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: Accepted)

    #include<bits/stdc++.h>
    using namespace std;
    long long n,m,x,y,a[100005],ans,dp[100005];
    vector<long long>v[100005];
    long long dfs(long long i)
    {
        if(dp[i]!=-1)
        return dp[i];
        for(int j=0;j<v[i].size();j++)
            dp[i]=max(dp[i],dfs(v[i][j])+1);
        return dp[i];
    }
    int main()
    {
        cin>>n>>m;
        for(int i=0;i<=n;i++)
        dp[i]=-1;
        for(int i=0;i<m;i++)
        {
            cin>>x>>y;
            x--;
            y--;
            v[x].push_back(y);
            a[y]=1;
        }
        for(int i=0;i<n;i++)
        {
            if(a[i]==0)
            ans=max(ans,dfs(i)+1);
        }
        cout<<ans;
        return 0;
    }