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Rescue Alice
Description Long
long ago, there was a princess named Alice. She was taken by the evil
Cent Dragon. Many warriors had tried to rescue her, but none of them
ever came back. One day, a prince called Jack showed up. He told the
King that he would go to rescue Alice in voluntary. The King responded
in despair, ¡°It¡¯s no use fighting with Cent Dragon.¡± But that did not
stop Jack. He set off immediately for the rescue. Jack rode his
way to the mountain where Cent Dragon lived. Unfortunately, he lost
himself in the forest before the mountain and was unable to find Cent
Dragon¡¯s castle. After wandering for a while, Jack saw an old man on a
stone smiling at him. He was surprised by the encounter and asked the
old man for the way. ¡°The forest is cursed in spells. An ordinal human
being won¡¯t be able to find a way out.¡± said the old man, ¡°If you want
to go to Cent Dragon¡¯s castle, you must find the Tree of Moon for help.¡± In
spite of hardships, Jack succeeded in locating the Tree of Moon ¨C a big
blue tree with spirits. He told his story to it, and it answered, ¡°In
this forest there are some magical wells. They are the entries of the
mountain. You can see all of them on a high tower nearby. You choice of
entry will decide how soon you can enter the mountain. Precisely
speaking, the time it takes can be measured by the sum of the distances
between the well you choose and the other ones.¡± In that ancient
times, distance was measured in a manner similar to what we now call
the Manhattan distance. Positions of the wells were described in a
Cartesian plane. Instead of taking the sum of absolute differences in
the abscissa and the ordinate, distances in Jack¡¯s adventure were found
by taking the maximum of them. Given the coordinates of the wells, can
you tell how much time did Jack need at least to spend entering the
mountain to rescue Alice in terms of distance? Input The input contains a single test case. The first line of input contains a positive integer N (N ¡Ü 100,000), the number of wells. Then follow N lines, each contains two integers xi and yi (|xi|, |yi| ¡Ü 1,000,000), which are the Cartesian coordinate of the ith well. Output Output one line containing only the minimum time Jack needed for entry into the mountain. Sample Input Sample Output Hint Sums of distances of the wells are 11, 13, 8 and 10. 8 is the minimum. Source |
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