Problem:
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Breadth First Search

Write a program which reads an directed graph $G = (V, E)$, and finds the shortest distance from vertex $1$ to each vertex (the number of edges in the shortest path). Vertices are identified by IDs $1, 2, ... n$.

Input

In the first line, an integer $n$ denoting the number of vertices, is given. In the next $n$ lines, adjacent lists of vertex $u$ are given in the following format:

$u$ $k$ $v_1$ $v_2$ ... $v_k$

$u$ is ID of the vertex and $k$ denotes its degree.$v_i$ are IDs of vertices adjacent to $u$.

Constraints

$1 \leq n \leq 100$

Output

For each vertex $u$, print $id$ and $d$ in a line. $id$ is ID of vertex $u$ and $d$ is the distance from vertex $1$ to vertex $u$. If there are no path from vertex $1$ to vertex $u$, print -1 as the shortest distance. Print in order of IDs.

Sample Input 1

4
1 2 2 4
2 1 4
3 0
4 1 3

Sample Output 1

1 0
2 1
3 2
4 1

Reference

Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press.

Solution in JavaScript (judge verdict: Accepted)

(function main() {
  const lines = require('fs').readFileSync('/dev/stdin', 'utf8').trim().split('\n');
  const n = Number(lines.shift());
  const adjLists = Array.from(Array(n), () => []);
  const d = [];
  lines.forEach((l, i) => l.split(' ').splice(2).forEach(e => adjLists[i].push(e-1)));
  bfs(adjLists, d);
  for (let i = 0; i < n; i++) {
    console.log(i + 1, d[i]);
  }
})();

function bfs(adjLists, d) {
  const WHITE = 0, GRAY = 1, BLACK = 2;
  const color = Array.from(adjLists, () => WHITE);
  d[0] = 0;
  for (let i = 1; i < adjLists.length; i++) d[i] = -1;
  queue = [0];
  let u;
  while ((u = queue.shift()) !== undefined) {
    adjLists[u].forEach(v => {
      if (color[v] === WHITE) {
        color[v] = GRAY;
        d[v] = d[u] + 1;
        queue.push(v);
      }
    });
    color[u] = BLACK;
  }
}