Codeforces Round 783 (Div. 1) |
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Finished |

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B. Optimal Partition

time limit per test

4 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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 $$$s<0$$$.

Input

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 $$$5 \cdot 10^5$$$.

Output

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

Example

Input

531 2 -340 -2 3 -45-1 -2 3 -1 -16-1 2 -3 4 -5 671 -1 -1 1 -1 -1 1

Output

1 2 1 6 -1

Note

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 $$$3+(-1)=2$$$.

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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