# Round and Round We Go

Time Limit: 1 Second Memory Limit: 32768 KB

A cyclic number is an integer n digits in length which, when multiplied by any
integer from 1 to n, yields a *cycle* of the digits of the original number.
That is, if you consider the number after the last digit to *wrap around* back
to the first digit, the sequence of digits in both numbers will be the same,
though they may start at different positions.

For example, the number 142857 is cyclic, as illustrated by the following table:

Write a program which will determine whether or not numbers are cyclic.

## Input

The input file is a list of integers from 2 to 60 digits in length.
(Note that preceding zeros should not be removed, they are considered part of
the number and count in determining n. Thus, *01* is a two-digit number, distinct
from *1* which is a one-digit number.)

## Output

For each input integer, write a line in the output indicating whether or not it is cyclic.

## Sample Input

142857 142856 142858 01 0588235294117647

## Sample Output

142857 is cyclic 142856 is not cyclic 142858 is not cyclic 01 is not cyclic 0588235294117647 is cyclicSubmit

Source: Greater New York 2001