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
import sys

read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

N = int(readline())
A = sorted(map(int, readline().split()))

def main(A):
    N = len(A)
    if A[0] == A[-1]:
        x = A[0]
        return x == N - 1 or 2 * x <= N
    if A[0] + 1 != A[-1]:
        return False
    a, b = A[0], A[-1]
    full = b
    unique = A.count(a)
    people, color = N - unique, A[-1] - unique
    return color > 0 and 2 * color <= people

print('Yes' if main(A) else 'No')