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 Rust (1.15.1) (judge verdict: Wrong Answer)

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();
    let other = n - four - two;

    println!("{}", if two == 0 { if other <= four + 1 { "Yes" } else { "No" } } else { if other <= four { "Yes" } else { "No" } });
}