###### Category

###### Similar Problems

## 0760. Trace

###### Time limit : 1000 ms

Memory limit : 64 mb

One day, as Sherlock Holmes was tracking down one very important criminal, he found a wonderful painting on the wall. This wall could be represented as a plane. The painting had several concentric circles that divided the wall into several parts. Some parts were painted red and all the other were painted blue. Besides, any two neighboring parts were painted different colors, that is, the red and the blue color were alternating, i. e. followed one after the other. The outer area of the wall (the area that lied outside all circles) was painted blue. Help Sherlock Holmes determine the total area of red parts of the wall.

*Let us remind you that two circles are called
concentric if their centers coincide. Several circles are called concentric if
any two of them are concentric.*

### Input

### The first line contains the
single integer *n* (1 ≤ *n* ≤ 100).
The second line contains *n* space-separated
integers *r*_{i} (1 ≤ *r*_{i} ≤ 1000) — the
circles' radii. It is guaranteed that all circles are different.

_{i}

_{i}

### Output

Print the single real
number — total area of the part of the wall that is painted red. The answer should
be printed with precision 10^{ - 4}.

Samples

№ |
Input |
Output |

1 |
5 7 3 6 1 9 |
188.4956 |

Text from: codeforces.ru