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[100005];
int dp[100005];

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

int main() {
	int n, m;
	scanf("%d %d", &n, &m);
	for (int i = 0; i < m; i++) {
		int x, y;
		scanf("%d %d", &x, &y);
		adj[x].push_back(y);
	}
	int ans = 0;
	for (int i = 1; i <= n; i++) {
		solve(i);
		ans = max(ans, dp[i]);
	}
	printf("%d", ans - 1);
}