# Optimal Partition

## 题目描述

You are given an array $a$ consisting of $n$ integers. You should divide $a$ into continuous non-empty subarrays (there are $2^{n-1}$ ways to do that). Let $s=a_l+a_{l+1}+\ldots+a_r$ . The value of a subarray $a_l, a_{l+1}, \ldots, a_r$ is: - $(r-l+1)$ if $s>0$ , - $0$ if $s=0$ , - $-(r-l+1)$ if $s<0$ . What is the maximum sum of values you can get with a partition?

## 输入输出格式

### 输入格式

The input consists of multiple test cases. The first line contains a single integer $t$ ( $1 \le t \le 5 \cdot 10^5$ ) — the number of test cases. The description of the test cases follows. The first line of each test case contains a single integer $n$ ( $1 \le n \le 5 \cdot 10^5$ ). The second line of each test case contains $n$ integers $a_1$ , $a_2$ , ..., $a_n$ ( $-10^9 \le a_i \le 10^9$ ). It is guaranteed that the sum of $n$ over all test cases does not exceed $5 \cdot 10^5$ .

### 输出格式

For each test case print a single integer — the maximum sum of values you can get with an optimal parition.

## 输入输出样例

### 输入样例 #1

5
3
1 2 -3
4
0 -2 3 -4
5
-1 -2 3 -1 -1
6
-1 2 -3 4 -5 6
7
1 -1 -1 1 -1 -1 1

### 输出样例 #1

1
2
1
6
-1

## 说明

Test case $1$ : one optimal partition is $[1, 2]$ , $[-3]$ . $1+2>0$ so the value of $[1, 2]$ is $2$ . $-3<0$ , so the value of $[-3]$ is $-1$ . $2+(-1)=1$ . Test case $2$ : the optimal partition is $[0, -2, 3]$ , $[-4]$ , and the sum of values is $3+(-1)=2$ .