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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 [0,0] and [4,4] on. The grid representing which cells are lit looks like this, where [0,0] is the top left corner, and [4,4] is the bottom right corner: 1 1 1 1 1 1 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 1 1 1 1 Then the query at [1, 1] returns 1 because the cell is lit. After this query, the lamp at [0, 0] turns off, and the grid now looks like this: 1 0 0 0 1 0 1 0 0 1 0 0 1 0 1 0 0 0 1 1 1 1 1 1 1 Before performing the second query we have only the lamp [4,4] on. Now the query at [1,0] returns 0, because the cell is no longer lit.

**Note:**

`1 <= N <= 10^9`

`0 <= lamps.length <= 20000`

`0 <= queries.length <= 20000`

`lamps[i].length == queries[i].length == 2`