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=map(int,input().split())
c=[0]*n
col=0
mx=0
for i in a:
	if c[i]==0:
		col+=1
	c[i]+=1
	mx=max(mx,i)
if col>2:
	print("No")
elif col==1:
	if mx==n-1 or 2*mx<=n:
		print("Yes")
	else:
		print("No")
else:
	x,y=c[mx-1],c[mx]
	if x+1<=mx and mx<=x+y/2:
		print("Yes")
	else:
		print("No")