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
from bisect import bisect_left

N = int(input())
A = sorted(list(map(int, input().split())))
flag = False
if A[-1] - A[0] == 0:
    a = A[0]
    if N == a + 1 or N >= 2 * a:
        flag = True
elif A[-1] - A[0] == 1:
    c = bisect_left(A, A[-1])
    if A[-1] > c and 2 * A[-1] - c <= N:
        flag = True
print("Yes" if flag else "No")