) f_cnt += 1;
        else if(tmp % 2 == 0) t_cnt += 1;
        else o_cnt += 1;
    }
    bool f = false;
    if(t_cnt){
        f_cnt += t_cnt / 2;
        t_cnt %= 2;
        if(o_cnt + t_cnt <= f_cnt + 1) f = true;
    }else if(o_cnt <= f_cnt + 1) f = true;

    if(f) cout << "Yes" << endl;
    else cout << "No" << endl; 

    return 0;
}