Setting

A group of friends regularly go on trips together to visit different cities. Because friendship is magic.

The group agrees in advance to share expenses equally, but it is not practical to share every expense as it occurs. Thus individuals in the group pay for particular things, such as meals, hotels, taxi rides, and entrance fees to wrestling events. After the trip, each student's expenses are tallied and money is exchanged so that the net cost to each is the same, to within one cent.

Your job is to compute, from a list of expenses, the minimum amount of money that must change hands in order to equalize (within one cent) all the students' costs.

Input

Standard input will contain the information for several trips. Each trip consists of a line containing a positive integer \(n\) denoting the number of students on the trip. This is followed by \(n\) lines of input, each containing the amount spent by a student in dollars and cents. There are no more than 1000 students and no student spent more than $10,000.00. A single line containing 0 follows the information for the last trip.

Output

For each trip, output a line stating the total amount of money, in dollars and cents, that must be exchanged to equalize the students' costs.

Sample Input

3
10.00
20.00
30.00
4
15.00
15.01
3.00
3.01
0

Sample Output

$10.00
$11.99

This challenge is provided by the ACM International Collegiate Programming Contest. Test input is provided by uDebug.

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Statistics

Difficulty (3 votes)
Average test runtime 0.20
Points (changes over time) 10
Tried by 25 users
Solved by 13 users

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# Name Runtime Points worth
1 ,s/java/NaN/gi 0.12 15
2 Brian 0.14 13
3 贝尔恩德 0.14 13
4 Jan 0.15 12
5 Marvin 0.15 12
6 Pascal 0.16 11
7 Chris Danger 0.20 9
8 IeM 0.22 8
9 Nis 0.23 8
10 JB 0.24 8
11 Mac 0.25 7
12 Dark 0.30 6
13 Eren B. Yilmaz 0.32 6