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;

using ull = unsigned long long;
using ll = long long;
#define endl "\n"

#define REP(i, n) for (ll i = 0; i < n; i++)
#define REPR(i, n) for (ll i = n; i >= 0; i--)
#define FOR(i, m, n) for (ll i = m; i < n; i++)
#define pb push_back
#define fill(x, y) memset(x, y, sizeof(x))
#define even(x) (x) % 2 == 0
#define odd(x) (x) % 2 != 0
#define all(x) x.begin(), x.end()
#define pcnt __builtin_popcount
#define buli(x) __builtin_popcountll(x)
#define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end());
#define IN1(type, x) type x; cin >> x;
#define inll(x) ll x; cin >> x;
#define indo(x) double x; cin >> x;

// these functions return the position of result of Binary Search.
#define LB(s, t, x) (int) (lower_bound(s, t, x) - s)
#define UB(s, t, x) (int) (upper_bound(s, t, x) - s)

const ll MOD_CONST = (ll)(1e9 + 7);
const ll CFMOD = (ll)(998244353);
ll qp(ll a, ll b, int mo) { ll ans = 1; do { if (b & 1) ans = 1ll * ans * a % mo; a = 1ll * a * a % mo; } while (b >>= 1); return ans; }
ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
ll lcm(ll a, ll b) { ll temp = gcd(a, b); return temp ? (a / temp * b) : 0; }
int mDays[] = { 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31 };
int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
int dx8[] = { 1, -1, 0, 0, 1, 1, -1, -1 }, dy8[] = { 0, 0, -1, 1, -1, 1, -1, 1 };

template<typename F>
class
#if defined(__has_cpp_attribute) && __has_cpp_attribute(nodiscard)
[[nodiscard]]
#elif defined(__GNUC__) && __GNUC_PREREQ(3, 4)
__attribute__((warn_unused_result))
#endif  // defined(__has_cpp_attribute) && __has_cpp_attribute(nodiscard)
FixPoint : F
{
public:
  explicit constexpr FixPoint(F&& f) noexcept
    : F(std::forward<F>(f))
  {}

  template<typename... Args>
  constexpr decltype(auto)
  operator()(Args&&... args) const
  {
    return F::operator()(*this, std::forward<Args>(args)...);
  }
};  // class FixPoint
template<typename F>
static inline constexpr decltype(auto)
makeFixPoint(F&& f) noexcept {
  return FixPoint<F>{std::forward<F>(f)};
}

template <typename T>
vector<T> make_v(size_t a) { return vector<T>(a); }
template <typename T, typename... Ts>
auto make_v(size_t a, size_t b, Ts... ts) { return vector<decltype(make_v<T>(b, ts...))>(a, make_v<T>(b, ts...)); }
template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type
fill_v(T &t, const V &v) { t = v; }
template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type
fill_v(T &t, const V &v) { for (auto &e : t) fill_v(e, v); }

template <typename T>
vector<T> pows(int b, int n) { // vec{b^0, b^1, b^2, ...}
    vector<T> ret;
    T x = 1;
    while (ret.size() < n) {
        ret.push_back(x);
        x *= b;
    }
    return ret;
}
template <class T>
bool chmax(T &a, const T &b) { if (a < b) { a = b; return 1; } return 0; }
template <class T>
bool chmin(T &a, const T &b) { if (b < a) { a = b; return 1; } return 0; }

inline tuple<ll, ll> rotate45(tuple<ll, ll> point) { ll x = get<0>(point), y = get<1>(point); return tuple<ll, ll>(x + y, x - y); }
inline bool rangeCheck2D(int nx, int ny, int Width, int Height) { return nx >= 0 and nx < Width and ny >= 0 and ny < Height; }

template <typename T>
vector<T> INPA(ll n) {
	vector<T> x;
	REP(i, n) {
		T tmp; cin >> tmp;
		x.push_back(tmp);
	}
	return move(x);
}
// base^x % MOD  - O(x)
ll p_base(ll base, ll x) {
	ll ans = 1;
	REP(i, x) {
		ans *= base;
		ans %= MOD_CONST;
	}
	return ans;
}
template <typename T>
void out(T o) { cout << o << endl; }
template <typename T>
void out(vector<T> &out) { REP(i, (int)out.size()) { cout << out[i]; if (i == (int)out.size() - 1) cout << endl; else cout << " "; } }
template <typename T>
void out(vector<vector<T>> o) { REP(i, o.size()) out(o[i]); }
void YesNo(bool f) { cout << (f?"Yes":"No") << endl; }
void YESNO(bool f) { cout << (f?"YES":"NO") << endl; }

class ListG {
public:
	// there's directed edge between A and B
	// if to[A] has element B
	vector<vector<int>> to; 

	map<pair<int, int>, ll> cost;
	void setCost(int u, int v, ll c) { 
		cost[{min(u, v), max(u, v)}] = c;
	}
	ll getCost(int u, int v) {
		return cost[{min(u, v), max(u, v)}];
	}

