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 long long
#define pb push_back
#define mp make_pair
const int N=100050;
int dp[N];
vector<int> G[N];
bool was[N];
int ans;
void DFS(int u)
{
was[u]=1;
for(int v:G[u])
{
if(!was[v])
DFS(v);
dp[u]=max(dp[u],dp[v]+1);
}
ans=max(ans,dp[u]);
}
int main()
{
int n,m,u,v;
scanf("%i %i",&n,&m);
for(int i=1;i<=m;i++)
scanf("%i %i",&u,&v),
G[u].pb(v);
for(int i=1;i<=n;i++)
if(!was[i])
DFS(i);
printf("%i",ans);
return 0;
}