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
hritwik:
20200416 17:31:39
Just focus on this HINT: Wine transport between adjacent blocks= 1 work 

chinmay0402:
20200405 19:52:59
Awesome question!! Couldn't have done it in O(n) if I hadn't read the comments :)


sayan_244:
20191215 09:29:36
Don't need to use queue


grvkmrpandit:
20191129 11:28:15
no need to short.AC in one go O(n) 

importme:
20191010 10:02:21
Use long long int...


kk7:
20190627 21:31:28
AC in one go :)


pandey101299:
20190401 14:27:56
nice question


silentknight16:
20190321 15:37:28
Use long long int ........ 

ankkt16:
20190207 18:13:00
AC in one go!:D


devil_3:
20190109 23:46:01
can we sort the numbers in some order here? IF not then please tell me how the answer of first test case of example is achieved. 
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 