CF323B Tournament-graph
Description
In this problem you have to build tournament graph, consisting of $ n $ vertices, such, that for any oriented pair of vertices $ (v,u) $ $ (v≠u) $ there exists a path from vertex $ v $ to vertex $ u $ consisting of no more then two edges.
A directed graph without self-loops is a tournament, if there is exactly one edge between any two distinct vertices (in one out of two possible directions).
Input Format
The first line contains an integer $ n $ $ (3
Output Format
Print -1 if there is no graph, satisfying the described conditions.
Otherwise, print $ n $ lines with $ n $ integers in each. The numbers should be separated with spaces. That is adjacency matrix $ a $ of the found tournament. Consider the graph vertices to be numbered with integers from $ 1 $ to $ n $ . Then $ a_{v,u}=0 $ , if there is no edge from $ v $ to $ u $ , and $ a_{v,u}=1 $ if there is one.
As the output graph has to be a tournament, following equalities must be satisfied:
- $ a_{v,u}+a_{u,v}=1 $ for each $ v,u $ $ (1