No hidden tricks here, read in an adjacency matrix for an unweighted but directed graph (no self-edges). Output the iterative DFS traversal order. Graphs are labelled from \(0\) to \(V\).

Input Specification

The first line contains a single integer \(V\), the number of vertices in the graph.

The next \(V\) lines will contain \(V\) space-separated integers specifying an adjacency matrix.

For any element \(v_{i,j}\), a \(0\) indicates no edge from \(u\) to \(v\), a \(1\) indicates there is an edge from \(u\) to \(v\).

Output Specification

A single line of space-separated integers, the labels of each vertex in the order they are discovered in the search.

Bounds

This problem has two sub-problems, the first is the test data, the second has the following bounds.

• \(1 \leq V \leq 2000\)
• \(v_{i,j} \in \{0,1\}\)

Sample Input 1

4
0 0 0 1 
0 0 0 0 
0 1 0 1 
1 0 0 0

Sample Output 1

0 3

Sample Input 2

4
0 0 0 1 
1 0 0 1 
0 0 0 0 
1 1 0 0

Sample Output 2

0 3 1