A matrix is called binary if all its elements are either $$$0$$$ or $$$1$$$.

Ecrade calls a binary matrix $$$A$$$ good if the following two properties hold:

The bitwise XOR of all numbers in each row of matrix $$$A$$$ is equal to $$$0$$$.
The bitwise XOR of all numbers in each column of matrix $$$A$$$ is equal to $$$0$$$.

Ecrade has a binary matrix of size $$$n \cdot m$$$. He is interested in the minimum number of elements that need to be changed for the matrix to become good.

However, it seems a little difficult, so please help him!

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 400$$$). The description of the test cases follows.

The first line of each test case contains two integers $$$n, m$$$ ($$$1 \le n, m \le 100$$$).

This is followed by $$$n$$$ lines, each containing exactly $$$m$$$ characters consisting only of $$$0$$$ and $$$1$$$, describing the elements of Ecrade's matrix.

It is guaranteed that the sum of $$$n \cdot m$$$ across all test cases does not exceed $$$5 \cdot 10^4$$$.

Output

For each test case, output a single integer, the minimum number of elements that need to be changed.

Note

In the first test case, he needs to change 2 elements to obtain the following matrix $$$\begin{pmatrix}1&1&0\\1&0&1\\0&1&1\end{pmatrix}$$$.

In the second test case, he can make no changes to obtain the following matrix $$$\begin{pmatrix}0&0&0\\0&0&0\\0&0&0\end{pmatrix}$$$.

In the third test case, he needs to change 3 elements to obtain the following matrix $$$\begin{pmatrix}1&0&1\\0&0&0\\1&0&1\end{pmatrix}$$$.

Idx	Name	Rating	Status
A	Binary Matrix	800
B	Floor or Ceil	1600

Codeforces Round 1010 (Div. 2, Unrated)