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)

#include<bits/stdc++.h>
#define ll long long
#define ld long double
#define mk make_pair
#define fi first
#define se second
#define vll vector<ll>
#define pii pair<ll,ll>
#define vvll vector< vector<ll> >
#define pb push_back
#define inf 1e16
#define M 1000000007
#define all(v) (v).begin(),(v).end()
#define rep(i,a,b) for(ll i=a;i<b;++i)
#define IOS ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
using namespace std;
#define mx 1000010
ll dp[mx];
vvll v(mx);
ll f(vvll v,ll i){
	if(dp[i]!=-1)return dp[i];
	for(ll j=0;j<v[i].size();++j){
		dp[i]=max(dp[i],1+f(v,v[i][j]));
	}
	return dp[i];
}

int main(){
	IOS;
	ll n,m;cin>>n>>m;
	vector<pii>d;
	rep(i,0,n)d.pb({0,0});
	rep(i,0,m){
		ll x,y;cin>>x>>y;
		x--;y--;
		v[x].pb(y);
		d[x].fi+=1;d[y].se+=1;
	}
	rep(i,0,n){
		if(d[i].fi==0)dp[i]=0;
		else dp[i]=-1;
	}
	ll ans=-1;
	rep(i,0,n){
		if(d[i].fi!=0)ans=max(ans,f(v,i));
	}
	cout<<ans;
	return 0;
}