Tree and Primes

A tree with $N$ nodes is given. Pick two distinct nodes uniformly at random, then find the probability that the distance between them is a prime number.

The distance between two nodes is the number of edges on the unique path that joins them. All $\binom{N}{2}$ ways of picking two distinct nodes are equally likely.

The first line contains the number of nodes $N$. ($2 \le N \le 100000$)

Each of the next $N-1$ lines contains one edge of the tree, given as the numbers $u$ and $v$ of the two nodes it joins. ($1 \le u, v \le N$, $u \ne v$) The nodes are numbered from $1$ to $N$, and the given edges always form a tree.

Print the probability that the distance between the two chosen nodes is prime, as a fraction in lowest terms. If the probability is $\frac{p}{q}$ with coprime integers $p$ and $q$ and $q \ge 1$, print p/q on one line with no spaces. Print 0/1 when the probability is $0$, and 1/1 when it is $1$.