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()))
m = min(a)
M = max(a)
num_m = 0
num_M = 0
if M - m >= 2:
  print("No")
else:
  if m == M:
    if m == n-1:
      print("Yes")
    else:
      if m <= n/2:
        print("Yes")
      else:
        print("No")
  else:
    for i in range(n):
      if a[i] == m:
        num_m += 1
    more = n - num_m
    num_remain = M - num_m
    if 0 < num_remain <= more/2:
      print("Yes")
    else:
      print("No")