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`.

Examples

Input

3
1 10 100


Output

Yes


Input

4
1 2 3 4


Output

No


Input

3
1 4 1


Output

Yes


Input

2
1 1


Output

No


Input

6
2 7 1 8 2 8


Output

Yes
#include <iostream>
#include <cstdio>
#include <vector>
#include <string>

using namespace std;

int main(void){
    int n, a;
    cin >> n;
    vector<int> j(4, 0);
    for (int i = 0; i < n; i++) {
        cin >> a;
        j[a%4]++;
    }
    for (int i = 0; i < 4; i++) cout << j[i] << " "; cout << endl;
    
    if (j[0] >= j[1]+j[3]) {
        cout << "Yes" << endl;
        return 0;
    }
    else if (j[0] == j[i]+j[3]-1 && j[2] == 0) {
        cout << "Yes" << endl;
        return 0;
    }
    else {
        cout << "No" << endl;
        return 0;
    }
}