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<cstdio>
#include<vector>
#include<algorithm>


using namespace std;


int main(void)
{
	int n;

	while(scanf("%d", &n)==1)
	{
		vector<int> a(n);
		int ans=0;

		for(int i=0;i<n;i++)
		{
			scanf("%d", &a[i]);
		}
		sort(a.begin(), a.end());
		int a_min=a[0];
		int a_max=a.back();

		if(a_max==a_min)
		{
			// real=a[0]   real=a[0]+1
			if(a_min*2<=n || a_min==n-1) ans=1;
		}
		if(a_max==a_min+1)
		{
			int single=0;
			for(int i=0;a[i]==a_min;i++)
				single++;
			if(a_max>single && single+2*(a_max-single)<=n) ans=1;
		}

		printf("%s\n", ans?"Yes":"No");
	}

	return 0;
}
