MAXSUMSQ - Maximum Sum Sequences


Given an array A having n elements, let X be the maximum sum of any contiguous sequence in the array. How many contiguous sequences in A sum up to X ?

Input

The first line contains T the number of test cases. There follow 2T lines, 2 for each test case. The first line contains the n, the number of elements in the array. The second line contains n space seperated integers Ai.

Output

Output T lines, one for each test case. On each line, output two space seperated integers; the maximum sequence sum, and the number of sequences which obtain this maximum sum.

Example

Sample Input

2
3
-1 -1 -1
4
2 0 -2 2

Sample Output

-1 3
2 4

Constraints


1 <= T <= 35
1 <= n <= 100000
-1000 <= Ai <= 1000


hide comments
kmkhan_014: 2017-12-12 11:19:51

Awesome problem!!!

ydeepak1889: 2017-04-06 20:11:26

Finally AC after 4 WA and 2 TLE.

pranay: 2017-02-05 09:01:49

accepted using scanf and printf
got tle using cin and cout

Dushyant Singh: 2017-02-03 23:09:05

map -> TLE
unordered_map -> AC

scottt: 2016-11-02 02:27:25

Use long long for "the number of sequences which obtains this maximum sum".
The constraints of the problem allow this 'max_count' field to be > (n/2)^2, where n is 10^5
Thanks @Ankit Sultana!

amr_aly: 2016-08-20 06:05:41

@reddragon the first element only, the first and the second, the last element only, the whole array

hodobox: 2016-08-09 18:32:38

Can be done in O(n) time and O(1) space without any casing :)

rocode0001: 2015-12-16 17:58:27

Nice Problem!!learned many new thngs

msa21974: 2015-10-06 13:12:27

can somebody explain second test case . I think output should be : 2 3

Hi dear
i can :)
"2" , "2 0" , "2 0 -2 2 ", "2" !!!

maverick_10: 2015-09-25 14:57:52

will brute force work ?


Added by:Varun Jalan
Date:2010-01-24
Time limit:0.365s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: NODEJS OBJC PERL6 SQLITE VB.NET
Resource:own problem used for Codechef Snackdown Onsite