Code And Fun

Problem: Vestigium  Vestigium means "trace" in Latin. In this problem we work with Latin squares and matrix traces. The  trace  of a square matrix is the sum of the values on the main diagonal (which runs from the upper left to the lower right). An  N -by- N  square matrix is a  Latin square  if each cell contains one of  N  different values, and no value is repeated within a row or a column. In this problem, we will deal only with "natural Latin squares" in which the  N  values are the integers between 1 and  N . Given a matrix that contains only integers between 1 and  N , we want to compute its trace and check whether it is a natural Latin square. To give some additional information, instead of simply telling us whether the matrix is a natural Latin square or not, please compute the number of rows and the number of columns that contain repeated values. Input The first line of the input gives the number of test cases,  T .  T  test cases follo