BAISED  Biased Standings
Usually, results of competitions are based on the scores of participants. However, we are planning a change for the next year of IPSC. During the registration each team will be able to enter a single positive integer : their preferred place in the ranklist. We would take all these preferences into account, and at the end of the competition we will simply announce a ranklist that would please all of you.
But wait... How would that ranklist look like if it won't be possible to satisfy all the requests?
Suppose that we already have a ranklist. For each team, compute the distance between their preferred place and their place in the ranklist. The sum of these distances will be called the badness of this ranklist.
Problem specification
Given team names and their preferred placements find one ranklist with the minimal possible badness.
Input specification
The first line of the input file contains an integer T specifying the number of test cases. Each test case is preceded by a blank line.
Each test case looks as follows: The first line contains N : the number of teams participating in the competition. Each of the next N lines contains a team name (a string of letters and numbers) and its preferred place (an integer between 1 and N, inclusive). No two team names will be equal.
Output specification
For each of the test cases output a single line with a single integer : the badness of the best ranklist for the given teams.
Example
Input: 2 7 noobz 1 llamas 2 Winn3rz 2 5thwheel 1 NotoricCoders 5 StrangeCase 7 WhoKnows 7 3 ThreeHeadedMonkey 1 MoscowSUx13 1 NeedForSuccess 1 Output: 5 3Explanation:
In the first test case, one possible ranklist with the minimal badness is:
1. noobz 2. llamas 3. Winn3rz 4. 5thwheel 5. NotoricCoders 6. WhoKnows 7. StrangeCase
In the second test case all ranklists are equally good.
Note: the input file will not exceed 5MB.hide comments
Pranshul Agarwal:
20121214 10:53:50
O(n) worked for me.. :D Team name doesn't matter.. 

AC Srinivas:
20120819 19:51:36
team name doesn't matter right? 

AC Srinivas:
20120819 19:46:13
any specific test cases? getting WAs. 

saket diwakar:
20120303 17:19:44
yes...O(N) works... 

.::Manish Kumar::.:
20110630 14:12:50
Guys, plz don't write things like O(nlogn), it always tells me to do something with the input, and then it becomes a spoiler. 

:D:
20101005 07:43:04
It can be solved in O(N). Plus N can be bigger that sqrt(2^32) ;) 

Kick:
20100614 09:40:59
Any better algorithm other than O(NlogN)?? 

:(){ :: & };::
20100415 11:47:31


[Trichromatic] XilinX:
20091008 03:16:02
It's an error when applying the problem code. 

Paul Draper:
20090414 21:12:39
why is the name baised? 
Added by:  Fudan University Problem Setters 
Date:  20071201 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: C99 ERL JSRHINO 
Resource:  IPSC 2006 