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<iostream>
#include<cstdio>
#define N 100100
using namespace std;

int n,mx,num[N];

inline bool pd(int u)
{
	int tt=0,i,cnt=0;
	bool have=0;
	for(i=1;i<=n;i++)
	{
		if(num[i]==u)
		{
			cnt++;
			continue;
		}
		if(u-num[i]>=2) return 0;
		tt++;
	}
	return u>=(tt+(!!cnt))&&u<=(tt+cnt/2);
}

int main()
{
	int i,j;
	cin>>n;
	for(i=1;i<=n;i++)
	{
		scanf("%d",&num[i]);
		mx=max(mx,num[i]);
	}
	if(pd(mx)||pd(mx+1))
	{
		puts("Yes");
	}
	else puts("No");
}