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;
#define int long long

int N,M;
vector<int> radjlist[100000];
int d[100000];

int rec(int v) {
  if(d[v]!=-1) return d[v];
  int dv = 0;
  for(auto from : radjlist[v]) dv = max(dv, rec(from)+1);
  return d[v] = dv;
}

signed main() {
  cin >> N >> M;
  for(int i=0; i<M; i++) {
    int x,y;
    cin >> x >> y;
    radjlist[y-1].push_back(x-1);
  }
  fill(d, d+N, -1);
  int ans = 0;
  for(int i=0; i<N; i++) ans = max(ans, rec(i));
  cout << ans << endl;
}