Transitive closure P19374

Write a program to compute the transitive closure of a directed graph with n vertices. That is, you must compute an n × n matrix where at the j-th column of the i-th row there is a 1 if it is possible to go from i to j, and there is a 0 otherwise.

Input

Input consists of several cases. Every case begins with n followed by the number of arcs m. Follow m pairs x y to indicate an arc from x to y, with x ≠ y. Assume 1 ≤ n ≤ 200, that the vertices are numbered between 0 and n − 1, and that there are no repeated arcs.

Output

For every graph, print its transitive closure, followed by a line with 20 dashes.

Observation

In the “large” private test cases, we have m = Θ(n²).