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 N=100010;
int n, m, dis[N];
vector<int> adj[N];


int dfs(int u){
  if(dis[u]!=-1)return dis[u];
  dis[u]=0;
  for(auto v:adj[u])dis[u]=max(dis[u], 1+dfs(v));
  return dis[u];
}
int main(){
  memset(dis, -1, sizeof dis);

  scanf("%d%d", &n, &m);

  for(int i=0;i<m;i++){
    int a,b;scanf("%d %d", &a, &b);
    a--;b--;
    adj[a].emplace_back(b);
  }
  int ans=0;
  for(int i=0;i<n;i++)
    ans=max(ans, dfs(i));
  printf("%d\n", ans);
}