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
N, *A = map(int, open(0).read().split())

def solve():
    A.sort()

    if A[-1] - A[0] >= 2:
        return False

    if A[-1] - A[0] == 0:
        return (A[0] == N - 1) or (2 * A[-1] <= N)

    M = A.count(A[0])
    return (M < A[-1]) and (2 * (A[-1] - M) <= N - M)

if solve():
    print("Yes")
else:
    print("No")