Saeed and Ahmad are planning to go out on a trip to Treeland, The Treeland is a city that has $$$n$$$ tourist places, the roads between these tourist places are specific which means you can move from a tourist place to another if and only if there is a road between them, there are $$$n - 1$$$ road between all tourist places in total and it's guaranteed that you can go from any tourist place to any other tourist place throughout a finite sequence of roads, that is the $$$n$$$ tourist places form a connected tree.

Ahmad and Saeed want to visit all $$$n$$$ tourist places in the following way:

First of all, they will specify the order that they will visit tourist places, that is; they will give every tourist place a unique number between $$$1$$$ and $$$n$$$.

Secondly, they will start with the tourist place with the number $$$1$$$, go to the tourist place with the number $$$2$$$, then go to the tourist place with the number $$$3$$$, and so on till they visit the tourist place with the number $$$n$$$.

Ahmad is lazy, he will get tired after making a few steps, so Saeed wants to provide him with the number of steps of the trip before they go out, The problem is that they didn't plan the order that they will visit tourist places so that Saeed decided to calculate the expected number of steps of the trip over all possible orders.

The number of steps between two tourist places is the number of roads in the shortest path between them.