## HMSRECT - Rectangle

You are given n points on the coordinate plane.

Write a program which calculates the largest possible area of a rectangle such that each of its vertices

is one of the given points. You may assume that such a rectangle exists.

Input

The input is read from standard input. The ﬁrst line of input contains an integer n, the number of given points.

Each of the following n lines contains the coordinates of one point, two integers separated by a space.

The coordinates will be between −10^8 and 10^8.

No two points will be located at the same coordinates.

Output

Output should be written to standard output. The ﬁrst and only line of output should contain a single

integer, the largest possible area of a rectangle.

Example

Input

8

-2 3

-2 -1

0 3

0 -1

1 -1

2 1

-3 1

-2 1

Output

10

Image ->> http://www.csc.kth.se/contest/boi/rectangle.pdf

Added by: | DVH |

Date: | 2014-07-02 |

Time limit: | 2s |

Source limit: | 50000B |

Memory limit: | 1536MB |

Cluster: | Cube (Intel G860) |

Languages: | All except: ASM64 |

Resource: | BOI 2009 |