OpenKattis
Kattis Set 07 - Graph Matching and Easier Mathematics

#### Start

2021-03-01 04:00 AKST

## Kattis Set 07 - Graph Matching and Easier Mathematics

#### End

2021-03-08 00:30 AKST
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# Problem GAlloys

Pelle is building a new advanced underground drill. He wants to build the drill out of a new titanium-aluminium-magnesium alloy. Such an alloy can be mixed in many ways. If an alloy is made with the ratios $x, y, z$ ($x + y + z = 1$) of titanium, aluminium and magnesium, the alloy gets a hardness of $xy$, and a price of $x + y$ SEK per kilogram.

Pelle only has a fixed amount of money per kilogram that he can spend on alloys for his drills. What is the maximum hardness he can get on his new alloy?

## Input

The first and only line of input contains a decimal number $c$ ($0 \le c < 2$, between $1$ and $6$ digits after the decimal point) – the amount of money in SEK that Pelle can spend per kilogram alloy.

## Output

Output a single decimal number, the maximum hardness of Pelle’s alloy.

Your answer will be considered correct if you have an absolute error of at most ${10}^{-6}$.

Sample Input 1 Sample Output 1
1.0

0.25