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 $i$.

Sample Input 1

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

Sample Output 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.