Description

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

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

Given the order of the notes, determine whether the scale is ascending, descending, or mixed.

Input Format

One line with eight integers, containing all integers 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.

1 2 3 4 5 6 7 8

ascending

8 7 6 5 4 3 2 1

descending

8 1 7 2 6 3 5 4

mixed

Hint

[Explanation]

The score settings of this problem follow the original COCI problem, with a full score of $30$.

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

Translated by ChatGPT 5