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<iostream>
#include<cstdio>

#define EXIT puts("No"),exit(0)

using namespace std;

int n,x,cnt[100000],a,b;

int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;++i)scanf("%d",&x),++cnt[x];
	for(int i=1;i<n;++i){if(cnt[i]&&b)EXIT;if(cnt[i])if(a)b=i;else a=i;}
	if(b-a>1)EXIT;
	if(!b)if(a<<1<=n||a==n-1)puts("Yes"),exit(0);else puts("No"),exit(0);
	else{
		int c=b-cnt[a];
		if(c<1)EXIT;
		if(c!=cnt[b]-1&&c<<1>cnt[b])EXIT;
		if(cnt[b]==2){
			if(c+cnt[a]-1!=a&&cnt[b]+cnt[a]-1!=a)EXIT;
			puts("Yes");
			return 0;
		}
		if(c<<1>cnt[b])c=cnt[b];
		if(c+cnt[a]-1!=a)puts("No");else puts("Yes");
	}
}