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;
#define ll int
const ll N = 1e5 + 5;
vector<ll> a[N];
ll n, m, u, v, ans[N];
ll dfs(ll x)
{
    if (ans[x])
        return ans[x];
    for (ll e : a[x])
        ans[x] = max(ans[x], dfs(e) + 1);
    return ans[x];
}
int main()
{
    ios::sync_with_stdio(0), cin.tie(0);
    cin >> n >> m;
    while (m--)
        cin >> u >> v, a[u].push_back(v);
    for (ll i = 1; i <= n; i++)
        dfs(i);
    cout << *max_element(ans + 1, ans + n + 1);
}