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;
const int maxn = 100100;
vector<int> e[maxn];
int f[maxn];
int solve(int x){
  if(f[x] != -1) return f[x];
  int ans = 0;
  for(int v : e[x]) ans = max(ans, 1 + solve(v));
  return f[x] = ans;
}
int main(){
  int n, m; cin >> n >> m;
  for(int i = 0; i < m; i++) {
    int x, y; cin >> x >> y;
    e[x].push_back(y);
  }
  int ans = 0;
  memset(f, -1, sizeof(f));
  for(int i = 1; i <= n; i++) ans = max(ans, solve(i));
  cout << ans << endl;
  return 0;
}