###### 编程介的小学生

# 销售员的旅行的问题，图伦在数据上的编程，怎么利用C语言的程序的设计实现的？

Problem Description

After travelling around for years, Salesman John has decided to settle. He wants to build a new house close to his customers, so he doesn't have to travel as much any more. Luckily John knows the location of all of his customers.

All of the customers' locations are at (distinct) integer coordinates. John's new house should also be built on integer coordinates, which cannot be the same as any of the customers' locations. Since John lives in a large and crowded city, the travelling distance to any customer is the Manhattan distance: |x - xi| + |y - yi|, where (x, y) and (xi, yi) are the coordinates of the new house and a customer respectively.

What is the number of locations where John could settle, so the sum of the distance to all of his customers is as low as posible?

Input

On the first line an integer t (1 <= t <= 100): the number of test cases. Then for each test case:

One line with an integer n (1 <= n <= 2 000): the number of customers John has.

n lines with two integers xi and yi (-1 000 000 000 <= xi, yi <= 1 000 000 000): the coordinates of the i-th customer.

Output

For each test case:

Two space-separated integers: the minimum summed distance to all customers, and the number of spots on which John can build his new house to achieve this minimum.

Sample Input

2

4

1 -3

0 1

-2 1

1 -1

2

-999888777 1000000000

1000000000 -987654321

Sample Output

10 4

3987543098 3975087573110998514

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