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_macros)]
#![allow(dead_code)]
#![allow(unused_imports)]

use itertools::Itertools;

const U_INF: usize = 1 << 60;
const I_INF: isize = 1 << 60;

fn main() {
    let mut sc = Scanner::new();
    let n = sc.next_usize();
    let mut a = Vec::with_capacity(n);
    for _ in 0..n {
        let ai = sc.next_usize();
        a.push(f(ai));
    }
    
    let a = a.into_iter().map(|m| if m > 2 { 2 } else { m }).collect_vec();
    let two = a.iter().filter(|j| **j == 2).count();
    let one = a.iter().filter(|j| **j == 1).count();
    let zero = a.iter().filter(|j| **j == 0).count();
    
    if zero == 0 {
        println!("Yes");
    } else {
        if zero <= two {
            println!("Yes");
        } else if zero - 1 == two && one == 0 {
            println!("Yes");
        } else {
            println!("No");
        }
    }
}

fn f(u: usize) -> usize {
    if u % 2 != 0 {
        0
    } else {
        1 + f(u / 2)
    }
}

pub struct Scanner {
    buf: std::collections::VecDeque<String>,
}

impl Scanner {
    pub fn new() -> Self {
        Self {
            buf: std::collections::VecDeque::new(),
        }
    }
    
    fn scan_line(&mut self) {
        let mut flag = 0;
        while self.buf.is_empty() {
            let mut s = String::new();
            std::io::stdin().read_line(&mut s).unwrap();
            let mut iter = s.split_whitespace().peekable();
            if iter.peek().is_none() {
                if flag >= 5 {
                    panic!("There is no input!");
                }
                flag += 1;
                continue;
            }
            
            for si in iter {
                self.buf.push_back(si.to_string());
            }
        }
    }
    
    pub fn next<T: std::str::FromStr>(&mut self) -> T {
        self.scan_line();
        self.buf.pop_front().unwrap().parse().unwrap_or_else(|_| panic!("Couldn't parse!"))
    }
    
    pub fn next_usize(&mut self) -> usize {
        self.next()
    }
    
    pub fn next_isize(&mut self) -> isize {
        self.next()
    }
    
    pub fn next_chars(&mut self) -> Vec<char> {
        self.next::<String>().chars().collect()
    }
    
    pub fn next_string(&mut self) -> String {
        self.next()
    }
    
    pub fn next_char(&mut self) -> char {
        self.next()
    }
    
    pub fn next_float(&mut self) -> f64 {
        self.next()
    }
}