p01082 Escape of Lappin the Phantom Thief
Problem Description
Problem
Phantom thief Rappan came to steal the jewels. It was easy to get the jewel, but the jewel was equipped with a sensor and was surrounded by security robots.
The guard robot is designed to move towards the jewel. The sensor didn't seem to be easy to remove, so I decided to put a jewel and escape. I decided to keep the jewels as far away from the guard robot as possible to give me time to escape.
The site has a rectangular shape consisting of n x m squares and there are no obstacles. The k-body security robots are arranged in squares (xi, yi) (0 ≤ xi ≤ n−1, 0 ≤ yi ≤ m−1), respectively, and can move to the upper, lower, left and right squares in a unit time. The security robot moves to the square with the jewel in the shortest path.
Find the maximum travel time it takes for one or more guard robots to reach the jeweled square when you are free to place jewels on the premises.
Constraints
- 1 ≤ n, m ≤ 5 × 104
- 1 ≤ k ≤ min (105, n x m)
- 0 ≤ xi ≤ n−1
- 0 ≤ yi ≤ m−1
- All given coordinates are different
Input
n m k x1 y1 x2 y2 ... xk yk
All inputs are given as integers. The first line is given n, m, k separated by blanks. The coordinates (xi, yi) of the square where the guard robot is located are given in the second and subsequent lines k, separated by blanks.
Output
Output the travel time to the place where it takes the longest time for the security robot to reach in one line.
Examples
Input
20 10 1 0 0
Output
28
Input
20 10 2 0 0 17 5
Output
15
Input
20 10 3 0 0 17 5 6 9
Output
11
Contest Information
- Contest ID: 0
- Problem Index:
- Points: 0.0
- Rating: 0
- Tags:
- Time Limit: {'seconds': 8, 'nanos': 0} seconds
- Memory Limit: 268435456 bytes
Task
Solve this competitive programming problem. Provide a complete solution that handles all the given constraints and edge cases.