CLOPPAIR  Closest Point Pair
You are given N points on a plane and your task is to find a pair of points with the smallest euclidean distance between them.
All points will be unique and there is only one pair with the smallest distance.
Input
First line of input will contain N (2<=N<=50000) and then N lines follow each line contains two integers giving the X and Y coordinate of the point. Absolute value of X,Y will be atmost 10^6.
Output
Output 3 numbers a b c, where a,b (a<b) are the indexes (0 based) of the point pair in the input and c is the distance between them. Round c to 6 decimal digits.
See samples for more clarification.
Input:
5
0 0
0 1
100 45
2 3
9 9
Output:
0 1 1.000000Input:
5
0 0
4 1
7 2
4 5
1 1
Output:
0 4 1.414214
hide comments
Utkarsh Shahdeo:
20130206 13:02:27
Last edit: 20130529 05:43:06 

Ben Dean:
20121115 03:16:51
There is not even one correct python submission.


!(NULL):
20120518 17:50:39
CLOSEST is a similar and more challenging problem. 

ramz:
20120326 17:55:17
can you increase the time limit for Ruby. 1s is too less for an input of 50000 entries. 

SALVO:
20110528 04:20:25
You can easily write an O(N^2) brute force solution and check for yourself. 

Krzysztof Lewko:
20110528 00:08:24
Could i receive some tricky test case, SALVO ?:) 
Added by:  SALVO 
Date:  20110414 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 
Resource:  Standard Problem 