GERGOVIA  Wine trading in Gergovia
Gergovia consists of one street, and every inhabitant of the city is a wine salesman. Everyone buys wine from other inhabitants of the city. Every day each inhabitant decides how much wine he wants to buy or sell. Interestingly, demand and supply is always the same, so that each inhabitant gets what he wants.
There is one problem, however: Transporting wine from one house to another results in work. Since all wines are equally good, the inhabitants of Gergovia don't care which persons they are doing trade with, they are only interested in selling or buying a specific amount of wine.
In this problem you are asked to reconstruct the trading during one day in Gergovia. For simplicity we will assume that the houses are built along a straight line with equal distance between adjacent houses. Transporting one bottle of wine from one house to an adjacent house results in one unit of work.
Input
The input consists of several test cases.
Each test case starts with the number of inhabitants N (2 ≤ N ≤ 100000).
The following line contains n integers a_{i} (1000 ≤ a_{i} ≤ 1000).
If a_{i} ≥ 0, it means that the inhabitant living in the i^{th} house wants to buy a_{i} bottles of wine. If a_{i} < 0, he wants to sell a_{i} bottles of wine.
You may assume that the numbers a_{i} sum up to 0.
The last test case is followed by a line containing 0.
Output
For each test case print the minimum amount of work units needed so that every inhabitant has his demand fulfilled.
Example
Input:
5
5 4 1 3 1
6
1000 1000 1000 1000 1000 1000
0
Output:
9
9000
hide comments
bhargav_000007:
20230203 07:51:30
Good problem : ) 

om_2001:
20220803 04:08:59
use long long int 

p_yushh:
20220629 11:07:22
Easy....Solved in linear TC and constant space in one go! 

milindprajapat:
20220423 17:08:58
problem can be solved in linear time and constant space!! 

deshiyan:
20220331 20:31:06
Handle the case when 0 is a part of the array... 

satyam_2022:
20220303 20:27:40
Using


itachi_99:
20210817 14:41:27
long long 

mdriyaz_123:
20210811 17:10:37
Hint: *adjacent* Work Last edit: 20210811 17:12:18 

clary09:
20210728 05:28:36
Great Question ! (hint: use long long int) 

imran_2018:
20210619 10:26:26
Yes finally did it n O(n). 
Added by:  HNUE 
Date:  20091030 
Time limit:  0.5s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 NODEJS OBJC PERL6 SQLITE VB.NET 
Resource:  UVA 