### Hard Leetcode Problem: Grid Illumination

Here is the problem: https://leetcode.com/problems/grid-illumination/ On a N x N grid of cells, each cell (x, y) with 0 <= x < N and 0 <= y < N has a lamp. Initially, some number of lamps are on. lamps[i] tells us the location of the i -th lamp that is on. Each lamp that is on illuminates every square on its x-axis, y-axis, and both diagonals ( similar to a Queen in chess ). For the i-th query queries[i] = (x, y) , the answer to the query is 1 if the cell (x, y) is illuminated, else 0. After each query (x, y) [in the order given by queries ], we turn off any lamps that are at cell (x, y) or are adjacent 8-directionally (ie., share a corner or edge with cell (x, y) .) Return an array of answers. Each value answer[i] should be equal to the answer of the i -th query queries[i] . Example 1: Input: N = 5 , lamps = [[0,0],[4,4]] , queries = [[1,1],[1,0]] Output: [1,0] Explanation: Before performing the first query we have both lamps [0