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;
int n,a[111111];
bool chk(int cat,int color){
	if(color <= 0)return false;
	return cat >= 2 * color;
}
int main(){
	scanf("%d",&n);
	int S = n+1, E = -1;
	for(int i=1; i<=n; i++){
		scanf("%d",&a[i]);
		S = min(S,a[i]);
		E = max(E,a[i]);
	}
	if(E - S >= 2){
		puts("No");
		return 0;
	}
	if(E == S){
		if(E == 1 || E == n-1 || E * 2 <= n)
			puts("Yes");
		else
			puts("No");
		return 0;
	}
	int cnt = 0;
	for(int i=1; i<=n; i++)
		if(a[i] == S)
			cnt++;
	puts(chk(n-cnt,E-cnt)?"Yes":"No");
	return 0;
}
