Problem D
Planet Hopping

As part of the Constellation Commerce and Planetary Connections company (CCPC), you are tasked with mining resources from planets in the Milky Way. As a part of this task, you are given a spaceship that can travel to different planets in the Milky Way, as well as a device that can determine the resources on each planet near your location.

The device displays a matrix of size $n \times n$ where each cell represents a planet. Each planet has a certain amount of resources that can be mined. You want to mine as many resources as possible by visiting different planets in a certain order. You can start at any planet located at a cell that is touching a border, and end whenever you either have no more planets left to traverse, or when you can no longer travel to another planet (e.g. when your fuel is 0).

Your spaceship has limited fuel and can only travel a certain distance before needing to refuel. You can only travel to adjacent planets (up, down, left, right) that are within your fuel range, and one point of fuel is consumed per planet travelled to.

Your boss is on the spaceship with you and will only stay impressed if each planet you visit has more resources on it than the last one you mined, so you will mine a sequence of planets with strictly increasing resource values. Given this constraint, your goal is to determine the maximum amount of resources you can mine before running out of fuel. You can only visit each planet once, and you must mine every planet you go to including the starting planet.


The first line of input will contain two space-separated integers $n$ and $f$ where $1 \leq n \leq 20$ and $1 \leq f \leq 400$. This represents the size of the $n \times n$ matrix as well as the fuel you are given, $f$. The next $n$ lines consist of $n$ space-separated integers, where each integer represents the amount of resources on that planet. The resources on each planet will be integers between $0$ and $400$.


The output should be an integer representing the maximum amount of resources you can mine with the given constraints.

Sample Input 1 Sample Output 1
3 2
1 5 3
2 6 9
3 7 6
Sample Input 2 Sample Output 2
3 3
1 5 3
2 6 9
3 7 6

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