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: Runtime Error)

#define _CRT_SECURE_NO_WARNINGS
#pragma comment(linker, "/stack:256000000")
#include<utility>
#include<iostream>
#include<vector>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
#include<ctime>
#include<functional>
#include<random>
#include<climits>
#include<queue>
#include<stack>
#include<deque>
#include<bitset>
#include<map>
#include<set>
#include<unordered_map>
#include<unordered_set>
#include<cassert>
#include<ccomplex>

//4Head
#define all(x) x.begin(), x.end()
#define mp make_pair
#define X first
#define Y second

using namespace std;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
mt19937_64 gen(time(NULL));

// belik's shit
ll const mod = 1e9 + 7;
namespace {
	ll mult(ll& a, ll& b) {
		ll val = a * b - (ll)((ld)a * b / mod) * mod;
		if (val < 0) {
			val += mod;
		}
		if (val >= mod) {
			val -= mod;
		}
		return val;
	}
	ll poww(ll a, ll b)
	{
		ll val = 1;
		a %= mod;
		while (b > 0){
			if (b % 2) val = mult(a, val);
			a = mult(a, a);
			b >>= 1;
		}
		return val % mod;
	}
	ll inv(ll a) {
		return poww(a, mod - 2);
	}
}

ll const maxn = 3e3 + 5;

vector<ll>g[maxn];
bool used[maxn];
vector<ll>topsort;
void dfs(ll u) {
	used[u] = 1;
	for (ll v : g[u]) {
		if (!used[v])dfs(v);
	}
	topsort.push_back(u);
}
ll num[maxn], dp[maxn];

signed main() {
	ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
	ll n, m; cin >> n >> m;
	for (ll i = 0; i < m; i++) {
		ll a, b; cin >> a >> b;
		g[a].push_back(b);
	}
	for (ll i = 1; i <= n; i++) {
		if (!used[i]) dfs(i);
	}
	reverse(all(topsort));
	for (ll i = 0; i < topsort.size(); i++) {
		num[topsort[i]] = i;
	}
	for (ll i = 0; i < topsort.size(); i++) {
		for (ll j : g[topsort[i]]) {
			dp[num[j]] = max(dp[i] + 1, dp[num[j]]);
		}
	}
	cout << *max_element(dp, dp + maxn);

	return 0;
}
/*

*/