code_segments/segment_163.txt

Given a matrix $a$ of size $n \times m$, each cell of which contains a non-negative integer. The integer lying at the intersection of the $i$-th row and the $j$-th column of the matrix is called $a_{i,j}$.

Let's define $f(i)$ and $g(j)$ as the [XOR](https://en.wikipedia.org/wiki/Exclusive_or) of all integers in the $i$-th row and the $j$-th column, respectively. In one operation, you can either:

  * Select any row $i$, then assign $a_{i,j} := g(j)$ for each $1 \le j \le m$; or    * Select any column $j$, then assign $a_{i,j} := f(i)$ for each $1 \le i \le n$. 

![](CDN_BASE_URL/3bba110245afb461968dbb618fc60828) An example of applying an operation on column $2$ of the matrix.

In this example, as we apply an operation on column $2$, all elements in this column are changed:

  * $a_{1,2} := f(1) = a_{1,1} \oplus a_{1,2} \oplus a_{1,3} \oplus a_{1,4} = 1 \oplus 1 \oplus 1 \oplus 1 = 0$    * $a_{2,2} := f(2) = a_{2,1} \oplus a_{2,2} \oplus a_{2,3} \oplus a_{2,4} = 2 \oplus 3 \oplus 5 \oplus 7 = 3$    * $a_{3,2} := f(3) = a_{3,1} \oplus a_{3,2} \oplus a_{3,3} \oplus a_{3,4} = 2 \oplus 0 \oplus 3 \oplus 0 = 1$    * $a_{4,2} := f(4) = a_{4,1} \oplus a_{4,2} \oplus a_{4,3} \oplus a_{4,4} = 10 \oplus 11 \oplus 12 \oplus 16 = 29$ 

You can apply the operations any number of times. Then, we calculate the $\textit{beauty}$ of the final matrix by summing the absolute differences between all pairs of its adjacent cells.

More formally, $\textit{beauty}(a) = \sum|a_{x,y} - a_{r,c}|$ for all cells $(x, y)$ and $(r, c)$ if they are adjacent. Two cells are considered adjacent if they share a side.

Find the minimum $\textit{beauty}$ among all obtainable matrices.

The first line contains a single integer $t$ ($1 \le t \le 250$) — the number of test cases.

The first line of each test case contains two integers $n$ and $m$ ($1 \le n, m \le 15$) — the number of rows and columns of $a$, respectively.

The next $n$ lines, each containing $m$ integers $a_{i,1}, a_{i,2}, \ldots, a_{i,m}$ ($0 \le a_{i,j} < 2^{20}$) — description