The very same Munchhausen

1000ms

262144K

Description:

A positive integer $$$a$$$ is given. Baron Munchausen claims that he knows such a positive integer $$$n$$$ that if one multiplies $$$n$$$ by $$$a$$$, the sum of its digits decreases $$$a$$$ times. In other words, $$$S(an) = S(n)/a$$$, where $$$S(x)$$$ denotes the sum of digits of the number $$$x$$$.

Find out if what Baron told can be true.

Input:

The only line contains a single integer $$$a$$$ ($$$2 \le a \le 10^3$$$).

Output:

If there is no such number $$$n$$$, print $$$-1$$$.

Otherwise print any appropriate positive integer $$$n$$$. Your number must not consist of more than $$$5\cdot10^5$$$ digits. We can show that under given constraints either there is no answer, or there is an answer no longer than $$$5\cdot10^5$$$ digits.

Sample Input:

Sample Output:

Sample Input:

Sample Output:

Sample Input:

Sample Output:

-1

Informação

Provedor Codeforces

Código CF1120E