Jaccard index P67731

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

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 ≥ 0 and then follow its m integer elements in strictly increasing order. The second set B starts with its cardinality m ≥ 0 and then follow its n integer elements in strictly increasing order. For each case, m+n≥1.

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.