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 dp[100000] = {};
vector<int> edge[100000];

int calc(int tar){
  if(dp[tar] > 0) return dp[tar];
  for(int i: edge[tar]){
    dp[tar] = max(dp[tar], calc(i) + 1);
  }
  return dp[tar];
}

int main(){
  int n,m;
  cin >> n >> m;
  int x,y;
  for(int i=0;i<m;i++){
    cin >> x >> y;
    edge[--x].push_back(--y);
  }
  int mx = 0;
  for(int i=0;i<n;i++){
    calc(i);
    mx = max(mx, dp[i]);
  }
  cout << mx << endl;
}