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 <cstdio>
#include <vector>

int n, m;
std::vector<std::vector<int> > G;
int dp[100000];

int longest(int x){
  if(dp[x]) return dp[x];
  int r = 0;
  for(int y: G[x]){
    r = std::max(r, 1 + longest(y));
  }
  return dp[x] = r;
}

int main(){
  scanf("%d%d", &n, &m);
  G.resize(n);
  for(int i = 0; i < m; i++){
    int a, b;
    scanf("%d%d", &a, &b);
    G[b-1].push_back(a-1);
  }

  int ans = 0;
  for(int i = 0; i < n; i++) ans = std::max(ans, longest(i));

  printf("%d\n", ans);

  return 0;
}