CF33C  Wonderful Randomized Sum
Learn, learn and learn again — Valera has to do this every day. He is studying at mathematical school, where math is the main discipline. The mathematics teacher loves her discipline very much and tries to cultivate this love in children. That's why she always gives her students large and difficult homework. Despite that Valera is one of the best students, he failed to manage with the new homework. That's why he asks for your help. He has the following task. A sequence of n numbers is given. A prefix of a sequence is the part of the sequence (possibly empty), taken from the start of the sequence. A suffix of a sequence is the part of the sequence (possibly empty), taken from the end of the sequence. It is allowed to sequentially make two operations with the sequence. The first operation is to take some prefix of the sequence and multiply all numbers in this prefix by  1. The second operation is to take some suffix and multiply all numbers in it by  1. The chosen prefix and suffix may intersect. What is the maximum total sum of the sequence that can be obtained by applying the described operations?
Input
The first line of the input gives the number of test cases, T. T test cases follow, each with two lines. The first line contains integer n (1 ≤ n ≤ 10^{5}) — amount of elements in the sequence. The second line contains n integers ai (  10^{4} ≤ ai ≤ 10^{4}) — the sequence itself.
Output
For each test case, output one line containing the answer to the problem.
Example
Input: 3 3 1 2 3 5 4 2 0 5 0 5 1 10 5 10 2 Output: 6 11 18
hide comments
hamza007:
20140816 08:30:35
Unnecessary use of long long results in tle ... 

P.B.MUKUND:
20130420 17:04:47
Is there any test case where intersection of prefix and suffix actually comes into picture ?


RR:
20120706 15:47:15
I think it is stated somewhere in Codeforces that it is forbidden to add codeforces' problems to other sites. Last edit: 20120706 15:53:49 

Ashwin Menon:
20111017 14:13:02
(1) 10 5 10 (2)


LeppyR64:
20101009 14:41:30
@Kelwin: You only get to choose one preifx and one suffix, not choose each operation multiple times. 

Kelwin:
20101009 13:18:58
Hi, please check output.

Added by:  Ruslan Sennov 
Date:  20101008 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 NODEJS OBJC VB.NET 
Resource:  Codeforces #33 