You have an array $$$a$$$ of size $$$n$$$ consisting only of zeroes and ones. You can do the following operation:

choose two indices $$$1 \le i , j \le n$$$, $$$i \ne j$$$,
add $$$a_{i}$$$ to $$$a_{j}$$$,
remove $$$a_{i}$$$ from $$$a$$$.

Note that elements of $$$a$$$ can become bigger than $$$1$$$ after performing some operations. Also note that $$$n$$$ becomes $$$1$$$ less after the operation.

What is the minimum number of operations needed to make $$$a$$$ non-decreasing, i. e. that each element is not less than the previous element?

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 10^4$$$). The description of the test cases follows.

The first line of each test case contains an integer $$$n$$$ ($$$1 \le n \le 10^5$$$), the size of array $$$a$$$.

Next line contains $$$n$$$ integers $$$a_{1}, a_{2}, \ldots a_{n}$$$ ($$$a_i$$$ is $$$0$$$ or $$$1$$$), elements of array $$$a$$$.

It's guaranteed that sum of $$$n$$$ over all test cases doesn't exceed $$$2 \cdot 10^5$$$.

Output

For each test case print a single integer, minimum number of operations needed to make $$$a$$$ non-decreasing.

Note

In the first test case, $$$a$$$ is already non-decreasing, so you don't need to do any operations and the answer is $$$0$$$.

In the second test case, you can perform an operation for $$$i = 1$$$ and $$$j = 5$$$, so $$$a$$$ will be equal to $$$[0, 0, 1, 2]$$$ and it becomes non-decreasing.

In the third test case, you can perform an operation for $$$i = 2$$$ and $$$j = 1$$$, so $$$a$$$ will be equal to $$$[1]$$$ and it becomes non-decreasing.

Rebellion

Examples