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
N=int(input())

a=[int(i) for i in input().split()]
a.sort()


#1匹からでは不可能なので
if a[-1]-a[0]>1:
	print("No")
else:
	#全部が同じではない場合
	for i in range(1,N):
		#a[i]の要素が1個増えたタイミング
		if a[i]!=a[0]:
			if 1<=a[-1]-i<=int((N-i)/2):
				print("Yes")
			else:
				print("No")
			break
	else:
		#全部同じ場合
		if 1<=a[0]<=int(N/2) or a[0]==N-1:
			print("Yes")
		else:
			print("No")
