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 ll long long
using namespace std;
const int M=1e5+10;
int n,m,ans;
int dp[M];
vector<int> G[M];
int dfs(int u)
{
    if(dp[u])
        return dp[u];
    int re=0;
    for(int v: G[u])
        re=max(re,dfs(v));
    return dp[u]=re+1;
}
int main()
{
    scanf("%d%d",&n,&m);
    for(int i=0,u,v;i<m;i++)
        scanf("%d%d",&u,&v),G[u].push_back(v);
    for(int i=1;i<=n;i++)
        ans=max(ans,dfs(i));
    printf("%d\n",ans-1);
    return 0;
}