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 dump(x) cout << (x) << '\n'
#define Int int64_t
#define fi first
#define se second
#define all(x) (x).begin(), (x).end()
 
Int INF = 1e18;
int inf = 1e9;
Int mod = 1e9+7;

vector<Int> G[100001];
bool rev[100001];
Int memo[100001];

Int rec(Int x) {
    if (memo[x] >= 0) {
        return memo[x];
    }
    Int ret = 0;
    for (Int i = 0; i < (Int)G[x].size(); i++) {
        Int to = G[x][i];
        ret = max(ret, rec(to) + 1);
    }
    return memo[x] = ret;
}

int main() {
    Int n, m;
    cin >> n >> m;
    vector<Int> x(m), y(m);
    for (Int i = 0; i < m; i++) {
        cin >> x[i] >> y[i];
        x[i]--, y[i]--;
        G[x[i]].push_back(y[i]);
        rev[y[i]] = true;
    }
    fill(memo, memo + n, -1);
    for (Int i = 0; i < n; i++) {
        if (rev[i]) continue;
        rec(i);
    }
    Int res = 0;
    for (Int i = 0; i < n; i++) {
        res = max(res, memo[i]);
    }
    dump(res);
    return 0;
}