# Problem C

Decreasing Paths

Imagine you are on a large grid of square steps, where each step is at a different height, labeled by an integer. Starting from some step, you can move to any one of its $8$ orthogonal or diagonal neighbors that is a lower height than the current step – in other words, is labeled by a strictly smaller integer. You want to find the length of the longest strictly-decreasing path through this grid, starting at any step.

## Input

Each input starts with a pair of numbers $r$, $c$ representing the number of rows and columns in the grid, where

\[ 1 \leq r,c \leq 256. \]This is followed by $r$ rows of $c$ integers representing the heights of the steps in the grid, with columns separated by spaces. Each integer $x$ in the grid will be in the range

\[ -(2^{30}) \leq x \leq 2^{30}. \]## Output

Your program should output the length of the longest strictly-decreasing path through the grid on a single line.

Sample Input 1 | Sample Output 1 |
---|---|

3 4 16 4 -32 7 22 -18 4 -17 8 25 6 429 |
6 |

Sample Input 2 | Sample Output 2 |
---|---|

6 6 0 1 2 3 4 5 1 2 3 4 5 6 2 3 4 5 6 7 3 4 5 6 7 8 4 5 6 7 8 9 5 6 7 8 9 10 |
11 |