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 + 50;

int n, m;
int dp[N];
vector<int> graph[N];
int a, b;
int in[N];

int solve(int node) {
    int& ret = dp[node];

    if(ret != -1)
        return ret;

    for(auto neigh : graph[node])
        ret = max(ret, solve(neigh) + 1);

    return ret;
}

void precomp() {
    for(int i = 0; i < n; ++i)
        if(graph[i].empty())
            dp[i] = 0;
}

void load() {
    scanf("%d%d", &n, &m);

    for(int i = 0; i < m; ++i) {
        scanf("%d%d", &a, &b);
        --a, --b;

        graph[a].push_back(b);
        //in[b]++;
    }

    precomp();

    for(int i = 0; i < n; ++i)
        if(dp[i] == -1)
            solve(i);

    printf("%d\n", *max_element(dp, dp + n));
}

int main() {
    memset(dp, -1, sizeof dp);

    load();
}