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::error::Error;
use std::io;

fn main() {
    if let Err(e) = run() {
        println!("{}", e);
    }
}

fn run() -> Result<(), Box<Error>> {
    let mut n = String::new();
    io::stdin().read_line(&mut n)?;
    let n: usize = n.trim().parse()?;
    let mut a = String::new();
    io::stdin().read_line(&mut a)?;
    let a: Vec<u64> = a.trim().split(" ").map(|e| e.parse().expect("")).collect();
    let mut n4 = 0;
    let mut n2 = 0;
    let mut ne = 0;
    for e in a {
        if e % 4 == 0 {
            n4 += 1;
        } else if e % 2 == 0 {
            n2 += 1;
        } else {
            ne += 1;
        }
    }
    if n2 == 1 {
        ne += 1;
    }
    if ne == 0 {
        println!("Yes");
        return Ok(());
    }
    if ne == 1 {
        if n4 < 1 {
            println!("No");
            return Ok(());
        }
    } else {
        if n4 < ne - 1 {
            println!("No");
            return Ok(());
        }
    }
    println!("Yes");
    Ok(())
}