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)

/*input
5 8
5 3
2 3
2 4
5 2
5 1
1 4
4 3
1 3
*/
#pragma comment(linker, "/stack:200000000")
#pragma GCC optimize ("Ofast")
#pragma GCC target ("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,tune=native")
#pragma GCC optimize ("unroll-loops")
#include<bits/stdc++.h>
using namespace std;
#define int long long
#define input(str) freopen(str,"r",stdin);
#define output(str) freopen(str,"w",stdout);
#define rep(i,n) for(int i=0;i<n;i++)
#define Rep(i,n) for(int i=1;i<=n;i++)
#define REP(i,a,n) for(int i=a;i<n;i++)
#define speed ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
#define INF  3e16+1
#define FF first
#define SS second
#define mp make_pair
#define pb push_back
#define sd(x) scanf("%d",&x)
#define slld(x) scanf("%lld\n",&x)
#define pd(x) printf("%d\n",x)
#define plld(x) printf("%lld\n",x)
#define modd 1000000007
#define len(x) x.size()
#define all(v) (v.begin(),v.end())
#define ll int
#define pi 3.1415926535897932384626
#define ld double
const int N =6e5+5;
typedef pair<int,int> pii;
typedef pair<pii,int> ppii;
int powmod(int base,int exp,int mod)
{
	int res=1LL;
	while(exp>0)
	{
		if(exp&1LL)
			res=(res*base)%mod;
		exp/=2LL;
		base=(base*base)%mod;
	}
	return res%mod;
}
vector<int> adj[N];
int dp[N];
int indeg[N];
bool visited[N];
void dfs(int node)
{
	if(visited[node])
		return ;
	visited[node]=true;
	int maxi=-1;
	for(auto it:adj[node])
	{
		if(!visited[it]);
		dfs(it);
		maxi=max(maxi,dp[it]);
	}
	dp[node]=maxi+1;
}
signed main()
{
	int n,m;
	cin>>n>>m;
	int x,y;
	rep(i,m)
	{
		cin>>x>>y;
		adj[x].pb(y);
		indeg[y]++;
	}
	int ans=0;
	Rep(i,n)
	{
		if(indeg[i]==0)
		{
			dfs(i);
		}
		ans=max(ans,dp[i]);
	}
	cout<<ans<<endl;

	return 0;
}