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;

int N, M, a, b, ans;
vector<int> V[100100];
int dp[100100];

int f(int a) {
	if (V[a].size() == 0) return 0;
	if (dp[a] != -1) return dp[a];
	dp[a] = 0;
	for(int i=0; i<V[a].size(); i++) {
		int b = V[a][i];
		dp[a] = max(dp[a], f(b)+1);
	}
	return dp[a];
}

int main() {
	cin >> N >> M;
	for(int i=0; i<M; i++) {
		cin >> a >> b;
		V[a].push_back(b);
	}
	memset(dp, -1, sizeof(dp));
	for(int i=1; i<=N; i++) {
		ans = max(ans, f(i));
	}
	cout << ans << endl;
	return 0;
}