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::fmt::{Debug, Display};
use std::io::{self, Read};
use std::str::{self, FromStr};


fn solve(a: Vec<u32>) -> bool {
    let (x, y, z) = {
        let (mut x, mut y, mut z) = (0, 0, 0);
        for v in a {
            if v % 4 == 0 {
                z += 1;
            } else if v % 2 == 0 {
                y += 1;
            } else {
                x += 1;
            }
        }
        if y == 1 {
            x += 1;
        }
        (x, y >= 2, z)
    };
    if y { x <= z } else { x <= z + 1 }
}


fn main() {
    let stdin = io::stdin();
    let mut sc = Scanner::new(stdin.lock().bytes());
    let n = sc.next();
    if solve(sc.vec(n)) {
        println!("Yes");
    } else {
        println!("No");
    }
}


struct Scanner<R: Read> {
    buf: Vec<u8>,
    bytes: io::Bytes<R>,
}

#[allow(dead_code)]
impl<R: Read> Scanner<R> {
    fn new(bytes: io::Bytes<R>) -> Self {
        Scanner {
            buf: Vec::with_capacity(256),
            bytes: bytes,
        }
    }

    fn next<T: FromStr>(&mut self) -> T
    where
        <T as FromStr>::Err: Debug,
    {
        self.buf.clear();
        for c in self.bytes
            .by_ref()
            .map(|c| c.unwrap())
            .skip_while(|&c| c == ' ' as u8 || c == '\n' as u8)
            .take_while(|&c| !(c == ' ' as u8 || c == '\n' as u8))
        {
            self.buf.push(c);
        }
        str::from_utf8(&self.buf).unwrap().parse().unwrap()
    }

    fn vec<T: FromStr>(&mut self, n: usize) -> Vec<T>
    where
        <T as FromStr>::Err: Debug,
    {
        (0..n).map(|_| self.next()).collect()
    }

    fn pairs<A: FromStr, B: FromStr>(&mut self, n: usize) -> Vec<(A, B)>
    where
        <A as FromStr>::Err: Debug,
        <B as FromStr>::Err: Debug,
    {
        (0..n).map(|_| (self.next(), self.next())).collect()
    }

    fn trios<A: FromStr, B: FromStr, C: FromStr>(&mut self, n: usize) -> Vec<(A, B, C)>
    where
        <A as FromStr>::Err: Debug,
        <B as FromStr>::Err: Debug,
        <C as FromStr>::Err: Debug,
    {
        (0..n)
            .map(|_| (self.next(), self.next(), self.next()))
            .collect()
    }

    fn mat<T: FromStr>(&mut self, m: usize, n: usize) -> Vec<Vec<T>>
    where
        <T as FromStr>::Err: Debug,
    {
        (0..n).map(|_| self.vec(m)).collect()
    }
}


#[allow(dead_code)]
fn print_foreach<T: Display>(answer: &[T]) {
    for x in answer {
        println!("{}", x);
    }
}


#[allow(dead_code)]
fn print_yn(answer: bool, yes: &str, no: &str) {
    println!("{}", if answer { yes } else { no });
}


#[allow(dead_code)]
fn print_or<T: Display>(answer: &Option<T>, or: &T) {
    match *answer {
        Some(ref x) => println!("{}", x),
        None => println!("{}", or),
    }
}