Integer Square

Interview

Time limit2sMemory limit512 MB

Summary

Given an integer area s, decide whether a square with integer-coordinate vertices can have that area, and if so output the four vertices.

Level: Medium5 of 10
Topics: Math, Number theory, Geometry, Implementation
Solved: No attempts yet

Problem

Iris likes to draw different shapes on a grid paper. Her favorite shape is a square. She has recently tried to draw a square with area $s$ , but since she uses a grid paper, she wants all the vertices of the square to have integer coordinates.

Can you help her find such a square?

Input

The input contains a single integer $s$ ( $1\le s\le 1000$ ).

Output

If it is possible to construct the required square, output four pairs of integers: the coordinates of the vertices of the square, in any order. All coordinates should be in the range from $-10^9$ to $10^9$ . If there are multiple answers, output any of them.

If it is impossible to construct the required square, print "Impossible".

Examples2

Example 1
Input
```
5
```
Expected output
```
2 4
3 2
4 5
5 3
```
Example 2
Input
```
3
```
Expected output
```
Impossible
```