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)

#![allow(unused_imports)]
#![allow(dead_code)]
use std::cmp::*;
use std::collections::*;

const INF: i64 = 0x3f3f3f3f3f3f3f3f;
const NOTHING: usize = std::usize::MAX;
const DX: [usize; 4] = [1, 0, std::usize::MAX, 0];
const DY: [usize; 4] = [0, 1, 0, std::usize::MAX];

fn main() {
    let n: usize = readln();
    let mut xs: Vec<usize> = readln();
    xs.sort();

    if xs[0] == xs[n - 1] && xs[0] <= n / 2 {
        println!("Yes");
        return;
    }

    if xs[0] == xs[n - 1] && xs[0] == n - 1 {
        println!("Yes");
        return;
    }

    if xs[0] + 1 == xs[n - 2] && xs[n - 2] == xs[n - 1] {
        let mut freq = 0;
        for i in 0..n {
            if xs[i] == xs[0] {
                freq += 1;
            } else {
                break;
            }
        }
        if n - freq >= 2 * (xs[n - 1] - freq) && xs[n - 1] > freq {
            println!("Yes");
            return;
        }
    }

    println!("No");
}


fn get_line() -> String {
    let mut buf = String::new();
    std::io::stdin().read_line(&mut buf).unwrap();
    buf.trim_right().to_string()
}

fn get_chars() -> Vec<char> {
    get_line().chars().collect()
}

fn readln<T: Read>() -> T {
    let mut buf = String::new();
    std::io::stdin().read_line(&mut buf).unwrap();
    T::read(buf.trim_right())
}

trait Read {
    fn read(s: &str) -> Self;
}

macro_rules! read_impl{
    ($($t:ty)*) => ($(
        impl Read for $t {
            fn read(s: &str) -> $t{
                s.parse().unwrap()
            }
        }
    )*)
}
read_impl! { usize u8 u16 u32 u64 isize i8 i16 i32 i64 f32 f64 }

impl<T: Read> Read for Vec<T> {
    fn read(s: &str) -> Self {
        s.split_whitespace().map(T::read).collect()
    }
}

impl<A: Read, B: Read> Read for (A, B) {
    fn read(s: &str) -> Self {
        let tokens: Vec<_> = s.split_whitespace().collect();
        (A::read(tokens[0]), B::read(tokens[1]))
    }
}

impl<A: Read, B: Read, C: Read> Read for (A, B, C) {
    fn read(s: &str) -> Self {
        let tokens: Vec<_> = s.split_whitespace().collect();
        (A::read(tokens[0]), B::read(tokens[1]), C::read(tokens[2]))
    }
}

impl<A: Read, B: Read, C: Read, D: Read> Read for (A, B, C, D) {
    fn read(s: &str) -> Self {
        let tokens: Vec<_> = s.split_whitespace().collect();
        (A::read(tokens[0]), B::read(tokens[1]), C::read(tokens[2]), D::read(tokens[3]))
    }
}