Shortest Distance to DashMart

You are given a 2-D grid that represents a city map. Each cell can be one of three characters:

• 'D' – a DashMart store (there may be many);
• 'X' – an obstacle (building, wall, etc.) that you cannot travel through;
• '.' – an open road you can travel on.

You may move only up, down, left, or right (no diagonals) and you cannot leave the grid. Your task is to pre-compute, for every open road cell, the shortest travel distance to the nearest DashMart. If a cell is itself a DashMart the distance is 0; if a cell is blocked or unreachable from every DashMart its distance remains infinity (represented as -1 in output). After the pre-processing you must be able to answer many client queries in O(1) time each: given a specific row and column, return the shortest distance you computed, or -1 if none exists.