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=input()
a=map(int, raw_input().split())
if max(a)-min(a)>=2:
	print "No"
	exit()
if max(a)==min(a):
	print "Yes" if a[0]==n-1 or a[0]*2<=n else "No"
else:
	one_cnt=a.count(min(a))
	more_cnt=min(a)+1-one_cnt
	print "No" if one_cnt+more_cnt*2>n or more_cnt<=0 else "Yes"