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 <fstream>
#include <cstdio>
#include <cmath>
#include <vector>
#include <string>
#include <set>
#include <map>
#include <stack>
#include <queue>
#include <deque>
#include <bitset>
#include <algorithm>
#include <complex>
#include <array>
using namespace std;

#define REP(i,n) for(int i=0; i<n; ++i)
#define FOR(i,a,b) for(int i=a; i<=b; ++i)
#define FORR(i,a,b) for (int i=a; i>=b; --i)
#define ALL(c) (c).begin(), (c).end()

typedef long long ll;
typedef vector<int> VI;
typedef vector<ll> VL;
typedef vector<long double> VD;
typedef vector<VI> VVI;
typedef vector<VL> VVL;
typedef vector<VD> VVD;
typedef pair<int,int> P;
typedef pair<ll,ll> PL;

template<typename T> void chmin(T &a, T b) { if (a > b) a = b; }
template<typename T> void chmax(T &a, T b) { if (a < b) a = b; }

int in() { int x; scanf("%d", &x); return x; }
ll lin() { ll x; scanf("%lld", &x); return x; }
#define INF 1LL<<60

int main() {
    int N, M;
    cin >> N >> M;
    vector<int> x(M), y(M);
    set<int> sx, sy;
    map<int, vector<int>> g;
    for(int i=0 ; i<M; i++) {
        int tmp1, tmp2;
        cin >> tmp1 >> tmp2;
        x[i] = tmp1 - 1;
        y[i] = tmp2 - 1;
        g[x[i]].push_back(y[i]);
        sx.insert(tmp1-1);
        sy.insert(tmp2-1);
    }

    set<int> sources;
    set_difference(sx.begin(), sx.end(), sy.begin(), sy.end(), inserter(sources, sources.end()));

    vector<int> dp(N, 0);
    queue<int> v_queue;

    int ans = 0;
    for(auto s: sources) {
        dp[s] = 0;
        v_queue.push(s);
        while(!v_queue.empty()) {
            int from = v_queue.front();
            v_queue.pop();
            if(!g[from].empty()) {
                for(auto v: g[from]){
                    if(dp[v] < dp[from]+1) {
                        v_queue.push(v);
                        dp[v] = dp[from]+1;
                        if(ans < dp[from]+1) ans = dp[from] + 1;
                    }
                }
            }
        }
    }

    cout << ans << endl;
    return 0;
}