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;
inline int read(){
	int x=0;char ch=getchar();
	while (!isdigit(ch)) ch=getchar();
	while (isdigit(ch)) x=x*10+ch-'0',ch=getchar();
	return x;
}
int n,a[100005],mx=0;
int main(){
	n=read();
	for (int i=1;i<=n;++i){
		a[i]=read();
		mx=max(mx,a[i]);
	}
	for (int i=1;i<=n;++i) if (mx-a[i]>1){
		puts("No");
		return 0;
	}
	int c=0;
	for (int i=1;i<=n;++i) if (a[i]<mx) ++c;
	if (!c){
		if (mx==n-1){
			puts("Yes");
			return 0;
		}
	}
	if (c>=mx){
		puts("No");
		return 0;
	}
	if (n-c<(mx-c)*2){
		puts("No");
		return 0;
	}
	puts("Yes");
	return 0;
}
