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()))

l.sort()
ans = "Yes"
count = 1
if l[0] == l[-1]:
  if ((n // 2) < l[0]) and (l[0] != 1) and (l[0] != n - 1):
    ans = "No"
elif l[-1] - l[0] >= 2:
    ans = "No"
else:
  for i in range(n-1):
    if l[i+1] - l[i] == 0:
      count += 1
    elif l[i+1] - l[i] == 1:
      break
  umax = count + (n - count) // 2
  if (l[-1] > umax) or (l[-1] <= count):
    ans = "No"

print(ans)