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
from collections import Counter
n = int(input())
a = [int(item) for item in input().split()]

cnt = Counter(a)
if len(cnt) == 1:
    color_num = max(cnt)
    if color_num == n-1 or color_num <= n // 2:
        print("Yes")
    else:
        print("No")
elif len(cnt) == 2:
    color_num = max(cnt)
    # Cout can be 2 sequential number
    if color_num - 1 not in cnt:
        print("No") 
        exit()
    if cnt[color_num-1] <= color_num - 1 and cnt[color_num-1] >= 2*color_num - n:
        print("Yes")
    else:
        print("No")
else:
    print("No")