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
#!/usr/bin/env python3
import sys
def debug(*args): print(*args, file=sys.stderr)
def exit(): sys.exit(0)

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

min_ = min(a)
max_ = max(a)

if max_ > min_ + 1:
    print("No")
    exit()

if min_ == max_:
    if min_ == N-1:
        print("Yes")
        exit()
    if 2*min_ <= N:
        print("Yes")
        exit()
    print("No")
    exit()
else:
    # max_ == min_ + 1
    count_min = a.count(min_)
    count_max = a.count(max_)
    if count_min >= max_:
        print("No")
        exit()
    if count_min + 2*(max_ - count_min) <= N:
        debug("hoge")
        print("Yes")
        exit()
    print("No")
