Problem: 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.

Examples

Input

4 5
1 2
1 3
3 2
2 4
3 4


Output

3


Input

6 3
2 3
4 5
5 6


Output

2


Input

5 8
5 3
2 3
2 4
5 2
5 1
1 4
4 3
1 3


Output

3

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;

int N, M;
vector<int> G[100100];

int dp[100100];
int rec(int v){
    if(dp[v]!=-1) return dp[v];
    int res=0;
    for(auto nv :G[v]){
        res = max(res, rec(nv)+1);
    }
    return dp[v]=res;
}

int main(){
    cin >> N >> M;
    for(int i=0; i<M; i++){
        int x, y; cin >> x >> y;
        G[x].push_back(y);
    }
    for(int i=1; i<=N; i++) dp[i]=-1;
    int res=0;
    for(int i=1; i<=N; i++) res = max(res,rec(i) );
    cout << res << endl;
}