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<vector<int> > v(100010);
int dp[100010];

int solver(int i){
	if(dp[i] != -1) return dp[i];
	int res = 0;
	for(auto next: v[i]) {
		res = max(res, solver(next) + 1);
	}
	return dp[i] = res;
}

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