Bedelia Mini Kaftan Dress by Celia Dragouni ReviewEndtml Let me analyze this problem step by step. We have a grid of 3 rows and N columns. Each cell has a value. We need to find the maximum sum path from the leftmost column to the rightmost column, where: - We start from any cell in the leftmost column - We end at any cell in the rightmost column - We can move right, up, or down (but not left) - We cannot visit a cell more than once Wait, let me re-read the problem. We can move right, up, or down. Since we can move up or down without moving right, we could potentially traverse multiple cells in the same column. But we can't visit a cell more than once. Let me think about this more carefully. The key constraint is that we can move right, up, or down, but not left. And we can't revisit cells. So in a given column, we could move up and down within that column before moving right. But since we can't revisit cells, the path within a column must be contiguous. Actually, let me think about this differently. Since the grid has only 3 rows, the states are manageable. For each column, we need to track which row we're currently in, and which cells in the current column we've already visited. Wait, but since we can move up and down freely (without going left), when we're in a column, we can visit multiple cells in that column. But the path must be connected and non-self-intersecting. Let me think about the possible states when transitioning from one column to the next. When we enter a column from the left (moving right), we enter at some row. Then we can move up or down within that column, collecting values. Then we move right to the next column from some row. Since the grid has 3 rows (0, 1, 2), let's think about what paths are possible within a column: If we enter at row r, we can: 1. Stay at row r, then exit right from row r 2. Move up from row r (collecting cells above), then exit right from some row above r 3. Move down from row r (collecting cells below), then exit right from some row below r 4. Move up, then come back down past r, then exit from below r 5. Move down, then come back up past r, then exit from above r Wait, but we can't revisit cells. So if we enter at row 1, we could: - Go up to row 0, then we can't go back to row 1 (already visited) - Go down to row 2, then we can't go back to row 1 So actually, within a column, the path is a contiguous segment of rows, and we enter from one end (or the middle) and exit from one end. Let me reconsider. We enter a column at row `r_in` (coming from the left). Then we can move up or down. The cells we visit in this column form a contiguous vertical segment. We exit the column to the right from row `r_out`. The path within the column must be: enter at r_in, then move to r_out, visiting all cells between them (inclusive). But we can only move up or down, so the path within the column is just a straight line from r_in to r_out (visiting all cells in between). Wait, but could we go up first and then down? Like enter at row 1, go to row 0, then go back to row 1, then to row 2? No, because we'd revisit row 1. So within a column, we enter at r_in and can go either up or down (or stay). The cells visited are all cells from min(r_in, r_out) to max(r_in, r_out). And we exit at r_out. Actually wait, could we enter at row 1, go up to row 0, and then exit right from row 0? Yes. Or enter at row 1, go down to row 2, and exit right from row 2. Or just stay at row 1 and exit right from row 1. Could we enter at row 0, go down to row 2, visiting rows 0, 1, 2, and exit right from row 2? Yes. Could we enter at row 0, go down to row 1, and exit right from row 1? Yes. So