Problem:
Score : 700 points

Problem Statement

There are N cats.
We number them from 1 through N.

Each of the cats wears a hat.
Cat i says: "there are exactly a_i different colors among the N - 1 hats worn by the cats except me."

Determine whether there exists a sequence of colors of the hats that is consistent with the remarks of the cats.

Constraints

2 ≤ N ≤ 10^5

1 ≤ a_i ≤ N-1

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 ... a_N

Output

Print Yes if there exists a sequence of colors of the hats that is consistent with the remarks of the cats; print No otherwise.

Sample Input 1

3
1 2 2

Sample Output 1

Yes

For example, if cat 1, 2 and 3 wears red, blue and blue hats, respectively, it is consistent with the remarks of the cats.

Sample Input 2

3
1 1 2

Sample Output 2

No

From the remark of cat 1, we can see that cat 2 and 3 wear hats of the same color.
Also, from the remark of cat 2, we can see that cat 1 and 3 wear hats of the same color.
Therefore, cat 1 and 2 wear hats of the same color, which contradicts the remark of cat 3.

Sample Input 3

5
4 3 4 3 4

Sample Output 3

No

Sample Input 4

3
2 2 2

Sample Output 4

Yes

Sample Input 5

4
2 2 2 2

Sample Output 5

Yes

Sample Input 6

5
3 3 3 3 3

Sample Output 6

No

Solution in Rust (1.15.1) (judge verdict: Accepted)

use std::io;
use std::collections::VecDeque;

fn main() {
    let mut input = Input::new();
    let n = input.next().parse::<usize>().unwrap();
    let mut a = vec![0; n];
    let mut max = 0;
    for i in 0..n {
        a[i] = input.next().parse::<usize>().unwrap();
        if max < a[i] {
            max = a[i];
        }
    }
    a.sort();
    let mut ok = false;
    for i in max..max + 2 {
        let mut t = true;
        for j in 0..n {
            let v = if i as i32 + i as i32 - n as i32 > j as i32 {
                i - 1
            } else {
                i
            };
            t &= v == a[j];
        }
        ok |= t;
    }
    println!("{}", if ok { "Yes" } else { "No" });
}

struct Input {
    queue: VecDeque<String>,
}

impl Input {
    fn new() -> Input {
        Input { queue: VecDeque::new() }
    }

    fn next(&mut self) -> String {
        if self.queue.is_empty() {
            let mut line = String::new();
            let _ = io::stdin().read_line(&mut line);
            for x in line.split_whitespace() {
                self.queue.push_back(String::from(x));
            }
        }
        return self.queue.pop_front().unwrap();
    }
}