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: Wrong Answer)

#include "iostream"
#include "climits"
#include "list"
#include "queue"
#include "stack"
#include "set"
#include "functional"
#include "algorithm"
#include "string"
#include "map"
#include "iomanip"

using namespace std;

const long long int MOD = 1000000007;

long long int N, M, K, H, W, L, R;


int main() {
	ios::sync_with_stdio(false);
	cin.tie(0);

	cin >> N;
	vector<int>num(N);
	int l = INT_MAX;
	int r = 0;
	for (int i = 0; i < N; i++) {
		cin >> num[i];
		l = min(l, num[i]);
		r = max(r, num[i]);
	}
	if (r - l > 1) {
		cout << "No\n";
		return 0;
	}
	if (r == l) {
		if (r * 2 > N&&r+1!=N) {
			cout << "No\n";
		}
		else {
			cout << "Yes\n";
		}
		return 0;
	}
	for (int i = 0; i < N; i++) {
		if (num[i] == l) {
			K++;
		}
	}
	if (K + 1 == r) {
		cout << "Yes\n";
		return 0;
	}
	cout << "No\n";
	return 0;
}