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 = sorted(list(map(int, input().split())))
data = [[-1, 0]]
for x in a:
    if data[-1][0] == x:
        data[-1][1] += 1
    else:
        data.append([x, 1])
data = data[1:]

if len(data) == 1:
    print("Yes" if data[0][0] * 2 <= n or data[0][0] + 1 == n else "No")
elif len(data) == 2:
    if data[0][0] + 1 == data[1][0] and data[0][0] >= data[0][1] and data[1][1] >= 2 * (data[1][0] - data[0][1]):
        print("Yes")
    else:
        print("No")
else:
    print("No")
