2. Sum of Divisors
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Find a natural number in the range from 1 to $$$10^9$$$ that is equal to the sum of some $$$n$$$ of its divisors (the selected divisors must be distinct).

Input

One integer $$$n$$$ is given ($$$1 \le n \le 30$$$).

Output

In the first line of the output, print the sought number $$$m$$$. In the second line, print $$$n$$$ distinct natural numbers — the divisors of the number $$$m$$$, the sum of which equals $$$m$$$. The divisors can be printed in any order. If there are multiple correct answers, print any of them. If there is no solution, print -1.

Scoring

Each test is scored independently.

Example
Input
3
Output
6
3 2 1