	ListG(int s) : root(-1) {
		size = s;
		to = make_v<vector<int>>(size);
	}

	void setDirectedEdge(int f, int t) {
		to[f].push_back(t);
	}
	void setIndirectedEdge(int v1, int v2) {
		setDirectedEdge(v1, v2);
		setDirectedEdge(v2, v1);
	}

	ll dfs(int current) {
		// do something
	}

	void makeTree(int r) {
		root = r;
		p = make_v<int>(size);
		p[root] = -1;
		depth = make_v<int>(size);
		mtdfs(root, 0);
		// count leaf node
		auto idxs = make_v<int>(size);
		iota(all(idxs), 0);
		leaf_idx = set<int>(all(idxs));
		REP(i, size) {
			if (i == root) continue;
			leaf_idx.erase(p[i]);
		}
	}

	void makeEulerTour() {
		assert(root >= 0);
		et_begin = make_v<int>(size);
		et_end = make_v<int>(size);
		tmp_k = 0;
		etdfs(root, -1);
	}

	vector<vector<int>> children() {
		assert(root >= 0);
		auto ret = make_v<vector<int>>(size);
		REP(i, size) {
			int prt = p[i];
			if (prt == -1) continue;
			ret[prt].push_back(i);
		}
		return ret;
	}

	int stronglyConnectedConponent() {
		auto rto = make_v<vector<int>>(size);
		REP(from, size) {
			for (auto&& t : to[from])
				rto[t].push_back(from);
		}
		auto cmp = make_v<int>(size);
		fill_v(cmp, 0);
		auto used = make_v<char>(size);
		fill_v(used, 0);
		vector<int> rets; // return index in order
		REP(i, size) {
			if (not used[i]) {
				makeFixPoint([&](auto dfs, int v) -> void {
					used[v] = 1;
					for (auto&& t : to[v]) {
						if (not used[t])
							dfs(t);
					}
					rets.push_back(v);
				})(i);
			}
		}
		fill_v(used, 0);
		int ret = 0;
		REPR(i, rets.size()-1) {
			if (not used[i]) {
				makeFixPoint([&](auto rdfs, int v, int k) -> void {
					used[v] = 1;
					cmp[v] = k;
					for (auto&& rt : rto[v]) {
						if (not used[rt])
							rdfs(rt, k);
					}
					rets.push_back(v);
				})(rets[i], ret++);
			}
		}
		return ret;
	}

	vector<int> topologicalSorted() {
		vector<int> ret;
		auto used = make_v<char>(size);
		fill_v(used, 0);
		REP(i, size) {
			makeFixPoint([&](auto dfs, int v) -> void {
				if (used[v]) return;
				used[v] = 1;
				for (auto&& t : to[v]) 
					dfs(t);
				ret.push_back(v);
			})(i);
		}
		reverse(all(ret));
		return ret;
	}

	int size, root;
	vector<int> p; // parent for each node. parent of root = -1
	vector<int> depth; // for each node. depth of root node = 0
	vector<int> euler_tour;
	vector<int> et_begin, et_end;
	set<int> leaf_idx;

	int tmp_k;
private:	
	void mtdfs(int c, int d) {
		depth[c] = d;
		REP(i, to[c].size()) {
			int next = to[c][i];
			if (p[c] == next) continue;
			p[next] = c;
			mtdfs(next, d + 1);
		}
	}
	void etdfs(int vidx, int pidx) {
		et_begin[vidx] = tmp_k;
		euler_tour.push_back(vidx);
		tmp_k++;
		REP(i, to[vidx].size()) {
			if (to[vidx][i] != pidx) {
				etdfs(to[vidx][i], vidx);
				euler_tour.push_back(vidx);
				tmp_k++;
			}
		}
		et_end[vidx] = tmp_k;
	}
};

// use " for (const auto& e : V)

// lambda expression
// auto f = [](int arg1, double arg2) { return ret; };
// lambda recursion
// auto result = makeFixPoint([&](auto rec, int pos, int v) -> int {
//	   rec(pos, v);
// })(0, 1);

// tuple binding
// auto t = make_tuple(0, 0);
// int x, y; tie(x, y) = t;

// bitset<N> bs(ini_val); // N must be constant
// bs.reset(); // reset all

int main(void)
{
    cin.tie(0); ios::sync_with_stdio(0); cout << fixed << setprecision(20);

	inll(N); inll(M);
	ListG lg(N);
	REP(i, M) {
		int f, t; cin >> f >> t;
		lg.setDirectedEdge(f-1, t-1);
	}


	auto ts = lg.topologicalSorted();
	reverse(all(ts));
	vector<int> dp(N, 0);
	int ans = 0;
	for(int i: ts){
		for(int u : lg.to[i]){
			chmax(dp[i], dp[u] + 1);
		}
		ans = max(ans, dp[i]);
	}
	out(ans);

	return 0;
}