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;
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<int64_t,int64_t> pll;
typedef vector<int64_t> vl;
int dx[]={1,-1,0,0,1,-1,1,-1};
int dy[]={0,0,1,-1,1,-1,-1,1};
const long double PI = acos(-1);
#define INF (2147483647)
#define mod (1000000007)
#define limit (7368791)
#define rep(i,a,b) for (int64_t i = (a); i < (b); i++)
#define REP(i,n) rep(i,0,n)
#define sz(s) (s).size()
#define ALL(a) begin(a),end(a)
#define mp make_pair
#define pb push_back
#define eb emplace_back
#define fi first
#define se second

vector<int>G[100010];
vector<int>dp(100010,0);
int r(){int x;cin>>x;return x;}
int dfs(int v){
    int &count=dp[v];
    if(count)return count;
    for(auto it:G[v])count=max(count,dfs(it)+1);
    return count;
}

void solve() 
{
    int n,m,ans=0;cin>>n>>m;
    REP(i,m)G[r()-1].pb(r()-1);
    REP(i,n)ans=max(ans,dfs(i));
    cout<<ans<<endl;
}
int main()
{
    cin.tie(0);
	ios::sync_with_stdio(false);
    solve();
    return 0;
}