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
from collections import Counter
n = int(input())
a = [int(i) for i in input().split()]
a.sort()
c = Counter(a)
if len(c)>2 or a[0]+1<a[-1]: print("No")
elif len(c)==1:
	if a[0]+1==n or n>=2*a[0]: print("Yes")
	else: print("No")
else:
	x,y = c[a[-1]],c[a[0]]
	if y+1<=a[-1]<=x//2+y: print("Yes")
	else: print("No")