# Easier than you may think!

Computer Science Level pending

Suppose we have a $$n$$-tuple $$d=(0,2,2,\dots,n-2,n-2,n)$$ for a certain even integer $$n$$.

$$d$$ represents the list of degrees of the $$n$$ nodes in a undirected graph.

Suppose $$n=2^{2^6}-2,$$ how many distinct graphs with $$n$$ nodes have a permutation of $$d$$ as list of degrees?

Give the answer modulo $$10^9+7$$.

Note:

The degree of a node in a graph is the number of edges connected to it. Every pair of vertices is connected by at most one edge. Every node cannot be connected with itself.

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