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 = [int(x) for x in input().split()]

A_set = sorted(set(A))
if len(A_set) == 1:
    print("Yes" if A_set[0] <= N // 2 or A_set[0] == N - 1 else "No")
elif len(A_set) == 2 and A_set[0] + 1 == A_set[1]:
    cnt_min = A.count(A_set[0])
    cnt_max = N - cnt_min
    if cnt_min <= A_set[0] and cnt_min + 1 <= A_set[1] <= cnt_min + cnt_max // 2:
        print("Yes")
    else:
        print("No")
else:
    print("No")
