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.
Given team names and their preferred placements find one ranklist with the minimal possible badness.
The first line of the input file contains an integer T at most 100 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. N is at most 100,000. 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.
For each of the test cases output a single line with a single integer – the badness of the best ranklist for the given teams.
2 7 noobz 1 llamas 2 Winn3rz 2 5thwheel 1 NotoricCoders 5 StrangeCase 7 WhoKnows 7 3 ThreeHeadedMonkey 1 MoscowSUx13 1 NeedForSuccess 1
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 (or bad).