# Problem D

Janitor Troubles

*Professor E. I. N. Stein*who earlier in the day solved the elusive

*maximum quadrilateral problem*! Quick, you have to redo his work so no one noticed what happened.

The *maximum quadrilateral problem* is
quite easy to state: given four side lengths $s_1, s_2, s_3$ and $s_4$, find the maximum area of any
quadrilateral that can be constructed using these lengths. A
quadrilateral is a polygon with four vertices.

## Input

The input consists of a single line with four positive integers, the four side lengths $s_1$, $s_2$, $s_3$, and $s_4$.

It is guaranteed that $2s_ i < \sum _{j=1}^4 s_ j$, for all $i$, and that $1 \leq s_ i \leq 1\, 000$.

## Output

Output a single real number, the maximal area as described above. Your answer must be accurate to an absolute or relative error of at most $10^{-6}$.

Sample Input 1 | Sample Output 1 |
---|---|

3 3 3 3 |
9 |

Sample Input 2 | Sample Output 2 |
---|---|

1 2 1 1 |
1.299038105676658 |

Sample Input 3 | Sample Output 3 |
---|---|

2 2 1 4 |
3.307189138830738 |