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;





int dp[100010];
vector<int> g[100010];
int dfs(int x){
    if( dp[x] != -1 ) return dp[x];

    int ans = 0;
    for(int i : g[x]){
        ans = max(ans, dfs(i) + 1);
    }
    return dp[x] = ans;
}

void solve(long long N, long long M, vector<long long> x, vector<long long> y){
    for(int i = 0 ; i < x.size() ; i++){
        g[x[i]-1].push_back(y[i]-1);
    }
    memset(dp, -1, sizeof(dp));
    int ans = 0;
    for(int i = 0 ; i < N ; i++)
        ans = max(ans, dfs(i));
    cout << ans << endl;

}

int main(){
    long long N;
    scanf("%lld",&N);
    long long M;
    scanf("%lld",&M);
    vector<long long> x(M);
    vector<long long> y(M);
    for(int i = 0 ; i < M ; i++){
        scanf("%lld",&x[i]);
        scanf("%lld",&y[i]);
    }
    solve(N, M, x, y);
    return 0;
}