The program committee of the school programming contests, which are often held
at the Ural State University, is a big, joyful, and united team. In fact, they are so
united that the time spent together at the university is not enough for them,
so they often visit each other at their homes. In addition, they are quite
athletic and like walking.
Once the guardian of the traditions of the sports programming at the Ural State University decided that the members of the program committee spent too much time walking from home to home. They could have spent that time inventing and preparing new problems instead. To prove that, he wanted to calculate the average distance that the members of the program committee walked when they visited each other. The guardian took a map of Yekaterinburg, marked the houses of all the members of the program committee there, and wrote down their coordinates. However, there were so many coordinates that he wasn't able to solve that problem and asked for your help.
The city of Yekaterinburg is a rectangle with the sides parallel to the coordinate axes. All the streets stretch from east to west or from north to south through the whole city, from one end to the other. The house of each member of the program committee is located strictly at the intersection of two orthogonal streets. It is known that all the members of the program committee walk only along the streets, because it is more pleasant to walk on sidewalks than on small courtyard paths. Of course, when walking from one house to another, they always choose the shortest way. All the members of the program committee visit each other equally often.
The first line contains the number n of members of the program committee (2 ≤ n ≤ 105). The i-th of the following n lines contains space-separated coordinates xi, yi of the house of the i-th member of the program committee (1 ≤ xi, yi ≤ 106). All coordinates are integers.
Output the average distance, rounded down to an integer, that a member of the program committee walks from his house to the house of his colleague.
Problem Author: Denis Dublennykh
Problem Source: Ural Regional School Programming Contest 2009