A13713. Array Cancellation

You're given an array $a$ of $n$ integers, such that $a_1 + a_2 + \cdots + a_n = 0$ .

In one operation, you can choose two different indices $i$ and $j$ ( $1 \le i, j \le n$ ), decrement $a_i$ by one and increment $a_j$ by one. If $i < j$ this operation is free, otherwise it costs one coin.

How many coins do you have to spend in order to make all elements equal to $0$ ?

Each test contains multiple test cases. The first line contains the number of test cases $t$ ( $1 \le t \le 5000$ ). Description of the test cases follows.

The first line of each test case contains an integer $n$ ( $1 \le n \le 10^5$ ) — the number of elements.

The next line contains $n$ integers $a_1, \ldots, a_n$ ( $-10^9 \le a_i \le 10^9$ ). It is given that $\sum_{i=1}^n a_i = 0$ .

It is guaranteed that the sum of $n$ over all test cases does not exceed $10^5$ .

For each test case, print the minimum number of coins we have to spend in order to make all elements equal to $0$ .

Possible strategy for the first test case:

- Do $(i=2, j=3)$ three times (free), $a = [-3, 2, 0, 1]$ .
- Do $(i=2, j=1)$ two times (pay two coins), $a = [-1, 0, 0, 1]$ .
- Do $(i=4, j=1)$ one time (pay one coin), $a = [0, 0, 0, 0]$ .