Determine the Order of the C Major Scale

The C major scale consists of 8 notes: c, d, e, f, g, a, b, C. Each note is assigned a number from 1 to 8 respectively. The scale may appear in ascending order (from 1 to 8), descending order (from 8 to 1), or in a mixed order.

Given a sequence of the 8 numbers representing the order of notes, determine whether the scale is ascending, descending, or mixed.

Note: The ordering is strict. Only when the numbers are exactly 1 2 3 4 5 6 7 8 is the order ascending, and only when they are exactly 8 7 6 5 4 3 2 1 is it descending. All other orders are considered mixed.

inputFormat

The input consists of a single line containing 8 integers separated by spaces, representing the numbering of the notes in the scale.

For example: 1 2 3 4 5 6 7 8

outputFormat

Output a single word: ascending if the sequence is in ascending order, descending if it is in descending order, or mixed otherwise.

sample

1 2 3 4 5 6 7 8

ascending