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 n,a[100010],mn,mx,cnt;

void work()
{
	scanf("%d",&n),mn=n;
	for (int i=1; i<=n; i++)
		scanf("%d",&a[i]),mn=min(mn,a[i]),mx=max(mx,a[i]);
	if (mn==mx)  puts((2*mn<=n)||(mn==n-1)?"Yes":"No"),exit(0);
	if (mn!=mx-1)  puts("No"),exit(0);
	for (int i=1; i<=n; i++)  cnt+=(a[i]==mn);
	if ((cnt>=mx)||(2*(mx-cnt)>n-cnt))  puts("No"),exit(0);
	puts("Yes");	
}

int main()
{
	work();
	return 0;
}
