matrix-1

We need to walk on the cells of an $M$ matrix, starting from any chosen starting cell. We can move to a horizontally or vertically adjacent cell, but only if the adjacent cell’s value is greater than the one we’re standing on. What is the maximum number of steps we can take ($S$)? How many cells are there from which we can take the maximum possible number of steps ($L$)?

Input specification

$T$ is the number of test cases. Description of a test case: First line: $R$ and $C$ (number of rows and columns of the matrix). Then $R$ lines follow, each containing $C$ integers.

Output specification

$T$ lines, each containing the requested numbers $S$ and $L$.

Constraints

$1\le T \le 100$
$1\le R \le 100$
$1\le C \le 100$
$1\le M \le 1\_000$

Sample input 1

1. 4
2. 2 2
3. 1 1
4. 2 4
5. 3 3
6. 1 2 3
7. 2 3 4
8. 3 4 5
9. 5 5
10. 1 2 3 2 1
11. 1 2 4 2 1
12. 1 3 5 3 1
13. 3 5 6 5 3
14. 3 5 7 5 3
15. 5 5
16. 1 1 1 1 1
17. 1 2 2 2 1
18. 1 2 3 2 1
19. 1 2 2 2 1
20. 1 1 1 1 1

Sample output 1

1. 2 1
2. 4 1
3. 6 2
4. 2 4