There are many fun things to do in preparation for Christmas. Some decorate Christmas trees, others bake gingerbread cookies, and computer scientists like Nella build graphs. In particular, Nella starts off with a collection of
Nella does not want her graph to be too disconnected or it would be too much of a hassle to clean up. Therefore, as her older sibling, you should help her determine the expected number of connected components in her graph.
Constraints
Subtask 1 [5%]
Subtask 2 [35%]
Subtask 3 [60%]
No additional constraints.
Input Specification
The first and only line contains an integer
Output Specification
Output
Sample Input
4
Sample Output
370370374
Explanation
Out of all
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