Problem I
Counting Subsequences (Hard)

$47$ is the quintessential random number," states the $47$ society. And there might be a grain of truth in that.

For example, the first ten digits of the Euler’s constant are:

2 7 1 8 2 8 1 8 2 8

And what’s their sum? Of course, it is $47$.

Try walking around with your eyes open. You may be sure that soon you will start discovering occurrences of the number $47$ everywhere.

You are given a sequence $S$ of integers we saw somewhere in the nature. Your task will be to compute how strongly does this sequence support the above claims. We will call a continuous subsequence of $S$ interesting if the sum of its terms is equal to $47$.

E.g., consider the sequence $S = (24, 17, 23, 24, 5, 47)$. Here we have two interesting continuous subsequences: the sequence $(23, 24)$ and the sequence $(47)$.

Given a sequence $S$, find the count of its interesting subsequences.


The first line of the input file contains an integer $T$ specifying the number of test cases. There are at most $10$ test cases and each test case is preceded by a blank line.

The first line of each test case contains the length of a sequence $N$, $N \leq 1\, 000\, 000$. The second line contains $N$ space-separated integers – the elements of the sequence. All numbers don’t exceed $20\, 000$ in absolute value.


For each test case output a single line containing a single integer – the count of interesting subsequences of the given sentence.

Sample Input 1 Sample Output 1

-2 7 1 8 2 8 -1 8 2 8 4 -5 -9

2 47 10047 47 1047 47 47
CPU Time limit 2 seconds
Memory limit 1024 MB
Statistics Show
Source IPSC 2006
License Creative Commons License (cc by-sa)

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