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 separated integers Ai.

Output

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

Example

Input:
2
3
-1 -1 -1
4
2 0 -2 2 Output: -1 3
2 4

Constraints

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


hide comments
Ankit Sultana: 2015-03-20 11:26:09

Use long long for the number of sequences which obtain the maximum sum.

Stupid Dog: 2015-02-28 05:04:20

scanf("%d\n", &n) : WA
scanf("%d", &n) : AC


Added by:Varun Jalan
Date:2010-01-24
Time limit:1s
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