Problem:
Score : 100 points

Problem Statement

There is a directed graph G with N vertices and M edges.
The vertices are numbered 1, 2, \ldots, N, and for each i (1 \leq i \leq M), the i-th directed edge goes from Vertex x_i to y_i.
G does not contain directed cycles.

Find the length of the longest directed path in G.
Here, the length of a directed path is the number of edges in it.

Constraints

All values in input are integers.

2 \leq N \leq 10^5

1 \leq M \leq 10^5

1 \leq x_i, y_i \leq N

All pairs (x_i, y_i) are distinct.

G does not contain directed cycles.

Input

Input is given from Standard Input in the following format:

N M
x_1 y_1
x_2 y_2
:
x_M y_M

Output

Print the length of the longest directed path in G.

Sample Input 1

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

Sample Output 1

3

The red directed path in the following figure is the longest:

Sample Input 2

6 3
2 3
4 5
5 6

Sample Output 2

2

The red directed path in the following figure is the longest:

Sample Input 3

5 8
5 3
2 3
2 4
5 2
5 1
1 4
4 3
1 3

Sample Output 3

3

The red directed path in the following figure is one of the longest:

Solution in JavaScript (node.js v5.12) (judge verdict: Wrong Answer)



function Main(input) {
  input = input.split("\n");
  var N = parseInt(input[0].split(" ")[0]);
  var M = parseInt(input[0].split(" ")[1]);
  var g = new Array(M);
  for(var i=0;i<M;i++){
    var tmp = input[i+1].split(" ");
    g[i]=[parseInt(tmp[0]),parseInt(tmp[1])];
  }
  var ans=0;
  var list=new Array([g[0][0],g[0][1],1]);
  for(var i=1;i<M;i++){
    var ll=list.length;
    for(var j=0;j<ll;j++){
      if(g[i][1]==list[j][0]&&g[i][0]!=list[j][1]){
        list.push([g[i][0],list[j][1],list[j][2]+1]);
        ans=Math.max(ans,list[j][2]+1);
      }else if(g[i][0]==list[j][1]&&g[i][1]!=list[j][0]){
        list.push([list[j][0],g[i][1],list[j][2]+1]);
        ans=Math.max(ans,list[j][2]+1);
      }else{
        list.push([g[i][0],g[i][1],1]);
      }
    }
  }

  console.log('%s', ans);
  return ans;
}
// "実行する"ボタンを押した時に実行される関数 (デバッグ用)
function debug(n){
  var input = document.getElementById("input"+n).value;
  var ans=Main(input);
  var result="WA";
  if(ans==document.getElementById("output"+n).value.split("\n")[0]){
    result="AC";
  }
  document.getElementById("result"+n).innerHTML=result;
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));