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<cstdio>
#include<vector>
#include<algorithm>
using namespace std;
int a[100010];
vector<int> vt;
int main()
{
	int n;
	scanf("%d", &n);
	for (int i = 0; i < n; i++) {
		int q;
		scanf("%d", &q);
		vt.push_back(q);
		a[q]++;
	}
	sort(vt.begin(), vt.end());
	vt.erase(unique(vt.begin(), vt.end()), vt.end());
	if (vt.size() == 1) {
		if (vt[0] == n - 1||n/2>=vt[0])puts("Yes");
		else puts("No");
		return 0;
	}
	int t = vt.size();
	if (vt[t - 1] - vt[0] > 1) {
		puts("No");
		return 0;
	}
	if (a[vt[0]] + 1 <= vt[1] && vt[1] <= a[vt[0]] + a[vt[1]] / 2)
		puts("Yes");
	else
		puts("No");
}