Bob has a tree with

nodes, the set of the edges of this tree is

.
Let

denote the edge set of n-clique, formally
Now give you an integer

, you need to find the number of pair
)
satisfies the following conditions:
1.

,

.
2.

,

.
3.

is an edge set of a tree with

nodes.
The answer may be very large, you only need to output the answer module

.