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
import collections
N = int(input())
A = [int(_) for _ in input().split()]
c = collections.Counter(A)
l = min(c)
r = max(c)
if r != l + 1:
    print('Yes' if r == l == N - 1 or r == l <= N // 2 else 'No')
    exit()
cl = c[l]
cr = c[r]
print('Yes' if cl + 1 <= r <= cl + cr // 2 else 'No')
