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
use std::io::*;

fn main() {
    let stdin = std::io::stdin();
    let mut reader = std::io::BufReader::new(stdin.lock());
    let mut s = String::new();
    let n: usize = reader.read_line(&mut s).unwrap();
    let mut s = String::new();
    reader.read_line(&mut s).unwrap();
    let a: Vec<usize> = s.split_whitespace().map(|x| x.parse().unwrap()).collect();

    let four = a.iter().filter(|x| **x % 4 == 0).count();
    let two = a.iter().filter(|x| **x % 4 != 0 && **x % 2 == 0).count();

    println!("{}", if (n - two) <= four * 2 { "Yes" } else { "No" });
}
