Jaccard index

The Jaccard index is a statistic used for comparing the similarity and diversity of two sets. Namely, the Jaccard index $J(A,B)$ of $A$ and $B$ is $J(A,B) = \frac{\mid A\cap B\mid }{\mid A\cup B\mid }.$

For example, the Jaccard index of the sets $\{1,2,3\}$ and $\{3,4\}$ is $0.25$ .

Write a program to compute the Jaccard index of pairs of sets of integers.

Input

The input consists of several cases. Each case starts describes two sets $A$ and $B$ . The first set $A$ starts with its cardinality $m \geq 0$ and then follow its $m$ integer elements in strictly increasing order. The second set $B$ starts with its cardinality $m \geq 0$ and then follow its $n$ integer elements in strictly increasing order. For each case, $m+n\ge1$ .

Output

For each case in the input, print the Jaccard index of its two sets in a different line with 3 digits of precision.

Hint

Basic set theory may save you some valuable coding time.
Use @cout.setf(ios::fixed); cout.precision(3);@ at the beginning of your program to print real numbers with 3 digits of precision.

Problem information

Author: Guillem Godoy, Jordi Petit

Generation: 2026-01-25T11:33:28.054Z