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;

#define rep(i,l,r) for(int i=l;i<=r;++i)
const int N=1e5+5;
int a[N];

void out()
{
	puts("No");
	exit(0);
}

int main()
{
	//freopen("1.in","r",stdin);
	int n;
	cin>>n;
	int mx=0;
	rep(i,1,n)
	{
		scanf("%d",a+i);
		mx=max(mx,a[i]);
	}
	int x=0,y=0;
	rep(i,1,n)
	if(a[i]==mx)++x; else
	if(a[i]==mx-1)++y; else
		out();
	if(x>1&&((mx>=y+1&&mx<=y+x/2)||(y==0&&mx==n-1)))puts("Yes");
	else out();
}