E. Binary Inversions
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given a binary array$$$^{\dagger}$$$ of length $$$n$$$. You are allowed to perform one operation on it at most once. In an operation, you can choose any element and flip it: turn a $$$0$$$ into a $$$1$$$ or vice-versa.

What is the maximum number of inversions$$$^{\ddagger}$$$ the array can have after performing at most one operation?

$$$^\dagger$$$ A binary array is an array that contains only zeroes and ones.

$$$^\ddagger$$$ The number of inversions in an array is the number of pairs of indices $$$i,j$$$ such that $$$i<j$$$ and $$$a_i > a_j$$$.

Input

The input consists of multiple test cases. The first line contains an integer $$$t$$$ ($$$1 \leq t \leq 10^4$$$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains an integer $$$n$$$ ($$$1 \leq n \leq 2\cdot10^5$$$) — the length of the array.

The following line contains $$$n$$$ space-separated positive integers $$$a_1$$$, $$$a_2$$$,..., $$$a_n$$$ ($$$0 \leq a_i \leq 1$$$) — the elements of the array.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2\cdot10^5$$$.

Output

For each test case, output a single integer  — the maximum number of inversions the array can have after performing at most one operation.

Example
Input
5
4
1 0 1 0
6
0 1 0 0 1 0
2
0 0
8
1 0 1 1 0 0 0 1
3
1 1 1
Output
3
7
1
13
2
Note

For the first test case, the inversions are initially formed by the pairs of indices ($$$1, 2$$$), ($$$1, 4$$$), ($$$3, 4$$$), being a total of $$$3$$$, which already is the maximum possible.

For the second test case, the inversions are initially formed by the pairs of indices ($$$2, 3$$$), ($$$2, 4$$$), ($$$2, 6$$$), ($$$5, 6$$$), being a total of four. But, by flipping the first element, the array becomes $$${1, 1, 0, 0, 1, 0}$$$, which has the inversions formed by the pairs of indices ($$$1, 3$$$), ($$$1, 4$$$), ($$$1, 6$$$), ($$$2, 3$$$), ($$$2, 4$$$), ($$$2, 6$$$), ($$$5, 6$$$) which total to $$$7$$$ inversions which is the maximum possible.