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
def check():
    N = int(input())
    A = list(map(int, input().split()))
    if len(set(A))==1:
        if max(A)==N-1:
            return 'Yes'
    large = max(A)
    small = large-1
    n_s = list(map(lambda x:x-small,A)).count(0)
    if large==n_s:
        if n_s==N:
            return 'Yes'
        return 'No'
    if large<n_s:
        return 'No'
    if 2*(large-n_s)+n_s<=N:
        return 'Yes'
    return 'No'
print(check())