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>
void maxs(int&a,int b){if(a<b)a=b;}
void mins(int&a,int b){if(a>b)a=b;}
int n,a[100007];
int main(){
	scanf("%d",&n);
	int mx=0,mn=n+1,c1=0,c2=0;
	for(int i=1;i<=n;++i){
		scanf("%d",a+i);
		maxs(mx,a[i]);
		mins(mn,a[i]);
	}
	if(mx==n-1&&mx==mn)return puts("Yes"),0;
	for(int i=1;i<=n;++i){
		if(a[i]<mx){
			if(a[i]!=mx-1)return puts("No"),0;
			++c1;
		}else ++c2;
	}
	puts(c2>1&&c1+1<=mx&&mx<=c1+c2/2?"Yes":"No");
	return 0;
}