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 JAVA):

Solution:
import java.util.*;

class Main {
    static List<Integer>[] graph;
    static int[] dp;

    public static int dfs(int pos) {
    	if(graph[pos].size() == 0) return 0;

    	if(dp[pos] == -1) {
    		for(int i = 0; i < graph[pos].size(); i++) {
    			dp[pos] = Math.max(dp[pos], dfs(graph[pos].get(i)) + 1);
    		}
    	}

    	return dp[pos];	
    }

    public static void main(String[] args) {
    	Scanner sc = new Scanner(System.in);

    	int n = sc.nextInt();
    	int m = sc.nextInt();

    	graph = new ArrayList[n+1];
    	for(int i = 0; i < n+1; i++)
    		graph[i] = new ArrayList<>();
    	for(int i = 0; i < m; i++) {
    		int x = sc.nextInt();
    		int y = sc.nextInt();
    		graph[x].add(y);
    	}
    	// System.out.println(Arrays.deepToString(graph));

    	dp = new int[n+1];
    	Arrays.fill(dp, -1);

    	int ans = 0;
    	for(int i = 1; i < n+1; i++) {
    		ans = Math.max(ans, dfs(i));
    	}

    	System.out.println(ans);
    }
}