# 1001. Grid Illumination

https://leetcode.com/problems/grid-illumination

## Description

There is a 2D `grid` of size `n x n` where each cell of this grid has a lamp that is initially **turned off**.

You are given a 2D array of lamp positions `lamps`, where `lamps[i] = [rowi, coli]` indicates that the lamp at `grid[rowi][coli]` is **turned on**. Even if the same lamp is listed more than once, it is turned on.

When a lamp is turned on, it **illuminates its cell** and **all other cells** in the same **row, column, or diagonal**.

You are also given another 2D array `queries`, where `queries[j] = [rowj, colj]`. For the `jth` query, determine whether `grid[rowj][colj]` is illuminated or not. After answering the `jth` query, **turn off** the lamp at `grid[rowj][colj]` and its **8 adjacent lamps** if they exist. A lamp is adjacent if its cell shares either a side or corner with `grid[rowj][colj]`.

Return _an array of integers_ `ans`_,_ _where_ `ans[j]` _should be_ `1` _if the cell in the_ `jth` _query was illuminated, or_ `0` _if the lamp was not._

**Example 1:**

![](https://assets.leetcode.com/uploads/2020/08/19/illu_1.jpg)

```
**Input:** n = 5, lamps = [[0,0],[4,4]], queries = [[1,1],[1,0]]
**Output:** [1,0]
**Explanation:** We have the initial grid with all lamps turned off. In the above picture we see the grid after turning on the lamp at grid[0][0] then turning on the lamp at grid[4][4].
The 0th query asks if the lamp at grid[1][1] is illuminated or not (the blue square). It is illuminated, so set ans[0] = 1. Then, we turn off all lamps in the red square.
![](https://assets.leetcode.com/uploads/2020/08/19/illu_step1.jpg)
The 1st query asks if the lamp at grid[1][0] is illuminated or not (the blue square). It is not illuminated, so set ans[1] = 0. Then, we turn off all lamps in the red rectangle.
![](https://assets.leetcode.com/uploads/2020/08/19/illu_step2.jpg)
```

**Example 2:**

```
**Input:** n = 5, lamps = [[0,0],[4,4]], queries = [[1,1],[1,1]]
**Output:** [1,1]
```

**Example 3:**

```
**Input:** n = 5, lamps = [[0,0],[0,4]], queries = [[0,4],[0,1],[1,4]]
**Output:** [1,1,0]
```

**Constraints:**

* `1 <= n <= 109`
* `0 <= lamps.length <= 20000`
* `0 <= queries.length <= 20000`
* `lamps[i].length == 2`
* `0 <= rowi, coli < n`
* `queries[j].length == 2`
* `0 <= rowj, colj < n`

## ac

```java
```
