The Elvish races of Middle Earth believed that certain numbers were more significant than others. When using a particular quantity n of metal to forge a particular sword, they believed that sword would be most powerful if the thickness k were chosen according to the following rule:
Given a nonnegative integer n, what is the smallest k such that the decimal representations of the integers in the sequence:
n, 2n, 3n, 4n, 5n, ..., kn
contain all ten digits (0 through 9) at least once?
Lord Elrond of Rivendell has commissioned you with the task to develop an algorithm to find the optimal thickness (k) for any given quantity of metal (n).
Input will consist of a single integer n (1 ≤ n ≤ 200000000) per line.
The output will consist of a single integer per line, indicating the value of k needed such that every digit from 0 through 9 is seen at least once.
1 10 123456789 3141592
10 9 3 5