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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;

vector <int> v;
int n;

int main() {
	cin >> n;
	for (int i = 0; i < n; i++) {
		int t;
		cin >> t;
		v.push_back(t);
	}
	sort (v.begin(), v.end());
	if (v.back() - v[0] > 1) {
		cout << "No";
		return 0;
	}
	if (v.back() == v[0]) {
		if (n == v[0] + 1 || n >= v[0] * 2) {
			cout << "Yes";
		}
		else
			cout << "No";
		return 0;
	}
	int k = 0;
	for (int i = 0; i < v.size(); i++) {
		if (v[i] == v[0])
			k = i;
	}
	k++;
	int t = v[0] - k + 1;
	if (t <= 0) {
		cout << "No";
		return 0;
	}
	if (n - k >= 2 * t) {
		cout << "Yes";
	}
	else
		cout << "No";
	return 0;
}