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;
vector<int> g[1<<17];
int dp[1<<17] = {0};
int dfs(int u) {
  if (dp[u]) return dp[u];
  for (int v : g[u]) dp[u] = max(dfs(v) + 1, dp[u]);
  return dp[u];
}
int main() {
  ios_base::sync_with_stdio(false); cin.tie(0);
  int n, m; cin >> n >> m;
  for (int i = 0; i < m; ++i) {
    int u, v; cin >> u >> v;
    --u, --v;
    g[u].push_back(v);
  }
  int ans = 0;
  for (int i = 0; i < n; ++i) ans = max(dfs(i), ans);
  cout << ans << '\n';
}