Arithmetic Progression Subsequences (2) X55634

Write a program that reads an integer $n>1$ followed by a sequence of integers, and finds out whether the sequence contains a consecutive subsequence of length $n$ that forms an arithmetic progression.

A consecutive subsequence of integers forms an arithmetic progression if the difference between two consecutive numbers equals a fixed integer value $r$. For instance, $4 5 6 7$ is an arithmetic progression with $r = 1$, and $22 33 44 55 66$ is an arithmetic progression with $r = 11$.

If the input sequence contains such a progression, the program must report the start number and the value $r$. Otherwise, the program must indicate "No arithmetic progression of length n found".

Input

The input is an integer $n>1$, followed by a sequence of integers containing at least 2 elements.

Output

If a progression subsequence of length $n$ exists, the output is the first element of the subsequence and the value of $r$. Otherwise, the output is "No arithmetic progression of length n found".