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) std::cout << (#x) << " = " << (x) << "\n"
#define rep(i, n) for (int i = 0; i < (int)(n); ++i)
#define REP(i, k, n) for (int i = (k); i < (int)(n); ++ i)
#define ALL(r) r.begin(), r.end()
#define YES puts("YES")
#define Yes puts("Yes")
#define NO puts("NO")
#define No puts("No")
#define IMP puts("IMPOSSIBLE")
#define Imp puts("Impossible")
#define pb push_back

template<typename T> T DUP(T x, T y) { return (x + y - 1) / y; };

using ll = int64_t;
using vint = vector<int32_t>;
using vvint = vector<vint>;
using vll = vector<ll>;
using vvll = vector<vll>;
using vstr = vector<string>;
using pint = pair<int32_t, int32_t>;
using setint = unordered_set<int32_t>;
using setstr = unordered_set<string>;
using qint = queue<int32_t>;

constexpr std::int32_t INF = 1001001001;

template <class T> inline bool chmax(T& a, T b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}
template <class T> inline bool chmin(T& a, T b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}

int n, m;
vvint G;
int dp[100005];
vint deg;   //各頂点の入次数

void Main() {
    cin >> n >> m;
    G.assign(n, vint());
    deg.assign(n, 0);
    rep(i, m) {
        int x, y; cin >> x >> y;
        --x, --y;
        G[x].pb(y);
        ++deg[y];
    }

    qint q;
    rep(v, n) {
        if (deg[v] == 0)q.push(v);
    }

    // BFS
    while (!q.empty()) {
        int v = q.front(); q.pop();
        for (const auto& nv : G[v]) {
            deg[nv]--;
            if (deg[nv] == 0) {
                q.push(nv);
                chmax(dp[nv], dp[v] + 1);
            }
        }
    }

    int res = 0;
    rep(i, n)chmax(res, dp[i]);
    cout << res << endl;
}

int main() {
    std::cin.tie(nullptr);
    std::ios_base::sync_with_stdio(false);
    std::cout << std::fixed << std::setprecision(15);
    Main();
    return 0;
}