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Ex - Manhattan Christmas Tree

Score : $600$ points

Problem Statement

There are $N$ Christmas trees in the two-dimensional plane. The $i$-th tree is at coordinates $(x_i,y_i)$.

Answer the following $Q$ queries.

Query $i$: What is the distance between $(a_i,b_i)$ and the $K_i$-th nearest Christmas tree to that point, measured in Manhattan distance?

Constraints

• $1\leq N \leq 10^5$
• $0\leq x_i\leq 10^5$
• $0\leq y_i\leq 10^5$
• $(x_i,y_i) \neq (x_j,y_j)$ if $i\neq j$.
• $1\leq Q \leq 10^5$
• $0\leq a_i\leq 10^5$
• $0\leq b_i\leq 10^5$
• $1\leq K_i\leq N$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

$x_1$ $y_1$

$\vdots$

$x_N$ $y_N$

$Q$

$a_1$ $b_1$ $K_1$

$\vdots$

$a_Q$ $b_Q$ $K_Q$

Output

Print $Q$ lines.
The $i$-th line should contain the answer to Query $i$.

4
3 3
4 6
7 4
2 5
6
3 5 1
3 5 2
3 5 3
3 5 4
100 200 3
300 200 1

1
2
2
5
293
489

The distances from $(3,5)$ to the $1$-st, $2$-nd, $3$-rd, $4$-th trees to that point are $2$, $2$, $5$, $1$, respectively.
Thus, the answers to the first four queries are $1$, $2$, $2$, $5$, respectively.