B"A football league has recently begun in Beautiful land. There are n teams participating in the league. Let's enumerate them with integers from 1 to n . There will be played exactly frac{n(n-1)}{2} matches: each team will play against all other teams exactly once. In each match, there is always a winner and loser and there is no draw. After all matches are played, the organizers will count the number of beautiful triples. Let's call a triple of three teams (A, B, C) beautiful if a team A win against a team B , a team B win against a team C and a team C win against a team A . We look only to a triples of different teams and the order of teams in the triple is important. The beauty of the league is the number of beautiful triples. At the moment, m matches were played and their results are known. What is the maximum beauty of the league that can be, after playing all remaining matches? Also find a possible results for all remaining frac{n(n-1)}{2} - m matches, so that the league has this maximum beauty. The first line contains two integers n, m ( 3 <= q n <= q 50, 0 <= q m <= q frac{n(n-1)}{2} ) -- the number of teams in the football league and the number of matches that were played. Each of m following lines contains two integers u and v ( 1 <= q u, v <= q n , u neq v ) denoting that the u -th team won against the v -th team. It is guaranteed that each unordered pair of teams appears at most once. Print n lines, each line having a string of exactly n characters. Each character must be either 0 or 1 . Let a_{ij} be the j -th number in the i -th line. For all 1 <= q i <= q n it should be true, that a_{ii} = 0 . For all pairs of teams i neq j the number a_{ij} indicates the result of the match between the i -th team and the j -th team: Also note that the results of"...