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 collections import Counter

N = int(input())
A = Counter(map(int, input().split()))

if len(A.keys()) >= 3:
    print('No')
    exit()

if len(A.keys()) == 1:
    p = list(A.keys())[0]
    print('Yes' if 2 * p <= N or p == N - 1 else 'No')
    exit()

p1, p2 = sorted(A.keys())
print('Yes' if p2 - p1 == 1 and (A[p1] + 1) <= p2 <= (A[p1] + A[p2] // 2) else 'No')
