#00026A

NOTE

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 whether the scale was played ascending, descending or mixed.



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


OutputIn 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.


Input:
1 2 3 4 5 6 7 8
Output:
ascending

Input:
8 7 6 5 4 3 2 1
Output:
descending

Input:
8 1 7 2 6 3 5 4
Output:
mixed

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