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;
template <class T> ll size(const T &x) { return x.size(); }
#define rep(i,a,b) for(ll i = (a); i < (b); i++)
#define iter(it,c) for(auto it = (c).begin(); it != (c).end();++it)
#define pb push_back
#define fs first
#define sc second
typedef pair<ll,ll> ii;
typedef vector<ll> vi;
typedef vector<ii> vii;

const int INF = ~(1<<31);
const double pi = acos(-1);
const double EPS = 1e-9;

vi edg[100100];
int mem[100100];
int dp(int at){
    if(mem[at] != -1) return mem[at];
    int ans = 0;
    rep(i,0,edg[at].size()){
        ans = max(ans, 1+dp(edg[at][i]));
    }
    return mem[at] = ans;
}


int main()
{
    cin.sync_with_stdio(false);
    int n, m;
    cin >> n >> m;
    memset(mem,-1,sizeof(mem));
    rep(i,0,m){
        int a,b;
        cin >> a >> b;
        a--;b--;
        edg[a].pb(b);
    }
    int ans = -1;
    rep(i,0,n){
        ans = max(ans, dp(i));
    }
    cout << ans << endl;
    return 0;
}