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<vector>
#include<cstdio>
#include<algorithm>
using namespace std;

vector<int> adj[100005];
int vis[100005], dp[100005];

void dfs( int u ) {
	vis[u] = 1;
	for( int v : adj[u] )
	{
		if( vis[v] == 0 )
			dfs(v);
		dp[u] = max(dp[u], 1+dp[v]);
	}
}

int main() {
	int n, m;
	scanf("%d%d", &n, &m);
	for( int i=0, u, v; i<m; ++i )
		scanf("%d%d", &u, &v), adj[u].push_back(v);
	int ans = -1;
	for( int i=1; i<=n; ++i ) {
		if( vis[i] == 0 )
			dfs(i);
		ans = max(ans, dp[i]);
	}
	printf("%d\n", ans);
}