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;
#define sz 100100
int val[sz];
vector<int>adj[sz];
int ret(int a)
{
    if (val[a] != -1)  return val[a];
    int &mx = val[a];
    for (auto it : adj[a])
        mx = max(mx, 1 + ret(it));
    return mx;
}
int main()
{
    int n, m, a, b, mx;
    scanf("%d", &n); scanf("%d", &m);
    for (int i = 0; i < m; ++i)
    {
        scanf("%d", &a);
        scanf("%d", &b);
        adj[a].push_back(b);
        val[a] = -1;
    }
    mx = 0;
    for (int i = 1; i <= n; ++i)
    {
        mx = max(mx, ret(i));
    }
    cout << mx;
    return 0;
}