# Given a rows x cols matrix grid representing a field of cherries. Each cell in grid represents the number of cherries that you can collect.
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# You have two robots that can collect cherries for you, Robot #1 is located at the top-left corner (0,0) , and Robot #2 is located at the top-right corner (0, cols-1) of the grid.
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# Return the maximum number of cherries collection using both robots  by following the rules below:
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# 	From a cell (i,j), robots can move to cell (i+1, j-1) , (i+1, j) or (i+1, j+1).
# 	When any robot is passing through a cell, It picks it up all cherries, and the cell becomes an empty cell (0).
# 	When both robots stay on the same cell, only one of them takes the cherries.
# 	Both robots cannot move outside of the grid at any moment.
# 	Both robots should reach the bottom row in the grid.
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# Example 1:
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# Input: grid = [[3,1,1],[2,5,1],[1,5,5],[2,1,1]]
# Output: 24
# Explanation: Path of robot #1 and #2 are described in color green and blue respectively.
# Cherries taken by Robot #1, (3 + 2 + 5 + 2) = 12.
# Cherries taken by Robot #2, (1 + 5 + 5 + 1) = 12.
# Total of cherries: 12 + 12 = 24.
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# Example 2:
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# Input: grid = [[1,0,0,0,0,0,1],[2,0,0,0,0,3,0],[2,0,9,0,0,0,0],[0,3,0,5,4,0,0],[1,0,2,3,0,0,6]]
# Output: 28
# Explanation: Path of robot #1 and #2 are described in color green and blue respectively.
# Cherries taken by Robot #1, (1 + 9 + 5 + 2) = 17.
# Cherries taken by Robot #2, (1 + 3 + 4 + 3) = 11.
# Total of cherries: 17 + 11 = 28.
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# Example 3:
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# Input: grid = [[1,0,0,3],[0,0,0,3],[0,0,3,3],[9,0,3,3]]
# Output: 22
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# Example 4:
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# Input: grid = [[1,1],[1,1]]
# Output: 4
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# Constraints:
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# 	rows == grid.length
# 	cols == grid[i].length
# 	2 <= rows, cols <= 70
# 	0 <= grid[i][j] <= 100 
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class Solution:
    def cherryPickup(self, grid: List[List[int]]) -> int:
        height, width = len(grid), len(grid[0])
        memoDict = {}
        def boundaryCheck(column):
            if 0 <= column < width:
                return False
            return True

        def optimal_pick(row, column_R1, column_R2):
            if row == height or boundaryCheck(column_R1) or boundaryCheck(column_R2):
                return 0
            if (row, column_R1, column_R2) in memoDict:    
                return memoDict[(row, column_R1, column_R2)]
            maximum = 0
            for firstOffset in (-1, 0, 1):
                for secondOffset in (-1, 0, 1):
                    next_col_1, next_col_2 = column_R1 + firstOffset, column_R2 + secondOffset
                    if next_col_1 >= next_col_2:
                        continue
                    maximum = max(maximum, optimal_pick(row+1, next_col_1, next_col_2) )
            memoDict[(row, column_R1, column_R2)] = maximum + grid[row][column_R1] + grid[row][column_R2]
            return memoDict[(row, column_R1, column_R2)] 
        return optimal_pick(0, 0, width-1)
