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.read
readline = sys.stdin.readline

N, *a = map(int, read().split())
a.sort()
if a[0] + 1 < a[-1]:
    print('No')
elif a[0] == a[-1]:
    if a[-1] == N - 1 or 2 * a[-1] <= N:
        print('Yes')
    else:
        print('No')
else:
    b = a.count(a[0])
    c = N - b
    if b < a[-1] and 2 * (a[-1] - b) <= c:
        print('Yes')
    else:
        print('No')
