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 = 1e5 + 10;

vector<int> graf[N];
int dp[N], n, m;

int dfs(int u) {
  if (dp[u]) 
    return dp[u];
  for(int v : graf[u]) 
    dp[u] = max(dp[u], dfs(v));
  dp[u]++;
  return dp[u];
}

int main() {
  cin >> n >> m;
  while (m--) {
    int u, v;
    cin >> u >> v;
    graf[u-1].push_back(v-1);
  }
  
  int ret = -1;
  for (int i = 0; i < n; i++) {
    ret = max(dfs(i), ret);
  }
  
  cout << ret-1 << endl;
}