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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
bool visited[100000]={false};
int dist[100000];
void dfs(int src,unordered_map<int,list<int> >&graph,int inDegree[])
{
    visited[src]=true;
    for(auto j:graph[src])
    {
        dist[j]=max(dist[j],dist[src]+1);
        inDegree[j]--;
        if(inDegree[j]==0) dfs(j,graph,inDegree);
    }
}
int main()
{
    int v,e,t1,t2,ans=0; cin>>v>>e;
    unordered_map<int,list<int> >graph;
    int inDegree[v+1]={0};
    for(int i=0;i<e;i++)
    {
        cin>>t1>>t2;
        graph[t1].push_back(t2);
        inDegree[t2]++;
    }
    for(int i=1;i<=v;i++)
    {
        if(!visited[i] and inDegree[i]==0)
        dfs(i,graph,inDegree);
    }
    for(int i=1;i<=v;i++)
    {
        ans=max(ans,dist[i]);
    }
    cout<<ans;
}