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: Time Limit Exceeded)

#include <bits/stdc++.h>

#define int long long

using namespace std;

int a[100001];

 main () {
	ios_base::sync_with_stdio (0);
	cin.tie (0);  	
	int n;
	cin >> n;
	int mn = 1e9 + 7;
	int mx = 0;
	int kl = 0, kr = 0;
	for (int i = 1;i <= n;i ++) {
		cin >> a[i];
		mn = min (mn, a[i]);
		mx = max (mx, a[i]);
	}
	for (int i = 1;i <= n;i ++) {
		if (a[i] == mn) kl ++;
		if (a[i] == mx) kr ++;
	}
	if (mn == mx) {
		if (mn == n - 1) {
			cout << "Yes";
			while (1) {}
			return 0;
		}
		if (mn + mn <= n) {
			while (1) {}
			cout << "Yes";
			return 0;
		}         
		cout << "No";
		return 0;
	}      
	int A = mx;
	if (A >= kl + 1 && kr / 2 + kl >= A) {
		while (1) {}
		cout << "Yes";         	
	}
	else {
		cout << "No";
	}
	return 0;
}