Admiral

You are the admiral of a naval troop with 21 battleships in 6 kinds. There is one flagship, denoted 0, and the admiral must be on it. Kinds 1 to 5 have 2, 3, 4, 5, and 6 ships, respectively.

The battlefield has 6 rows, and all battleships have the same rectangular shape. In the optimal arrangement, every battleship of kind $i$ is in row $i$ (rows are numbered from 0).

The initial state occupies the 21 required positions, but some ships may be in the wrong row. You can swap the flagship with an adjacent battleship. Two battleships are adjacent if they are not in the same row and share part of an edge. For example, cell $(2, 1)$ is adjacent to $(1, 0)$, $(1, 1)$, $(3, 1)$, and $(3, 2)$, where $(i, j)$ is the cell in row $i$ and position $j$ from the left (both numbered from 0).

Find the minimum number of swaps needed to reach the optimal arrangement, or report that more than 20 swaps are required.

The first line contains an integer $T$, the number of test cases ($1 \le T \le 10$).

Each test case consists of 6 lines. The $i$-th line contains $i$ space-separated integers, the kinds of battleships in row $i$ from left to right.

For each test case, print too difficult on a single line if the goal cannot be reached in 20 or fewer swaps. Otherwise, print the minimum number of swaps on a single line.