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

if len(ctr) >= 3:
    print('No')
    exit()
if len(ctr) == 1:
    k,v = list(ctr.items())[0]
    if k == 1:
        print('Yes')
    elif N <= k:
        print('No')
    elif N >= 2*k:
        print('Yes')
    else:
        print('Yes' if k==N-1 else 'No')

else:
    (k1,v1),(k2,v2) = list(sorted(ctr.items()))
    if k2-k1 != 1 or k2 >= N:
        print('No')
    elif v1 > k1:
        print('No')
    else:
        print('Yes' if v2//2 + v1 >= k2 else 'No')