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 ans1,ans2,n,a1=0,a2=0;
int main(){
	scanf("%d",&n);
	for(int i=1,x;i<=n;++i){
		scanf("%d",&x);
		if(!ans1)ans1=x;
		if(ans1==x)++a1;
		else{
			if(!ans2)ans2=x;
			if(ans2==x)++a2;else {puts("No");return 0;}
		}
	}
	if(abs(ans1-ans2)>1&&ans2!=0){puts("No");return 0;}
	if(ans1>ans2)swap(ans1,ans2),swap(a1,a2);
	if(ans1){n-=a1;ans2-=a1;if(ans2>0&&(n>=(ans1-a1+1)*2))puts("Yes");else puts("No");}
	else{if(n>=ans2*2||n==ans2+1)puts("Yes");else puts("No");}
	return 0;
}