Description:
Polycarp decided to generate a biome map for his game. A map is a matrix divided into cells $$$1 \times 1$$$. Each cell of the map must contain one of the available biomes.
Each biome is defined by two parameters: temperature (an integer from $$$1$$$ to $$$n$$$) and humidity (an integer from $$$1$$$ to $$$m$$$). But not for every temperature/humidity combination, a corresponding biome is available.
The biome map should be generated according to the following rules:
- each cell of the map belongs to exactly one biome;
- each available biome has at least one cell on the map;
- if two cells of the map are adjacent by the side and they belong to biomes with parameters ($$$t_1, h_1$$$) and ($$$t_2, h_2$$$), respectively, then the equality $$$|t_1-t_2| + |h_1-h_2| = 1$$$ holds;
- let the number of available biomes be equal to $$$k$$$, then the number of rows and columns of the map (separately) should not exceed $$$k$$$.
Help Polycarp generate a biome map that meets all the conditions described above (or report that this is impossible).
Input Format:
The first line contains a single integer $$$t$$$ ($$$1 \le t \le 20$$$) — the number of test cases.
The first line of each test case contains two integers $$$n$$$ and $$$m$$$ ($$$1 \le n, m \le 10$$$) — maximum temperature and humidity parameters.
The following $$$n$$$ lines contain $$$m$$$ integers each $$$a_{i,1}, a_{i, 2}, \dots, a_{i, m}$$$ ($$$0 \le a_{i, j} \le 100$$$), where $$$a_{i, j}$$$ — the biome identifier with the parameters $$$(i, j)$$$, if $$$a_{i, j} \neq 0$$$, otherwise the biome with such parameters is not available.
All biome identifiers are different, and there are at least two biomes available.
Output Format:
For each test case, print the answer in the following format:
- print $$$-1$$$ in a single line if there is no map that meets all the conditions;
- otherwise, in the first line, print two integers $$$h$$$ and $$$w$$$ — the number of rows and columns of the map, respectively. In the following $$$h$$$ lines, print $$$w$$$ integers — the identifiers of the biomes in the corresponding cells of the map.
Note:
None