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
from collections import Counter
input = sys.stdin.buffer.readline

N = int(input())
a = list(map(int, input().split()))

c = Counter(a)
if len(c.most_common()) > 2:
    print('No')
elif len(c.most_common()) == 1:
    if c.most_common()[0][0] == N-1:
        print('Yes')
    else:
        if c.most_common()[0][0] * 2 <= N:
            print('Yes')
        else:
            print('No')
else:
    x, nx = c.most_common()[0]
    y, ny = c.most_common()[1]
    if x > y:
        x, y = y, x
        nx, ny = ny, nx
    if y - x != 1:
        print('No')
    else:
        if 1 <= y - nx <= ny//2:
            print('Yes')
        else:
            print('No')
