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())
src = list(map(int,input().split()))
ctr = Counter(src)

if len(ctr) > 2:
    print('No')
    exit()

if len(ctr) == 1:
    k = src[0]
    print('Yes' if 2*k <= N or k == N-1 else 'No')
    exit()

min_k, max_k = min(ctr.keys()) ,max(ctr.keys())
min_v, max_v = ctr[min_k], ctr[max_k]
if min_v > min_k:
    print('No')
else:
    print('Yes' if (max_k - min_v)*2 <= max_v else 'No')