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 = list(map(int, input().split()))
max_a = max(a)
min_a = min(a)
if min_a == max_a:
  if min_a == n-1 or min_a <= n // 2:
    print("Yes")
  else:
    print("No")
elif min_a + 1 == max_a:
  x = a.count(min_a)
  y = a.count(max_a)
  if x < max_a and (max_a - x) * 2 <= y:
    print("Yes")
  else:
    print("No")
else:
  print("No")