B"In order to do some research, n^2 labs are built on different heights of a mountain. Let's enumerate them with integers from 1 to n^2 , such that the lab with the number 1 is at the lowest place, the lab with the number 2 is at the second-lowest place, ldots , the lab with the number n^2 is at the highest place. To transport water between the labs, pipes are built between every pair of labs. A pipe can transport at most one unit of water at a time from the lab with the number u to the lab with the number v if u > v . Now the labs need to be divided into n groups, each group should contain exactly n labs. The labs from different groups can transport water to each other. The sum of units of water that can be sent from a group A to a group B is equal to the number of pairs of labs ( u, v ) such that the lab with the number u is from the group A , the lab with the number v is from the group B and u > v . Let's denote this value as f(A,B) (i.e. f(A,B) is the sum of units of water that can be sent from a group A to a group B ). For example, if n=3 and there are 3 groups X , Y and Z : X = {1, 5, 6 }, Y = {2, 4, 9 } and Z = {3, 7, 8 } . In this case, the values of f are equal to: Please, divide labs into n groups with size n , such that the value min f(A,B) over all possible pairs of groups A and B ( A neq B ) is maximal. In other words, divide labs into n groups with size n , such that minimum number of the sum of units of water that can be transported from a group A to a group B for every pair of different groups A and B ( A neq B ) as big as possible. Note, that the example above doesn't demonstrate an optimal division, but it demonstrates how to calculate the values f for some division. If there are"...