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 <iostream>
#include <vector>
#include <algorithm>
#include <cmath>
#include <queue>
#include <iomanip>
#include <map>
#include <set>
#include <tuple>
#include <unordered_map>
#include <iterator>
#include <string>
#include <limits>

using namespace std;

using i64 = int64_t;
using P = pair<i64, i64>;
//i64 mod = 1000000007;
//int int_max = 2147483647;
i64 INF = 1e12;
int max_n = 1e5;

struct edge {
    edge() : link_to(0), cost(0) {}
    edge(int t, int c) : link_to(t), cost(c) {}
    int link_to;
    int cost;
};

vector<int> memo(100010, -1);

int rec(vector<vector<edge>>&graph, int v) {
    if (memo[v] != -1) return memo[v];
    int ret{0};

    for (auto e : graph[v]) {
        ret = max(ret, rec(graph, e.link_to) + e.cost);
    }
    return ret;
}

int main(int argc, char **argv) {
    i64 n,m;
    cin >> n >> m;

    vector<vector<edge>> graph(n);

    for (int i=0; i<m; ++i) {
        int x, y;
        cin >> x >> y;
        --x; --y;
        graph[x].push_back(edge(y, 1));
    }

    int ans{0};
    for (int i=0; i<n; ++i) {
        ans = max(ans, rec(graph, i));
    }
    cout << ans << endl;
    return 0;
}