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
def main():
    n = int(input())
    a = list(map(int,input().split()))
    if (max(a) - min(a)) > 1:
        print("No")
        return 0
    minor = a.count(min(a))
    if n != minor:
        major = n-minor

        mini = minor+1
        maxi = minor + (major//2)
        if mini <= max(a) and max(a) <= maxi:
            print("Yes")
        else:
            print("No")
    else:
        mini = 1
        maxi = minor//2
        if mini <= max(a) and max(a) <= maxi or max(a) == n-1:
            print("Yes")
        else:
            print("No")


main()
