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: Accepted)

use std::io::*;
use std::str::FromStr;

pub fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

fn main() {
    let n: usize = read();
    let mut a: Vec<usize> = vec![];
    for _ in 0..n {
        let ai = read();
        a.push(ai);
    }
    let mut cnt_one = 0;
    let mut cnt_two = 0;
    let mut cnt_four = 0;
    for i in 0..a.len() {
        let ai = a[i];
        if ai % 4 == 0 {
            cnt_four += 1;
        } else {
            if ai % 2 == 0 {
                cnt_two += 1;
            } else {
                cnt_one += 1;
            }
        }
    }
    if cnt_one <= cnt_four && cnt_two != 0 {
        println!("Yes");
    } else {
        if cnt_one <= cnt_four + 1 && cnt_two == 0 {
            println!("Yes");
        } else {
            println!("No");
        }
    }
}