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[100010];
int dp[100010];

int dfs(int v)
{
    int& res=dp[v];
    if (~res) return res;

    res=0;
    for(int u: G[v]) res=max(res, dfs(u)+1);
    return res;
}

int main()
{
    int n, m; cin>>n>>m;
    for(int i=0; i<m; ++i) {
        int x, y; cin>>x>>y;
        G[x-1].push_back(y-1);
    }
    fill(dp, dp+n, -1);

    for(int i=0; i<n; ++i) if (dp[i]<0) dfs(i);
    cout<<*max_element(dp, dp+n)<<endl;
}