For a positive integer n, we denote the integer obtained by reversing the decimal notation of n (without leading zeroes) by rev(n). For example, rev(123) = 321 and rev(4000) = 4.

You are given a positive integer D. How many positive integers N satisfy rev(N) = N + D?

Constraints

* D is an integer.
* 1 ≤ D < 10^9

Input

Input is given from Standard Input in the following format:


D


Output

Print the number of the positive integers N such that rev(N) = N + D.

Examples

Input

63


Output

2


Input

75


Output

0


Input

864197532


Output

1920
def func(diff, cnt9, cnt0):
    if cnt9 <= 0 : return diff == 0
    num = int("9" * cnt9 + "0" * cnt0)
    return sum(func(diff + i * num, cnt9 - 2, cnt0 + 1) * (9 - abs(i) + 1 - (cnt0 < 1)) for i in range(-9, 10) if abs(diff + i * num) < num)

D = input()
print sum(func(D, d, 0) * (10 - d % 2 * 9) for d in range(1, 21))