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
import sys

readline = sys.stdin.readline
MOD = 10 ** 9 + 7
INF = float('INF')
sys.setrecursionlimit(10 ** 5)


def main():
    n = int(readline())
    a = list(map(int, readline().split()))
    a_max = max(a)
    a_min = min(a)
    if a_max - a_min > 1:
        return print("No")
    elif a_max == a_min:
        if 1 <= a_min <= n // 2 or a_min == n - 1:
            return print("Yes")
        else:
            return print("No")
    else:
        c_min = a.count(a_min)
        c_max = a.count(a_max)

        if 1 <= a_max - c_min <= c_max // 2:
            return print("Yes")
        else:
            return print("No")


if __name__ == '__main__':
    main()
