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;

const int maxn=1e5+10;

int n,mx,mn,a[maxn],cnt[maxn];

int main()
{
#ifdef h10
	freopen("B.in","r",stdin);
	freopen("B.out","w",stdout);
#endif
	int i;
	scanf("%d",&n);
	mx=0; mn=0x7fffffff;
	for (i=1;i<=n;i++)
	{
		scanf("%d",&a[i]);
		mx=max(mx,a[i]);
		mn=min(mn,a[i]);
		cnt[a[i]]++;
	}
	if (mx-mn>1)
	{
		puts("No");
		return 0;
	}
	if (mn==mx)
	{
		puts(mx*2<=n||mn==n-1?"Yes":"No");
		return 0;
	}
	int p=cnt[mn];
	puts(p<mx&&p+2*(mx-p)<=n?"Yes":"No");
}
