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: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;
#define int long long
int dp[100002]={0};
vector<int> v[100002];
void solve(int i)
{
    //dp[i]=0;
    for(int j=0; j<v[i].size(); j++)
    {
        if(dp[i]+1>dp[v[i][j]])
        {
            dp[v[i][j]] = dp[i]+1;
            solve(v[i][j]);
        }
    }
}
int32_t main()
{
        int n,m;
        cin>>n>>m;
        int arr[n+1]={0};
        //vector<int> v[n];
        for(int i=0; i<m; i++)
        {
            int a,b;
            cin>>a>>b;
            arr[b]++;
            v[a].push_back(b);
        }
        //int dp[n]={0};
        for(int i=1; i<=n; i++)
        {
            if(arr[i]==0)
            {
                //cout<<i<<endl;
                solve(i);
            }
        }
        int ans=0;
        for(int i=1; i<=n; i++)
        {
            ans=max(ans,dp[i]);
        }
        cout<<ans;
        return 0;
}