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 = int(input())
As = list(map(int, input().split()))

if len(set(As)) >= 3:
    print("No")
    exit()
elif len(set(As)) == 1:
    print("Yes" if 1 <= As[0] <= N // 2 or As[0] == N - 1 else "No")
    exit()
else:
    p, q = sorted(set(As))
    if p + 1 != q:
        print("No")
        exit()
    t = As.count(p)
    u = N - t
    if t + 1 <= q <= t + u // 2:
        print("Yes")
    else:
        print("No")