PROBLEM C Optimisation Input File Name: C.DAT Source File Name:C.PAS or C.C or C.CPP A company decides to simulate on computer the process of manufacturing its own goods. In order to do that, it makes the following observations: 1. The whole process can be splitted into several steps; between them there are some dependencies. This can be represented by a diagram (graph), which we suppose to be only one for all goods produced by company as in figure 1; 2. First step designates the start of manufacturing process;there is only one first step, denoted by the number 1; 3. There are not steps isolated or outside the process (every step is linked by a path with the first step); 4. Some steps are total dependants; so, we claim that the step i is total dependant of step j if every path in the fabrication process cannot arrive to i without was passing through j. So, all steps are total dependants of step 1. Example: In the process shown by the figure 1 the step 4 is total dependant of step 3, steps 5,6 and 7 are total dependants of 4 (hence of 3), but step 3 is not total dependant of step 2. The Computing Center Dept. of company notes that whole manufacturing process is easier to be controlled if it would be structured by a tree, as follows: - All steps of manufacturing process are nodes of the tree; - Each node ensures total dependence of all its own descendants; The tree associated to the diagram from figure 1 is shown in figure 2. Your task is to write a program that builds this dependence tree. Input: The input file contains several input data sets. An input data set has the following format: n- number of steps of manufacturing process (2<=n<=99); a11 a12 ... a1n a21 a22 ... a2n ............... an1 an2 ... ann where aij=1 if step j follows directly step i in the process diagram, otherwise aij=0. Output: At output, the program must write n-1 lines for every input data set; each line has the format: i j with the meaning that node j is a direct descendant of node i in the tree. The pair (i1 j1) follows (i2 j2) if and only if (i1