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>
#include <cstring>
#define N 100005
using namespace std;
int n,a[N];
bool solve(){
	scanf("%d",&n);
	bool t=1,t1=1;
	int mn=1e9,mx=-1e9;
	for(int i=1;i<=n;i++){
		scanf("%d",&a[i]);
		if(a[i]!=n-1) t=0;
		if(a[i]!=a[1]) t1=0;
		mn=min(mn,a[i]);
		mx=max(mx,a[i]);
	}
	if(t) return 1;
	if(t1&&a[1]*2>n) return 0;
	if(mx-mn>1) return 0;
	int sum=0,tot=0;
	for(int i=1;i<=n;i++)
		if(a[i]==mx) sum++;
		else tot++;
	if(mx<=tot) return 0;
	if((mx-tot)*2>sum) return 0;
	return 1;
}
int main(){
	if(solve()) puts("Yes");
	else puts("No");
	return 0;
}