Description

A number is called a "perfect number" if it is exactly equal to the sum of its factors excluding itself. For example, the factors of $6$ are $1$, $2$, and $3$, and $6=1+2+3$, so $6$ is a perfect number. Write a program to find all perfect numbers not exceeding $N$ and output their factors in the format below (the factors do not include the number itself).

Input Format

An integer $n$ ($0 \le n \le 1000$).

Output Format

For each perfect number, output in the format: the integer, then its factors are followed by its factors. See the sample output for details.
? its factors are ? ? ?

Sample

10

6 its factors are 1 2 3