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: Wrong Answer)

(function main() {
  const lines = require('fs').readFileSync('/dev/stdin', 'utf8').trim().split('\n');
  const n = Number(lines.shift());

  const adjLists = Array.from(Array(n), () => []);
  lines.forEach((l, i) => l.split(' ').splice(2).forEach(e => adjLists[i].push(e-1)));

  const d = [], f = [];
  dfs(adjLists, d, f);
  str = '';
  for (let i = 0; i < n; i++) {
    str += `${i + 1} ${d[i]} ${f[i]}\n`;
  }
  console.log(str);
})();

function dfs(adjLists, d, f) {
  const WHITE = 0, GRAY = 1, BLACK = 2;
  const size = adjLists.length;
  const color = Array.from(adjLists, () => WHITE);

  let time = 0;
  function visit(u) {
    color[u] = GRAY;
    d[u] = ++time;
    adjLists[u].forEach(v => {
      if (color[v] === WHITE) {
        visit(v);
      }
    });
    color[u] = BLACK;
    f[u] = ++time;
  }
  adjLists.forEach((e, u) => {
    if (color[u] === WHITE) visit(u);
  });
}