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(x) for x in input().split()]
C = max(a)
ans = ""

if C - min(a) > 1:
	ans = "No"
elif C == min(a):
	if N >= 2 * C or N == C + 1:
		ans = "Yes"
	else:
		ans = "No"
else:
	if C - a.count(C - 1) > 0 and N - a.count(C - 1) >= 2 * (C - a.count(C - 1)):
		ans = "Yes"
	else:
		ans = "No"
print(ans)