# Programming contests

## DEIK Regionális Programozó Csapatverseny, középiskolai kategória, 2022. december 4.

December 4, 2022 10:00 AM – December 4, 2022 3:15 PM

# ski

The figure above represents a simplified map of some highland in a form of a matrix. The numbers show the altitudes of the locations. We like skiing and we are searching for a good path. A path through the highland is called good if the subsequent locations are horizontally or vertically (but not diagonally) adjacent and each of them has a strictly lower altitude than the previous one. In the figure the path that starts at `11` and follows the green arrows, is a sequence of the locations `(2,4),(2,5),(2,6),(3,6),(3,5),(4,5),(4,4),(4,3)`, where the first and second number are the row and column index respectively. Easy to verify that it is a good path, as well as the red one is. The length of a path is the number of locations in it. The green path is of length `8` and the red one is of length `7.`

Your task is to compute the length of the longest good path for a given map.

## Input Specification

``````
R C
t11 ... t1C
t21 ... t2C
...
tR1 ... tRC
```
```

The comma separated numbers `1 ≤ R,C ≤ 100 ` in the first row are the number of rows and columns of the map - respectively. In each of the subsequent `R` rows there are `C` comma separated positive integers, not larger than ` 106 `.

## Output Specification

```L
```

A single line with length `L` of the longest good path.

## Sample Input 1

1. `2 2`
2. `1 2`
3. `3 4`

1. `3`

## Sample Input 2

1. `3 4`
2. `1 2 3 3`
3. `4 5 4 2`
4. `7 6 5 6`

1. `7`

## Sample Input 3

1. `4 6`
2. `3 5 7 4 4 2`
3. `4 3 9 11 8 7`
4. `1 2 4 8 5 6`
5. `4 1 1 2 3 10`
1. `8`