## ELLIPSE - Ellipse

Given 5 points on a ellipse, calculate the area of the ellipse. We accept solutions with **absolute error less than 10 ^{-6} or relative error less than 10^{-9}**.

### Input

Many test cases. Each contains a line with 10 integers with absolute value less than 1000 - the X and Y coordinates of the 5 points, respectively.

Input terminates by EOF. Note that there can be extra spaces in a single line.

### Output

Each line contains a single float-point number - the area of the corresponding ellipse, or "IMPOSSIBLE" if the ellipse doesn't exist or can't be unique determined.

### Example

Input:6 1 3 2 -2 -3 -3 -2 1 6 7 -3 2 7 6 3 5 5 -2 -9Output:IMPOSSIBLE 157.079633

**Note: You can click on "Wrong Answer" to get further information.**

**Note: Judge is slightly modified to avoid some precision problems. **

Added by: | Fudan University Problem Setters |

Date: | 2009-03-27 |

Time limit: | 0.200s |

Source limit: | 50000B |

Memory limit: | 1536MB |

Cluster: | Cube (Intel G860) |

Languages: | All except: C99 ERL JS-RHINO NODEJS OBJC PERL6 SQLITE VB.NET |

Resource: | Classical Problem, description by Blue Mary |