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 <cstring>
#include <algorithm>
#include <vector>
using namespace std;
const int maxn = 100005;
int N, a[maxn];
int main() {
	scanf("%d", &N);
	int mx = 0, mn = N;
	for(int i=1; i<=N; ++i) {
		scanf("%d", a+i);
		mx = max(mx, a[i]);
		mn = min(mn, a[i]);
	}
	if(mx-mn>1 || mx>N) {
		puts("No"); return 0;
	}
	int cx = 0, cn = 0;
	for(int i=1; i<=N; ++i) {
		cx += a[i] == mx;
		cn += a[i] == mn;
	}
	if(mx==mn) {
		if(mx==N-1) puts("Yes");
		else if(N%mx==0) puts("Yes");
		else puts("No");
		return 0;
	}
	if(cn+cx/2<mx || cn+1>mx) puts("No");
	else puts("Yes");
	return 0;
}