Central Point

Problem code: CPOINT

All submissions for this problem are available.

Given a set of N integer points on the Cartesian plane. Your task is to find an integer point satisfying its sum of distances to N given points (S) is minimum.

Input

There are several test cases (fifteen at most), each formed as follows:

  • The first line contains a positive integer N (N ? 2,000).
  • N lines follow, each containing a pair of integers (each having an absolute value of 109 at most) describing coordinates of a given point.
The input is ended with N = 0.

Output

For each test case, output on a line a real number (with exactly 6 decimal places) which is the respective minimum sum S found.

Example

Input:
3
1 1
2 2
3 3
5
1 4
2 3
5 2
3 5
4 1
0

Output:
2.828427
9.640986
Author: anhdq
Date Added: 7-03-2011
Time Limit: 15 sec
Source Limit: 50000 Bytes
Languages: ADA, ASM, BASH, BF, C, C99 strict, CAML, CLOJ, CLPS, CPP 4.0.0-8, CPP 4.3.2, CS2, D, ERL, F#, FORT, GO, HASK, ICK, ICON, JAR, JAVA, JS, LISP clisp, LISP sbcl, LUA, NEM, NICE, PAS fpc, PAS gpc, PERL, PERL6, PHP, PIKE, PRLG, PYTH, PYTH 3.1.2, RUBY, SCALA, SCM guile, SCM qobi, ST, TCL, TEXT, WSPC


Comments

I was trying to use binary

gragluhar @ 20 Jan 2012 09:59 AM
I was trying to use binary search for getting final answer but I was getting WA. Why are people narrowing it down (with hi-lo <3 :P) and then choosing correct value by iterating over smaller set? Can't we get answer just with two binary searches directly? Thanks.

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