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>
#define fi first
#define se second
#define mp make_pair
#define pb push_back
using namespace std;

typedef pair <int, int> pii;
typedef long long ll;

const int inf = 1e9 + 1;
const double eps = 1e-9;
const int MAXN = 1e5 + 1;

int n, m;
vector <int> v[MAXN];
int dp[MAXN];
int sol;

int rek(int cvor){

    if (dp[cvor] != -1) return dp[cvor];

    for (int i = 0; i < v[cvor].size(); i++){
        dp[cvor] = max(dp[cvor], rek(v[cvor][i])+1);
    }

    if (dp[cvor] == -1) dp[cvor] = 0;

    return dp[cvor];

}

int main(){

    cin >> n >> m;
    for (int i = 0; i < m; i++){
        int x, y;
        cin >> x >> y;
        x--; y--;
        v[x].pb(y);
    }
    for (int i = 0; i < n; i++) dp[i] = -1;

    for (int i = 0; i < n; i++){
        if (dp[i] == -1) rek(i);
        sol = max(sol, dp[i]);
    }

    cout << sol;

    return 0;

}