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;
typedef pair<ll, ll> pll;

#define FOR(i, n, m) for (ll(i) = (m); (i) < (n); ++(i))
#define REP(i, n) FOR(i, n, 0)
#define OF64 std::setprecision(10)

const ll MOD = 1000000007;
const ll INF = (ll)1e15;

int main()
{
    int N;
    cin >> N;
    int x = 0, y = 0, z = 0;
    REP(i, N)
    {
        ll a;
        cin >> a;
        if (a % 4 == 0)
            x++;
        else if (a % 2 == 0)
            y++;
        else
            z++;
    }
    if (z + (y % 2) <= x + 1)
        cout << "Yes" << endl;
    else
        cout << "No" << endl;
    return 0;
}