There are 5 shapes on a 4x4 grid. Which shape is closest to the purple rectangle in terms of Manhattan distance? The final answer is the grid position of the closest shape like (row_index, column_index).
<think>Target shape: purple rectangle at (1, 2)
Distance from target shape to red rectangle at (1, 0): 2
Distance from target shape to cyan trapezoid at (2, 0): 3
Distance from target shape to blue trapezoid at (1, 3): 1
Distance from target shape to gray square at (2, 3): 2
Closest shape is the blue trapezoid at (1, 3) with distance 1</think>

<answer>(1, 3)</answer>