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


def main():
    N = int(input())
    A = list(map(int, input().split()))
    C = Counter(A)
    mn = min(C)
    mx = max(C)
    if mx - mn < 0 or 1 < mx - mn:
        print("No")
        return
    elif mx - mn == 0:
        if mx == N - 1:
            neccessary = N
        else:
            neccessary = mx * 2
    elif mx - mn == 1:
        single = C[mn]
        if mx <= single:
            print("No")
            return
        neccessary = single + (mx - single) * 2
    if neccessary <= N:
        print("Yes")
    else:
        print("No")


if __name__ == "__main__":
    main()
