Problem Description

The C major scale consists of 8 notes: $\texttt{c, d, e, f, g, a, b, C}$. Each note is numbered from 1 to 8.

The scale can be ascending (from 1 to 8), descending (from 8 to 1), or mixed.

Determine whether the scale is ascending, descending, or mixed based on the sequence of notes.

Input Format

A single line containing eight integers, ranging from 1 to 8. Each integer appears exactly once in the input.

Output Format

If the scale is descending, output descending.

If the scale is ascending, output ascending.

If the scale is mixed, output mixed.

Sample Input and Output

Sample Input #1

1 2 3 4 5 6 7 8

Sample Output #1

ascending

Sample Input #2

8 7 6 5 4 3 2 1

Sample Output #2

descending

Sample Input #3

8 1 7 2 6 3 5 4

Sample Output #3

mixed

Notes

This problem is scored according to the original COCI settings, with a maximum score of 30.

The problem is translated from COCI2009-2010 CONTEST #1 T1 NOTE.

见题面 Input 部分

见题面 Output 部分