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())
xs = [int(x) for x in input().split()]

def solve(n, xs):
    x_min = min(xs)
    x_max = max(xs)

    if x_max - x_min > 1:
        return "No"

    if x_max == x_min:
        if n == x_max+1:
            return "Yes"
        elif x_max*2 <= n:
            return "Yes"
        else:
            return "No"

    solo_num = sum(1 for x in xs if x==x_min)

    if solo_num >= x_max:
        return "No"

    dup_color = x_max - solo_num
    dup_cat = sum(1 for x in xs if x==x_max)

    if dup_cat < dup_color*2:
        return "No"

    return "Yes"

print(solve(n, xs))
