문제

Author: Marko Ivanković C major scale consists of 8 tones: c d e f g a h C. For this task we number the notes using numbers 1 through 8. The scale can be played ascending, from 1 to 8, descending, from 8 to 1, or mixed. Write a program that, given the sequence of notes, determines wether the scale was played ascending, descending or mixed.

입력

First and only line of input will contain 8 integers, from 1 to 8 inclusive. Each integer will appear exactley once in the input.

출력

In the first and only line of input print "descending" if the scale was played descending, "ascending" if the scale was played ascending and "mixed" if the scale was played mixed.

예제 입력 1

1 2 3 4 5 6 7 8

예제 출력 1

ascending

예제 입력 2

8 7 6 5 4 3 2 1

예제 출력 2

descending

예제 입력 3

8 1 7 2 6 3 5 4

예제 출력 3

mixed