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
length = int(input())
target = [int(n) for n in input().split(" ")]
if max(target) - min(target) > 1:
    print("No")
elif max(target) >= length:
    print("No")
elif max(target) - min(target) == 1 and (target.count(min(target)) == min(target) and target.count(max(target)) > 1 or (target.count(min(target)) <= min(target) and target.count(max(target)) // 2 >= max(target) - target.count(min(target)) )  ):
    print("Yes")
elif max(target) - min(target) == 0 and ( (length % 2 == 0 and min(target) * 2 <= length) or (length % 2 == 1 and 2 * (min(target) - 1) + 3 <= length)  or min(target) + 1 == length):
    print("Yes")
else:
    print("No")