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: Time Limit Exceeded)

'use strict';
(function(input){
  input=input.trim().split(/\n/).map(str=>str.split(/\s+/).map(x=>x-0));
  const N=input[0][0];
  const M=input[0][1];
  input.shift();
  
  const Node=function(idx){
    var t=this;
    t.index=idx;
    t.children=[];
    t.scanned=false;
    t.height=0;
  }
    
  const nodes=new Array(N+1).fill(0).map((x,i)=>new Node(i));
  //console.log(nodes);
  input.forEach(function(xy){
    var p=xy[0],c=xy[1];
    nodes[p].children.push(nodes[c]);
  });
  //console.log(nodes);
  var ans=0;
  var i=1;
  while(i<=N){
    if(nodes[i].scanned){
      ans=Math.max(ans,nodes[i].height);
      i++;
      continue;
    }
    let I=i;
    while(nodes[I].children.length>0){
      if(nodes[I].children[nodes[I].children.length-1].scanned){
        nodes[I].height=Math.max(nodes[I].height,nodes[I].children.pop().height+1);
      }else{
        I=nodes[I].children[nodes[I].children.length-1].index;
      }
    }
    nodes[I].scanned=true;
  }
  //console.log(nodes);
  console.log(ans);
})(require('fs').readFileSync('/dev/stdin','utf8'));