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 solve(A):
    N = len(A)
    p = max(A)
    if p > min(A)+1:
        return False

    cnt = sum(int(a==p) for a in A)

    if p == N-1 and cnt == N:
        return True

    cnt_max = 2*(N-p)
    cnt_min = N-p+1

    return cnt_min <= cnt <= cnt_max

if __name__ == '__main__':
    N = int(input())
    A = tuple(map(int,input().split()))
    print('Yes' if solve(A) else 'No')