You are given a (2n \times 2n) grid (a) where each column is a permutation(^{\text{∗}}) of length (2n). We want to sort all columns in ascending order from top to bottom by performing the following operation: Choose a (2 \times 2) subgrid and swap the two top elements with the two bottom elements. More formally, you can choose two integers (i) and (j) ((1 \leq i, j \lt 2n)), then swap (a_{i,j}) with (a_{i+1,j}) and swap (a_{i,j+1}) with (a_{i+1,j+1}). More formally, you can choose two integers (i) and (j) ((1 \leq i, j \lt 2n)), then swap (a_{i,j}) with (a_{i+1,j}) and swap (a_{i,j+1}) with (a_{i+1,j+1}). You have to sort all columns using at most (n \cdot \binom{2n}{2} + 9n) operations, or determine that it is impossible. Note that you do not need to minimize the number of operations. (^{\text{∗}})A permutation of length (m) is an array consisting of (m) distinct integers from (1) to (m) in arbitrary order. For example, (2,3,1,5,4) is a permutation, but (1,2,2) is not a permutation ((2) appears twice in the array), and (1,3,4) is also not a permutation ((m=3) but there is (4) in the array). Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 500)). The description of the test cases follows. The first line of each test contains a single integer (n) ((1 \leq n \leq 80)). The (i)-th line of the next (2n) lines contains (2n) integers (a_{i,1},a_{i,2},\ldots,a_{i,2n}) ((1 \leq a_{i,j} \leq 2n)) — the elements of the (i)-th row of the grid. It is guaranteed that every column in the grid forms a permutation of length (2n). It is guaranteed that the sum of (n^3) over all test cases does not exceed (80^3). For each test case, if it is impossible to sort all columns in at most (n \cdot \binom{2n}{2} + 9n) operations, print $$$-1