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::cmp;

fn main() {
    let s = std::io::stdin();
    let mut sc = Scanner { stdin: s.lock() };
    let n: usize = sc.read();
    let mut count = vec![0; n];
    for _ in 0..n {
        let a: usize = sc.read();
        count[a] += 1;
    }
    if solve(count) {
        println!("Yes");
    } else {
        println!("No");
    }
}

fn solve(count: Vec<usize>) -> bool {
    let n = count.len();
    let mut min = 1;
    let mut max = n;
    for colors in 0..n {
        if count[colors] == 0 {
            continue;
        }
        min = cmp::max(min, colors);
        max = cmp::min(max, colors + 1);
    }

    for total_colors in min..(max + 1) {
        let mut ok = true;
        let mut sum = 0;
        let mut group = vec![];
        for colors in 0..n {
            if count[colors] == 0 {
                continue;
            }
            let count = count[colors];
            let others = n - count;
            if count == 1 && colors + 1 != total_colors {
                ok = false;
            }
            if count == 1 {
                sum += 1;
            }
            if count > 1 {
                if total_colors == colors {
                    for groups in 1..(count / 2 + 1) {
                        if total_colors >= groups && total_colors - groups <= others {
                            group.push(groups);
                        }
                    }
                } else if total_colors == colors + 1 && count - 1 <= colors {
                    sum += count;
                } else {
                    ok = false;
                }
            }
        }

        if ok
            && ((group.is_empty() && sum == total_colors)
                || (sum < total_colors && group.contains(&(total_colors - sum))))
        {
            return true;
        }
    }
    false
}

pub struct Scanner<R> {
    stdin: R,
}

impl<R: std::io::Read> Scanner<R> {
    pub fn read<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .stdin
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&b| b == b' ' || b == b'\n' || b == b'\r')
            .take_while(|&b| b != b' ' && b != b'\n' && b != b'\r')
            .collect::<Vec<_>>();
        unsafe { std::str::from_utf8_unchecked(&buf) }
            .parse()
            .ok()
            .expect("Parse error.")
    }
    pub fn vec<T: std::str::FromStr>(&mut self, n: usize) -> Vec<T> {
        (0..n).map(|_| self.read()).collect()
    }
    pub fn chars(&mut self) -> Vec<char> {
        self.read::<String>().chars().collect()
    }
}