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<iostream>

using namespace std;

const int N=1e5+5;
int n;
int a[N];

int main() {
	cin >> n;
	for (int i=0; i<n; i++)
		cin >> a[i];

	int mn=N,mx=0;
	for (int i=0; i<n; i++) {
		mn = min(mn,a[i]);
		mx = max(mx,a[i]);
	}

	if (mn == mx) {
		if (n == mx+1 || n >= 2*mx)
			cout << "Yes\n";
		else
			cout << "No\n";
	} else if (mn == mx-1) {
		int loct=0,hict=0;
		for (int i=0; i<n; i++) {
			if (a[i] == mn) loct++;
			if (a[i] == mx) hict++;
		}
		if (mx >= loct+1 && hict >= 2*(mx-loct)) {
			cout << "Yes\n";
		} else {
			cout << "No\n";
		}
	} else {
		cout << "No\n";
	}
}