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.

Examples

Input

3
1 2 2


Output

Yes


Input

3
1 1 2


Output

No


Input

5
4 3 4 3 4


Output

No


Input

3
2 2 2


Output

Yes


Input

4
2 2 2 2


Output

Yes


Input

5
3 3 3 3 3


Output

No
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <map>
using namespace std;

#define SZ(a) (int)(a).size()
typedef long long ll;

int main() {
	cin.sync_with_stdio(false);
	int n;
	cin >> n;
	map<int, int> t;
	for (int i = 0; i < n; i++) {
		int x;
		cin >> x;
		t[x]++;
	}
	int mn = begin(t)->first;
	int mx = prev(end(t))->first;
	int m;
	if (mx > mn+1) {
		puts("No");
		return 0;
	}
	else if (mx == mn) {
		if (mx == n-1) {
			puts("Yes");
			return 0;
		}
		m = mx;
	}
	else {
		m = mx-t[mn];
		n -= t[mn];
	}
	puts(m <= n/2 && m >= 1 ? "Yes" : "No");
	return 0;
}
