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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Main main = new Main();
        main.solve();
    }
    public void solve() {
        Scanner scan = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        int N = scan.nextInt();
        int[] a = new int[N];
        for (int i = 0; i < N; i++) {
            a[i] = scan.nextInt();
        }
        int min = Arrays.stream(a).min().getAsInt();
        int max = Arrays.stream(a).max().getAsInt();
        if (N == 2) {
            System.out.println("Yes");
            return;
        }
        if (2 <= max - min) {
            System.out.println("No");
            return;
        }
        if (max - min == 0) {
            if (max == N - 1 || max * 2 <= N) {
                System.out.println("Yes");
            } else {
                System.out.println("No");
            }
            return;
        }
        long max_count = Arrays.stream(a).filter(i -> i == max).count();
        long min_count = Arrays.stream(a).filter(i -> i == min).count();
        if (min_count < max && 2 * (max-min_count) <= max_count){
            System.out.println("Yes");
        } else {
            System.out.println("No");
        }
    }
}