1219 - Path with Maximum Gold\.

Medium

In a gold mine grid of size m x n, each cell in this mine has an integer representing the amount of gold in that cell, 0 if it is empty.

Return the maximum amount of gold you can collect under the conditions:

• Every time you are located in a cell you will collect all the gold in that cell.

• From your position, you can walk one step to the left, right, up, or down.

• You can't visit the same cell more than once.

• Never visit a cell with 0 gold.

• You can start and stop collecting gold from any position in the grid that has some gold.

Example 1:

Input: grid = \[\[0,6,0],5,8,7,0,9,0]

Output: 24

Explanation:

[[0,6,0],
 [5,8,7],
 [0,9,0]]
Path to get the maximum gold, 9 -> 8 -> 7.

Example 2:

Input: grid = \[\[1,0,7],2,0,6,3,4,5,0,3,0,9,0,20]

Output: 28

Explanation:

[[1,0,7],
 [2,0,6],
 [3,4,5],
 [0,3,0],
 [9,0,20]]
Path to get the maximum gold, 1 -> 2 -> 3 -> 4 -> 5 -> 6 -> 7.

Constraints:

• m == grid.length

• n == grid[i].length

• 1 <= m, n <= 15

• 0 <= grid[i][j] <= 100

• There are at most 25 cells containing gold.