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

const int MAXN = 100005;

int n, a[MAXN];

int main()
{
	ios::sync_with_stdio(false);
	cin >> n;
	for (int i = 1; i <= n; i++) cin >> a[i];
	auto solve = [](int tot) {
		int cnt = 0;
		for (int i = 1; i <= n; i++) {
			if (a[i] != tot && a[i] != tot-1) return false;
			if (a[i] == tot-1) cnt++;
		}
		if (tot < cnt) return false;
		int col = tot-cnt, cat = n-cnt;
		if (cat && col == 0) return false;
		return cat >= 2*col;
	};
	if (solve(a[1]) || solve(a[1]+1)) puts("Yes");
	else puts("No");
	return 0;
}
