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) = |
| . |

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.

Public test cases

**Input**

3 1 2 3 2 3 4 11 -9 -7 -5 -1 3 4 5 8 11 17 19 11 -8 -5 -4 1 3 6 8 9 11 12 17 0 3 1 2 3

**Output**

0.250 0.294 0.000

Information

- Author
- Guillem Godoy, Jordi Petit
- Language
- English
- Translator
- Original language
- Catalan
- Other languages
- Catalan
- Official solutions
- C++
- User solutions
- C++