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 pb push_back

//var 
int n,m,t1,t2,dp[100001],ans = 0;
vector<int> e[100001];
bool v[100001];

void dfs(int g){
	dp[g] = 1; int am = 0;
	v[g] = 1;
	for(int u : e[g]){
		if(!v[u])dfs(u);
		am = max(am,dp[u]);
	}dp[g] += am;
}

int main(){
	cin >> n >> m;
	for(int i = 1; i<=m; i++){
		cin >> t1 >> t2;
		e[t1].pb(t2);
	}

	for(int i = 1; i<=n; i++){
		if(!v[i])dfs(i); ans = max(ans,dp[i]);
	}cout << --ans << endl;
}