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;

const int N = 1e5 + 1;

int n, m, dp[ N ], vis[ N ];
vector<int> g[ N ];

int dfs(int u) {
    vis[ u ] = 1;
    for(int v : g[ u ]) {
        if( !vis[ v ] )
            dfs(v);
        dp[ u ] = max(dp[ u ], 1 + dp[ v ]);
    }
    return dp[ u ];
}

int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);

    cin >> n >> m;
    while( m-- ) {
        int u, v;
        cin >> u >> v;
        g[ u ].push_back(v);
    }
    for(int i = 0; i <= n; i += 1) dp[ i ] = 0, vis[ i ] = 0;
    int ans = 0;
    for(int i = 1; i <= n; i += 1) {
        if( !vis[ i ] ) {
            ans = max(ans, dfs(i));
        }
    }
    cout << ans << '\n';
    return 0;
}