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 cat():
    N = int(input())
    A = list(map(int, input().split()))

    # こいつらは絶対いける
    if A == [1] * N:
        return True
    if A == [N - 1] * N:
        return True

    # 数字は高々隣り合う数2種になるはず
    Aset = set(A)
    if len(Aset) == 1:
        Amax = A[0]
        cnt = N - Amax + 1
        if N <= 2 * cnt - 2:
            return True
        else:
            return False
    elif len(Aset) == 2:
        A.sort()
        Amax = A[-1]
        Amin = A[0]
        if Amin + 1 != Amax:
            return False
        lower = N - Amax + 1
        upper = 2 * lower - 2
        c = Counter(A)
        if lower <= c[Amax] <= upper:
            return True
        else:
            return False
    else:
        return False


if __name__ == "__main__":
    if cat():
        print("Yes")
    else:
        print("No")