Find robots by distances to the nearest blocker

You are given an m x n board. Each cell is one of:

• 'O': a robot
• 'E': an empty cell
• 'X': a blocker

You are also given a query of four integers [left, top, bottom, right]. For a robot, each number is the distance to the nearest blocker in that direction. Distance is the number of steps from the robot until you land on the blocker, so a blocker in the adjacent cell is distance 1. The edge of the board also acts as a blocker: if there is no 'X' in a direction, count the steps until you step off the board. Robots and empty cells do not block.

Return the positions [row, col] of every robot whose four distances match the query exactly, in row-major order. Return an empty list if no robot matches.

Then extend your solution: the board stays fixed and you receive many queries. Make each query as fast as you can.

Constraints

• 1 <= m, n <= 1000
• Up to 10^5 queries

Example 1

board = [["O","E","X"],
         ["E","O","E"],
         ["X","E","O"]]
query = [2, 2, 2, 2]

Output: [[1, 1]]. The center robot sees no 'X' in any direction; the board edge is two steps away each way.

Example 2

Same board, query = [1, 1, 2, 2]. Output: [[0, 0]]. The top-left robot touches the edge on its left and top, and an 'X' is two steps below it and two steps to its right.