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

seta = set(a)
if len(seta) == 1:
    if a[0] in (0, N-1) or a[0] <= N // 2:
        print("Yes")
    else:
        print("No")
elif len(seta) == 2:
    a1 = min(seta)
    a2 = max(seta)
    counta1 = a.count(a1)
    if a2 != a1 + 1:
        print("No")
    elif counta1 < a2 and counta1 + 2 * (a2 - counta1) <= N:
        print("Yes")
    else:
        print("No")
else:
    print("No")
