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
#define fop(i,m,n) for(ll i=m;i<n;i++)
using namespace std;
vector <ll> g[100005];
ll dp[100005];
ll dfs(ll u){
	if(dp[u] != -1) return dp[u];
	dp[u] = 0;
	fop(i,0,g[u].size()){
		dp[u] = max(dfs(g[u][i]) + 1, dp[u]);
	}
	return dp[u];
}
int main(){
	ll n, m;
	cin >> n >> m;
	fop(i,0,m){
		ll x, y;
		cin >> x >> y;
		g[x].push_back(y);
	}
	memset(dp,-1,sizeof(dp));
	ll ans = 0;
	fop(i,1,n+1){
		ans = max(ans,dfs(i));
	}
	cout << ans;
}