Slides X44801

A slide is a sequence of integers of at least three elements such that the difference $d$ between every two consecutive elements is the same and is different from 0. The slope of the slide is $d$, and the length of the slide is the number of elements in it. Slides are ascending when $d > 0$ and descending when $d < 0$.

For example, the following sequences are all slides:

• 1 2 3, with slope 1 and length 3;

• 5 10 15 20, with slope 5 and length 4;

• -11 -22 -33 -44 -55, with slope -11 and length 5.

The goal of the exercise is, given a sequence of integers as input, to find the longest consecutive subsequence that is an ascending slide, and the longest consecutive subsequence that is a descending slide. If there is more than one ascending slide with the same maximum length, the first one should be reported, and the same applies to descending slides. Additionally, we are interested in knowing at which position (which element of the entire input sequence) the slide begins, counting the position of the first element as 1.

Input

A sequence of integers without a sentinel. It is guaranteed that the sequence has at least two elements.

Output

The output must contain one line for each type of slide (ascending and descending). If no slides of either type have been found, the corresponding line should not be written. The line contains a character ("/" for ascending and "\" for descending), a space, and then 3 numbers separated by ":": the starting position of the longest slide, its slope, and its length.