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1. Labyrinth problem: Several items are placed in cells of an (n x m) board. No more than one item per cell is allowed. A robot, located in the upper left cell of the board, needs to collect as many of the items as possible and bring them to the bottom right cell. On each step, the robot can move either one cell to the right or one cell down from its current location. When the robot visits a cell with an item, it always picks it up. Let Flij) describe the largest number of items the robot can collect and bring to the cell Lj) in the i-th row and the j-th column. Also, c, 1 when there is a coin in cell (ij)l, ci-o otherwise