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())
    col = list(map(int, input().split()))
    col_min, col_max = min(col), max(col)
    if col_min == col_max:
        if col_min == 1 or col_min == n-1:
            print("Yes")
        elif 2*col_min <= n:
            print("Yes")
        else:
            print("No")
    elif col_min + 1 == col_max:
        cnt_min, cnt_max = 0, 0
        for v in col:
            if v == col_min:
                cnt_min += 1
            else:
                cnt_max += 1
        if cnt_max == 1:
            print("No")
        else:
            m = cnt_max//2
            if col_min < cnt_min-1 + 1 or cnt_min-1 + m < col_min:
                print("No")
            else:
                p = col_min - (cnt_min-1)
                if p + cnt_min == col_max:
                    print("Yes")
                else:
                    print("No")
    else:
        print("No")

if __name__ == "__main__":
    main()