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 = list(map(int, input().split()))
import collections
l1 = collections.Counter(a).most_common()
l1.sort()
if len(l1) > 2:
    print("No")
elif len(l1) == 1:#発言が１種類の場合
    if l1[0][0] * 2 <= n or l1[0][0] == n - 1:
        print("Yes")
    else:
        print("No")
else:
    if l1[1][0] - l1[0][0] > 1:
        print("No")
    elif l1[1][1] >= (l1[1][0] - l1[0][1]) * 2 and l1[1][0] > l1[0][1]:
        print("Yes")#多い発言の人数が残りの色数かけ２より多い、全体色数が少ない発言の人数より多い
    else:
        print("No")