Alpsoo

Time limit1sMemory limit512 MB

Summary

Given a positive integer, decide whether its digit sequence rises then falls, with no flat step, and each slope kept constant within its part.

Level: Easy3 of 10
Topics: Implementation, String, Simulation
Solved: No attempts yet

Problem

Take a positive integer and plot its digits in order at equal horizontal spacing as a line graph. If the resulting shape is a mountain whose uphill or downhill slope does not change partway, that positive integer is called an Alpsoo. A mountain shape starts uphill, ends downhill, and has no flat part. Given a positive integer $X$ , determine whether $X$ is an Alpsoo.

Uphill means a part of the graph with positive slope, downhill means a part with negative slope, and flat means a part with slope $0$ .

Input

The first line gives a positive integer $X$ .

Output

If $X$ is an Alpsoo, print ALPSOO; otherwise print NON ALPSOO.

Constraints

$3 ≤$ the number of digits of $X$ $≤ 10^5$

Examples3

Example 1
Input
```
135264
```
Expected output
```
ALPSOO
```
Example 2
Input
```
14540
```
Expected output
```
NON ALPSOO
```
Example 3
Input
```
3455517
```
Expected output
```
NON ALPSOO
```