CF1667B Optimal Partition

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

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 $ .

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

Test case $ 1 $ : one optimal partition is $ [1, 2] $ , $ [-3] $ . $ 1+2>0 $ so the value of $ [1, 2] $ is $ 2 $ . $ -3