Manhattan

Interview

Time limit1sMemory limit512 MB

Summary

Given the Euclidean distance between two grid-aligned houses, find the maximum Manhattan distance achievable between them.

Level: Easy3 of 10
Topics: Geometry, Math, Implementation
Solved: No attempts yet

Problem

In Manhattan, there are streets $x = i$ and $y = i$ for every integer $i$ . Both Snuke's house and Smeke's house lie on streets, and the Euclidean distance between them is exactly $d$ . Find the largest possible distance between their houses when they travel along streets.

Input

The input consists of a single number $d$ .

$0 < d \le 10$
$d$ has exactly three digits after the decimal point.

Output

Print the answer. The answer is considered correct if its absolute or relative error is at most $10^{-9}$ .

Examples2

Example 1
Input
```
1.000
```
Expected output
```
2.000000000000
```
Example 2
Input
```
2.345
```
Expected output
```
3.316330803765
```