Tournament Graph Distribution

A tournament graph is a directed graph where a single directed edge exists between every pair of nodes. Given n, your task is to calculate for each k = 1 \dots n the number of tournament graphs that have n nodes and k strongly connected components.

Input

The only line has an integer n: the number of nodes.

Output

Print n lines: for each k=1 \dots n the number of graphs modulo 10^9+7.

Constraints

$1 \le n \le 500$

Example

Input

3

Output

2
0
6