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;

vector < int > adj[100007];

int used[100007], dp[100007], mx;

void dfs( int v ) {
	if ( used[v] ) return;
	used[v] = 1;
	for ( auto u: adj[v] ) {
		dfs(u);
		dp[v] = max( dp[v], dp[u] + 1 );
	}
}

int main() {
	int n, m;
	cin >> n >> m;
	for ( int i = 0; i < m; i++ ) {
		int u, v;
		cin >> u >> v;
		adj[u].push_back(v);
	}
	for ( int i = 1; i <= n; i++ ) {
		dfs(i);
		mx = max( mx, dp[i] );
	}
	cout << mx << endl;
}