J. Sum of Squares
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

For a given natural number $$$n$$$, find $$$n+1$$$ positive integers, not exceeding $$$10^9$$$, such that the sum of the squares of the first $$$n$$$ of these numbers equals the square of the last one.

Input

An integer $$$n$$$ is given ($$$1 \le n \le 1000$$$).

Output

Output $$$n+1$$$ integers in the range from 1 to $$$10^9$$$. If there are multiple correct answers, output any. If there are no solutions, output the number -1.

Example
Input
2
Output
3 4 5