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>
#define ll long long

using namespace std;

ll Rec(ll i);

vector <ll> Edges[100100];

ll Dp[100100];

int main()
{
    memset(Dp,-1,sizeof(Dp));

    ll n,m; cin>>n>>m;

    while(m--)
    {
        ll x,y; scanf("%I64d%I64d",&x,&y);

        Edges[x].push_back(y);
    }

    ll Max = 0;

    for(ll i=1;i<=n;i++)    Max = max( Max , Rec(i) );

    cout<<Max;
}

ll Rec(ll i)
{
    if(Dp[i]+1) return Dp[i];

    ll Res = 0;

    for(ll j=0;j<Edges[i].size();j++)   Res = max( Res , 1 + Rec(Edges[i][j]) );

    return Dp[i] = Res;
}