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>

#define pb push_back

using namespace std;

int n, m, d[(int)1e5 + 7], ans;
vector<int>g[(int)1e5 + 7], w;

void dfs(int v){
    if(d[v]) return;
    d[v] = 1;
    for(auto to : g[v]){
        dfs(to);
        d[v] = max(d[v], d[to] + 1);
        ans = max(d[v], ans);
    }
}

int main(){
    cin >> n >> m;
    for(int i = 1; i <= m; i++){
        int x, y;
        cin >> x >> y;
        g[x].pb(y);
    }
    for(int i = 1; i <= n; i++)
        dfs(i);
    cout << ans - 1;
}