Write a program that will determine the total number of all connected graphs (undirected and unweighted) with vertices labelled 1 through N, and with the property that there is a unique shortest path from vertex 1 to every other vertex.
The first lines contains the integer N, i.e. the number of vertices of the graph.
- 2 \leq N \leq 300
Since the answer can be a very large number, output the answer modulo 1\,000\,000\,007.
In the figure below there are all four such graphs on 3 vertices.
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