- Time limit: 1.00 s
- Memory limit: 512 MB
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