Transitive closure

Write a program to compute the transitive closure of a directed graph with $n$ vertices. That is, you must compute an $n \times n$ 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 $x \ne y$ . Assume $1 \le n \le 200$ , 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 $m = \Theta(n^2)$ .

Problem information

Author: Unknown
Translator: Salvador Roura

Generation: 2026-01-25T10:23:45.083Z