## DMOPC '18 Contest 4 P1 - Dr. Henri and Differential Photometry

View as PDF

Points: 3 (partial)
Time limit: 2.0s
Memory limit: 64M

Author:
Problem type
Allowed languages
Ada, Assembly, Awk, Brain****, C, C#, C++, COBOL, CommonLisp, D, Dart, F#, Forth, Fortran, Go, Groovy, Haskell, Intercal, Java, JS, Kotlin, Lisp, Lua, Nim, ObjC, OCaml, Octave, Pascal, Perl, PHP, Pike, Prolog, Python, Racket, Ruby, Rust, Scala, Scheme, Sed, Swift, TCL, Text, Turing, VB, Zig

Dr. Henri is looking through his telescope at the MRD Observatory. He is observing a certain star and wants to find its magnitude (a measure of brightness), . The magnitude of a star can be any real number.

Dr. Henri is using a device called a differential photometer to measure magnitude. Although this device is very precise, it cannot directly measure the magnitude of a star; it can only measure the difference in magnitudes between two stars.

Fortunately, Dr. Henri knows the magnitude of a certain star . He decides to find by constructing a sequence of stars beginning with and ending with . Then, for each star on the list (except ), he records the difference between the magnitudes of the stars and , for a total of observations. He can then calculate a value for from this sequence.

Dr. Henri knows that he must take multiple measurements in order to ensure accuracy, so he constructs such sequences. Sequence consists of observations, and the value of calculated from is denoted as . Of course, due to natural error in measuring, the 's calculated from each sequence may not be exactly the same. So Dr. Henri will use the mean of the 's, , as the final , which he denotes .

#### Input Specification

The first line of input will contain one integer, .
The second line will contain one real number, .
The next lines will contain one integer , followed by space-separated real numbers , the observations from the -th list.

#### Output Specification

A single line containing one real number, . Your answer will be judged as correct if it has an absolute error of no more than .

#### Sample Input

3
-1.46
2 4.53 1.20
3 4.77 -1.45 2.35
1 5.69

#### Sample Output

4.236667