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. 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). For each test case, output a single integer — the maximum possible beauty. In the first test case, the mat