Falling Mugs

Time limit1sMemory limit256 MB

Summary

Given D, find nonnegative integers n1 and n2 with n2 squared minus n1 squared equal to D, smallest n1 first, or report impossible.

Level: Easy3 of 10
Topics: Number theory, Math
Solved: No attempts yet

Problem

Susan films falling coffee mugs with a high speed camera. She wants to know how tall the mugs are, but every mug broke during filming, so the video is all she has left.

The camera records 70 frames per second. Count frames from the moment the mug is released, so the release itself is frame 0. By frame $n$ the mug has fallen exactly $n^2$ millimeters.

Susan believes one mug is $D$ millimeters tall. To check that, she needs two frames $n_1$ and $n_2$ between which the mug fell exactly $D$ millimeters, that is, two frames with $n_2^2 - n_1^2 = D$ .

Input

The first and only line contains the distance $D$ to be measured, in millimeters ( $1 \le D \le 200000$ ).

Output

Print two non-negative integers $n_1$ and $n_2$ on one line, separated by a space, with $n_2^2 - n_1^2 = D$ .

Several pairs can satisfy the equation. In that case print the lexicographically smallest pair, which is the pair with the smallest $n_1$ . If no such pair exists, print impossible.

Examples2

Example 1
Input
```
88
```
Expected output
```
9 13
```
Example 2
Input
```
86
```
Expected output
```
impossible
```