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, *a = map(int, open(0).read().split())
M = max(a)
mcnt = a.count(M - 1)
Mcnt = a.count(M)
if Mcnt + mcnt == n:
	if mcnt == 0:
		if 2 * M <= n or M == n - 1:
			print("Yes")
			exit()
	else:
		if 0 < 2 * (M - mcnt) <= n - mcnt:
			print("Yes")
			exit()
print("No")