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())
l = list(map(int, input().split()))
if len(set(l)) == 1:
  if l[0] <= n//2 or l[0] == n-1:
    print('Yes')
  else:
    print('No')
elif len(set(l)) > 2 or max(l)-min(l) > 1:
  print('No')
else:
  ma = max(l)
  mi = ma - 1
  mac = l.count(ma)
  mic = n - mac
  if mic <= mi <= mic-1+mac//2:
    print('Yes')
  else:
    print('No')