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 (1.42.0) (judge verdict: Accepted)

#![allow(unused_imports)]
// use itertools::Itertools;
use proconio::{input, marker::*};

fn main() {
    input! {
        n: usize,
        aa: [usize; n]
    };
    let mut odds = 0;
    let mut amari2 = 0;
    let mut space4 = 0;
    for a in aa {
        match a % 4 {
            0 => space4 += 1,
            2 => amari2 += 1,
            _ => odds += 1,
        }
    }
    if amari2 == 0 {
        println!("{}", ["No", "Yes"][(odds <= (space4 + 1)) as usize])
    } else {
        // 2あまりは2個以上あれば打ち消しあえて一端は4の隣
        amari2 = 1;
        println!(
            "{}",
            ["No", "Yes"][((odds + amari2) <= (space4 + 1)) as usize]
        )
    }
}