Musical Scale

Time limit1sMemory limit128 MB

Summary

Given a permutation of 1 through 8, print whether it is strictly ascending, strictly descending, or otherwise mixed.

Level: Easy1 of 10
Topics: Array, Implementation
Solved: No attempts yet

Problem

The C major scale consists of the 8 notes c d e f g a b C. In this problem, those notes are represented by numbers: c is 1, d is 2, ..., and C is 8.

If the 8 played notes appear in the order 1 2 3 4 5 6 7 8, the sequence is ascending. If they appear in the order 8 7 6 5 4 3 2 1, the sequence is descending. In every other case, the sequence is mixed.

Write a program that determines which of the three cases the given performance order belongs to.

Input

The first line contains 8 integers separated by spaces. Each integer represents one note described above, and every integer from 1 through 8 appears exactly once.

Output

Print ascending if the performance order is increasing, descending if it is decreasing, and mixed otherwise.

Examples3

Example 1
Input
```
1 2 3 4 5 6 7 8
```
Expected output
```
ascending
```
Example 2
Input
```
8 7 6 5 4 3 2 1
```
Expected output
```
descending
```
Example 3
Input
```
8 1 7 2 6 3 5 4
```
Expected output
```
mixed
```