Problem

Figure 1. The graph from the dataset

The task is to use breadth-first search to compute single-source shortest distances in an unweighted directed graph.

Given: A simple directed graph with $n \le 10^3$ vertices in the edge list format.

Return: An array $D[1..n]$ where $D[i]$ is the length of a shortest path from the vertex $1$ to the vertex $i$ ($D[1]=0$). If $i$ is not reachable from $1$ set $D[i]$ to $-1$.

See Figure 1 for visual example from the sample dataset.

Sample Dataset

6 6
4 6
6 5
4 3
3 5
2 1
1 4

Sample Output

0 -1 2 1 3 2