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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <vector>
#include <queue>
#include <algorithm>
#include <cmath>
#include <bitset>
#include <iomanip>
#include <stack>
#include <list>
#include <map>
#include <unordered_map>
#include <chrono>
#include <numeric>
using namespace std;
using ll = long long;
const ll INF = (ll)1e18+1;
const ll DIV = 1000000007;
//#define TEST
int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);
#ifdef TEST
    chrono::system_clock::time_point start, end;
    start = chrono::system_clock::now();
#endif
    long N;
    cin >> N;
    vector<ll> a(N);
    bool times = true;
    ll times4=0;
    ll times2=0;
    ll other=0;
    for(size_t i=0;i<N; i++)
    {
        cin >> a[i];
        if(a[i] % 4 == 0) times4++;
        else if(a[i] % 2 == 0) times2++;
        else other++;
    }
    //cerr << times4 << ":" << times2 << ":" << other << endl;
    if(other>0)
    {
        if(other+times2%2 <= times4*2) cout << "Yes" << endl;
        else cout << "No" << endl;
    }
    else
    {
        if(times2 % 2 ==0) cout << "Yes" << endl;
        else cout << "No" << endl;
    }
#ifdef TEST
    end = chrono::system_clock::now();
    cerr << static_cast<double>(chrono::duration_cast<chrono::microseconds>(end - start).count() / 1000.0) << "[ms]" << endl;
#endif
    return 0;
}