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;

static int N, M, visit[100000] = {}, DP[100000] = {}, ANS = 0;
static vector<int> V[100000];

int Next(int X) {
	if (visit[X] == 1) return DP[X];
	visit[X] = 1;
	int RET = 0;
	for (int Y : V[X]) {
		RET = max(RET, Next(Y) + 1);
	}
	return DP[X] = RET;
}

int main() {
	cin >> N >> M;
	for (int i = 0; i < M; i++) {
		int X, Y;
		cin >> X >> Y;
		X--, Y--;
		V[X].push_back(Y);
	}
	for (int i = 0; i < N; i++) ANS = max(ANS, Next(i));
	cout << ANS << endl;
}