Easier than you may think!

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.