BSHEEP - Build the Fence


At the beginning of spring all the sheep move to the higher pastures in the mountains. If there are thousands of them, it is well worthwhile gathering them together in one place. But sheep don't like to leave their grass-lands. Help the shepherd and build him a fence which would surround all the sheep. The fence should have the smallest possible length! Assume that sheep are negligibly small and that they are not moving. Sometimes a few sheep are standing in the same place. If there is only one sheep, it is probably dying, so no fence is needed at all...

Input


t [the number of tests <= 100]
[empty line]
n [the number of sheep <= 100000]
x1 y1 [coordinates of the first sheep]
...
xn yn
[integer coordinates from -10000 to 10000]
[empty line]
[other lists of sheep]

Text grouped in [ ] does not appear in the input file. Assume that sheep are numbered in the input order.

Output


o [length of circumference, rounded to 2 decimal places]
p1 p2 ... pk
[the sheep that are standing in the corners of the fence; the first one should be positioned bottommost and as far to the left as possible, the others ought to be written in anticlockwise order; ignore all sheep standing in the same place but the first to appear in the input file; the number of sheep should be the smallest possible]
[empty line]
[next solutions]

Example

Input:
8

5
0 0
0 5
10 5
3 3
10 0

1
0 0

3
0 0
1 0
2 0

4
0 0
0 0
0 1
1 0

3
0 0
0 1
1 0

6
0 0
-1 -1
1 1
2 2
3 3
4 4

2
10 0
0 0

7
-3 -4
2 -3
4 3
-4 2
0 5
2 -3
-1 4

Output:
30.00
1 5 3 2

0.00
1

4.00
1 3

3.41
1 4 3

3.41
1 3 2

14.14
2 6

20.00
2 1

26.98
1 2 3 5 4

Warning: large Input/Output data, be careful with certain languages

hide comments
[Mayank Pratap]: 2016-09-27 06:38:29

AC in one Go :) THink Simple.

Sanjit Majumdar: 2016-08-18 17:03:50

Got accepted in 0.45s using Andrew's monotone chain convex hull algorithm

Sampath Ravolaparthi: 2016-02-01 19:05:15

Hell No.......!!
Kept debugging my algo when I just had to change float to double
Forgot to keep the sum In mind and Only assumed for one segment.....!!

krypto_phile: 2016-01-19 19:54:17

Easy question. Absolutely straightforward! AC in 1 go :P

kartikay singh: 2016-01-18 09:34:05

Easy convo hull :-)
Graham scan will be suffice :D

Last edit: 2016-01-18 09:34:25
CHANDAN KUMAR: 2016-01-18 08:26:36

My first convex hull problem really enjoying debugging it there are many corner cases but think systematically easy in one go

Mayank Garg: 2016-01-18 05:03:20

My first convex hull problem ... enjoyed solving and debugging it ;)

(Tjandra Satria Gunawan)(曾毅昆): 2015-08-08 14:18:23

First time I implemented full version of my own convex hull algo written in C :)

: 2014-06-22 23:13:01

Beware of I/O cost. iostream, Java I/O etc. will easily add up to 1+ seconds on this data. Some of the data is very large!
Other than that, in order to get to the top ranks, employ some pruning strategies. During loading the data, try to perform a cheap bounding box check and only store data that isn't obviously inside.

Jens Stimpfle: 2014-03-18 17:51:55

Haidar Abboud, if you tackle the problem the right way, there are no special cases to consider (repeated-points, less-than-3, all-colinear certainly are not).

- Do a stable sort + unique before searching a hull to remove the right repeated points.
- Find 2 half convex hulls as in most examples you find on the web. But don't find upper / lower half. Find left / right half, so that the right half hull starts with the bottommost then leftmost point.

edit: the halves should have the same endpoints contrary to some web examples.

Last edit: 2014-03-18 17:53:31

Added by:mima
Date:2004-06-01
Time limit:7s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: NODEJS PERL6 VB.NET
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