Round and Round We Go

Time Limit: 2 Seconds
Memory Limit: 65536 KB

**Problem**

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. 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.

**Example**

**Input**

142857

142856

142858

01

0588235294117647

**Output**

142857 is cyclic

142856 is not cyclic

142858 is not cyclic

01 is not cyclic

0588235294117647 is cyclic

Source:

**Greater New York 2001**
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