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;
ll n,m,x,y;
vector<ll>v[100009];
ll dp[100009];

ll f(ll N){
	if (v[N].empty())return 0;
	if(dp[N]!=-1)return dp[N];
	ll z=0;
	for(int i=0; i<v[N].size(); i++){
		z=max(z,f(v[N][i])+1);
	}
	dp[N]=z;
	return dp[N];
}

int main(){
	cin >> n >> m;
	memset(dp,-1,sizeof dp);
	for(int i=1; i<=m; i++){
		cin >> x >> y;
		v[x].push_back(y);
	}
	ll jwb=0;
	for(int i=1; i<=n; i++){
		jwb=max(jwb,f(i));
	}
	cout << jwb << endl;
}