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)

//Bismillahir rahmanir rahim
#include<bits/stdc++.h>
using namespace std;
#define ll long long
vector<int>g[100005];
int dp[100005];
int solve(int n)
{
    int &ret=dp[n];
    if(ret!=-1) return ret;
    ret=0;
    for(int i=0;i<g[n].size();i++){
        int v=g[n][i];
        ret=max(ret,solve(v)+1);
    }
    return ret;
}
int main()
{
    int n,m;
    scanf("%d %d",&n,&m);
    for(int i=0;i<m;i++){
        int u,v;
        scanf("%d %d",&u,&v);
        g[u].push_back(v);
    }
    int ans=0;
    memset(dp,-1,sizeof(dp));
    for(int i=1;i<=n;i++) ans=max(ans,solve(i));
    printf("%d\n",ans);
    return 0;
}