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: Runtime Error)

package 郵便配達;

import java.io.File;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.NoSuchElementException;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) throws FileNotFoundException {
		new Main().run();
	}

	void run() {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int[] a = new int[n];
		int ma = 0;
		int mi = Integer.MAX_VALUE >> 4;
		for (int i = 0; i < n; ++i) {
			a[i] = sc.nextInt();
			ma = Math.max(ma, a[i]);
			mi = Math.min(mi, a[i]);
		}
		int cnt_ma = 0, cnt_mi = 0;
		for (int i = 0; i < n; ++i) {
			if (ma == a[i]) {
				++cnt_ma;
			} else {
				++cnt_mi;
			}
		}
		if (ma == mi) {
			// cnt_maのみを考える
			if (ma == 1) {
				System.out.println("Yes");
				return;
			}
			if (ma == n - 1) {
				System.out.println("Yes");
				return;
			}
			System.out.println("No");
			return;
		}
		int v = ma - cnt_mi;
		if (v <= cnt_ma / 2 && v >= 1) {
			System.out.println("Yes");
		} else {
			System.out.println("No");
		}
	}

	void tr(Object... objects) {
		System.out.println(Arrays.deepToString(objects));
	}
}