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 a[100005];
void solve()
{
	int n;cin>>n;
	int mn=n,mx=0; 
	for(int i=1;i<=n;i++)
	{
		scanf("%d",&a[i]);
		mn=min(mn,a[i]);
		mx=max(mx,a[i]);
	}
	if(mx-mn>=2)
	{
		puts("No");
		return ;
	}
	if(mn==mx&&mx==n-1)
	{
		puts("Yes");
		return ;
	}
	int cnt1=0,cnt2=0; 
	for(int i=1;i<=n;i++)
		if(a[i]==mx-1) cnt1++;
		else cnt2++;
	int p=mx-cnt1;
	if(p*2>cnt2||p<=0)
	{
		puts("No");
		return ;
	}
	puts("Yes");
}
int main()
{
//	freopen("hat.in","r",stdin);
//	freopen("hat.out","w",stdout); 
	solve();
	return 0;
}