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()))

ls_A = len(set(A))

if ls_A >= 3:
  print("No")
  exit()
  
if max(A) - min(A) >= 2:
  print("No")
  exit()

if len(set(A)) == 1:
  if A[0] == N - 1:
    print("Yes")
    exit()
  if N // A[0] >= 2:
    print("Yes")
  else:
    print("No")
else:
  min_A = min(A)
  cnt_min = 0
  for a in A:
    if a == min_A:
      cnt_min += 1
  N -= cnt_min  
  if max(A) - cnt_min <= 0:
    print("No")
    exit()
  if N // (max(A) - cnt_min) >= 2:
    print("Yes")
  else:
    print("No")