Zonal Computing Olympiad 2013, 10 Nov 2012

10:00 am-1:00 pm IST



Problem 1 : Tournament


N teams participate in a league cricket tournament on Mars, where each pair of distinct teams plays each other exactly once. Thus, there are a total of (N × (N-1))/2 matches. An expert has assigned a strength to each team, a positive integer. Strangely, the Martian crowds love one-sided matches and the advertising revenue earned from a match is the absolute value of the difference between the strengths of the two matches. Given the strengths of the N teams, find the total advertising revenue earned from all the matches.

For example, suppose N is 4 and the team strengths for teams 1, 2, 3, and 4 are 3, 10, 3, and 5 respectively. Then the advertising revenues from the 6 matches are as follows:

Match Team A Team B Ad revenue
1 1 2 7
2 1 3 0
3 1 4 2
4 2 3 7
5 2 4 5
6 3 4 2

Thus the total advertising revenue is 23.



Input format

Line 1 : A single integer, N.

Line 2 : N space-separated integers, the strengths of the N teams.



Output format

A single integer, the total advertising revenue from the tournament.



Sample input

4
3 10 3 5


Sample output

23


Test data

In all subtasks, the strength of each team is an integer between 1 and 1,000 inclusive.

Subtask 1 (30 marks) : 2 ≤ N ≤ 1,000.

Subtask 2 (70 marks) : 2 ≤ N ≤ 200,000.



Live evaluation data

Subtask 1: Testcases 0,1,2.

Subtask 2: Testcases 3,4,5.



Limits

Time limit : 3s

Memory limit: 64 MB



Note

The answer might not fit in a variable of type int. We recommend that type long long be used for computing all advertising revenues. If you use printf and scanf, you can use %lld for long long.

CPU Timelimit: 3 seconds
Memory limit: 64M
Grading style: ioi
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