Cairo Corridor

The Cairo pentagonal tiling is a decomposition of the plane using semiregular pentagons. Its name is given because several streets in Cairo are paved using variations of this design.

Consider a bounded tiling where each pentagon is either clear (white) or filled in (grey). A corridor is a maximal set of clear adjacent pentagons that connect the four borders of the tiling. Pentagons are considered adjacent if they share an edge, not just a corner. It is easy to verify that there can be at most one corridor in each tiling. A corridor is said to be minimal if it has no superfluous pentagon, that is, if any pentagon of the corridor was filled in, the set of remaining pentagons would not be a corridor.

The figure above depicts four example tilings. In the first three cases, there is a corridor which is highlighted in yellow. Besides, the corridors of figures (a) and (b) are minimal, but the one in figure (c) is not: for example, the tiles marked 'X' (among others) could be filled in and a corridor would still exist. In the rightmost tiling there is no corridor. The tilings shown in figures (a) and (c) correspond to sample input $1$.

Write a program that reads textual descriptions of Cairo tilings, and for each one determines if a corridor exists and is minimal. In the latter case, the program should compute the size of the corridor, i.e., the number of clear pentagonal tiles of the corridor.

Input

The first line is a positive decimal integer $t$ (1 \leq t \leq 10) of tilings to be processed. Each tiling description $k$ has a first line with two positive decimal integers, n_k and m_k (1 \leq n_1 + n_2 + \ldots + n_t \leq 250 - total number of lines, 1 \leq m_1 + m_2 + \ldots + m_t \leq 250 - total number of tile pairs), separated by a space. The following n_k lines contain 2 \cdot m_k binary digits representing pairs a_{ij}, b_{ij} of tiles ($0$ is clear and $1$ is full) in alternating horizontal/vertical adjacency following a "checkerboard" pattern, as is illustrated in the figure below.