In what concerns the continuous evaluation solving exercises grade during the semester, you should submit until 23:59 of October 18th
(this exercise will still be available for submission after that deadline, but without couting towards your grade)
[to understand the context of this problem, you should read the class #02 exercise sheet]

[IP022] Spin me right round

Numbers have personalities too! Some like to climb up in ascending order, while others prefer to slide down in a nice, orderly descent. There are also those that form a perfect mountain shape, increasing until reaching a peak and then decreasing. But some other numbers? Well, they just can't make up their mind and zigzag all over the place! Your task today is to determine if a number has its act together or if it's simply a chaotic mess.

The Problem

Write a program that takes a positive integer number num and computes the shape of its digits:

• increasing: if the digits arranged in a strictly ascending order (e.g. 1234, 27 or 3589)
• decreasing: if the digits arranged in a strictly descending order (e.g 432, 80 or 9542)
• mountain: if the number can be divided into a strictly increasing sequence followed by a strictly decreasing sequence sharing its first digit with the first part (e.g. 12321, 4732 or 14693)
• chaotic: if none of the above cases happen

Input

The input consists of a single integer number n.

Output

The output should be a single line determining the order of the digits in the input number. The program should print increasing, decreasing, mountain or chaotic according to the type of number as described before.

Constraints

The following limits are guaranteed in all the test cases that will be given to your program:

1356

increasing

985

decreasing

157842

mountain

123212

chaotic