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
import sys

if __name__ == '__main__':
    N = int(input())
    a = list(map(int, input().split()))

    min_num = min(a)
    max_num = max(a)

    if max_num - min_num >= 2:
        print("No")
    elif max_num == min_num :
        if max_num == N -1 or 2*max_num <= N:
            print("Yes")
        else:
            print("No")
    else:
        x = a.count(min_num)
        y = a.count(max_num)
        if x < max_num and 2 * (max_num - x) <= y:
            print("Yes")
        else:
            print("No")