Graph Relabeling

You are given a directed graph with N vertices. Assign each vertex i a distinct new number M_i from 1 through N.

For every directed edge from vertex u to vertex v, the numbering must satisfy M_u < M_v.

After assigning numbers, the result is the sequence M_1, M_2, ..., M_N. Output the lexicographically smallest sequence among all valid numberings.

The first line contains the number of vertices N.

Each of the next N lines contains an adjacency matrix row. A 0 means there is no edge, and a 1 means there is a directed edge from the row vertex to the column vertex.

N is a positive integer no greater than 50.

Print the sequence elements in order on one line, separated by spaces.

If no valid numbering exists, print -1. If multiple valid numberings exist, print the lexicographically smallest one.