Distance to the nearest point

Given two sets $S$ and $Q$ of points on the plane, determine, for each point in $Q$ , the minimum of the Manhattan distances to the points in $S$ .

Input

Input consists of a natural $n$ , the coordinates of the $n$ points in $S$ , a natural $m$ , and the coordinates of the $m$ points in $Q$ . Assume $1 \le n \le 10^5$ and $0 \le m \le 10^5$ . The coordinates are real numbers. Points can be repeated.

Output

For every point in $Q$ , print the Manhattan distance to its closest point in $S$ .

Observation

This problem tolerates an error of $10^{-7}$ for each output.

Problem information

Author: Jordi Petit

Generation: 2026-01-25T10:34:18.335Z