3, 2, 1, ... We are the — RiOI Team!— Felix & All, Special Thanks 3

• Peter: Good news: My problem T311013 is approved!
• $\delta$: I'm glad my computer had gone out of battery so that I wouldn't have participated in wyrqwq's round and gained a negative delta.
• Felix: [thumbs_up] The problem statement concerning a removed song!
• Aquawave: Do I mourn my Chemistry?
• E.Space: ahh?
• Trine: Bread.
• Iris: So why am I always testing problems?

Time will pass, and we might meet again. Looking back at the past, everybody has lived the life they wanted.

Aquawave has a matrix $A$ of size $n\times m$, whose elements can only be integers in the range $[1, k]$, inclusive. In the matrix, some cells are already filled with an integer, while the rest are currently not filled, denoted by $-1$.

You are going to fill in all the unfilled places in $A$. After that, let $c_{u,i}$ be the number of occurrences of element $u$ in the $i$-th row. Aquawave defines the beauty of the matrix as

$$\sum_{u=1}^k \sum_{i=1}^{n-1} c_{u,i} \cdot c_{u,i+1}.$$

You have to find the maximum possible beauty of $A$ after filling in the blanks optimally.

Input

The first line of input contains a single integer $t$ ($1 \leq t \leq 2\cdot 10^4$) — the number of test cases. The description of test cases follows.

The first line of each test case contains three integers $n$, $m$, and $k$ ($2 \leq n \leq 2\cdot 10^5$, $2 \leq m \leq 2\cdot 10^5$, $n \cdot m \leq 6\cdot 10^5$, $1 \leq k \leq n\cdot m$) — the number of rows and columns of the matrix $A$, and the range of the integers in the matrix, respectively.

Then $n$ lines follow, the $i$-th line containing $m$ integers $A_{i,1},A_{i,2},\ldots,A_{i,m}$ ($1 \leq A_{i,j} \leq k$ or $A_{i,j} = -1$) — the elements in $A$.

It is guaranteed that the sum of $n\cdot m$ over all test cases does not exceed $6\cdot 10^5$.

Output

For each test case, output a single integer — the maximum possible beauty.

Note

In the first test case, the matrix $A$ is already determined. Its beauty is

$$\sum_{u=1}^k \sum_{i=1}^{n-1} c_{u,i} \cdot c_{u,i+1} = c_{1,1}\cdot c_{1,2} + c_{1,2}\cdot c_{1,3} + c_{2,1}\cdot c_{2,2} + c_{2,2}\cdot c_{2,3} + c_{3,1}\cdot c_{3,2} + c_{3,2}\cdot c_{3,3} = 1\cdot 1 + 1\cdot 1 + 2\cdot 0 + 0\cdot 1 + 0\cdot 2 + 2\cdot 1 = 4.$$

In the second test case, one can fill the matrix as follows:

$$ \begin{bmatrix} 2 &3 &3 \\ 2 &2 &3 \end{bmatrix}, $$

and get the value $4$. It can be proven this is the maximum possible answer one can get.

In the third test case, one of the possible optimal configurations is:

$$ \begin{bmatrix} 1 &1 &1 \\ 1 &2 &1 \\ 1 &1 &4 \end{bmatrix}. $$

In the fourth test case, one of the possible optimal configurations is:

$$ \begin{bmatrix} 1 &3 &2 &3 \\ 1 &3 &2 &1 \\ 3 &1 &5 &1 \end{bmatrix}. $$

In the fifth test case, one of the possible optimal configurations is:

$$ \begin{bmatrix} 5 &5 &2 \\ 1 &8 &5 \\ 7 &5 &6 \\ 7 &7 &4 \\ 4 &4 &4 \end{bmatrix}. $$