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(int(x) for x in input().split())

ma = max(A)
mi = min(A)

if ma - mi > 1:
    print("No")
    exit()

if ma == mi:
    if n >= ma * 2 or n == ma + 1:
        print("Yes")
    else:
        print("No")
    exit()

# ma = mi + 1
if A.count(mi) <= mi and A.count(ma) >= (ma - A.count(mi)) * 2:
    print("Yes")
else:
    print("No")