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>
#include "memory.h"
#include <string>
#include <set>

using namespace std;

vector<int> A;

int main() {
	int n;
	scanf("%d", &n);
	A.resize(n);
	for(int i = 0; i < n; i++) scanf("%d", &A[i]);
	sort(A.begin(), A.end());
	if (A.back() - A[0] > 1) { printf("No\n"); return 0; }
	int q = 0;
	while (A[q] == A.back() - 1) q++;
	if (A[0] == A.back() && A[0] == A.size() - 1) { printf("Yes\n"); return 0; }
	if (q > A[0]) { printf("No\n"); return 0; }
	if (A.size() - q < 2*(A.back() - q)) { printf("No\n"); return 0; }
	printf("Yes\n");
    return 0;
}