Problem:
Score : 100 points

Problem Statement

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.

Sample Input 1

4 5
1 2
1 3
3 2
2 4
3 4

Sample Output 1

3

The red directed path in the following figure is the longest:

Sample Input 2

6 3
2 3
4 5
5 6

Sample Output 2

2

The red directed path in the following figure is the longest:

Sample Input 3

5 8
5 3
2 3
2 4
5 2
5 1
1 4
4 3
1 3

Sample Output 3

3

The red directed path in the following figure is one of the longest:

Solution in Go (1.6) (judge verdict: Accepted)

package main

import "fmt"

func max(x, y int) int {
	if x > y {
		return x
	}
	return y
}

var memo []int
var list [][]int

func f(i int) int {
	if memo[i] != -1 {
		return memo[i]
	}
	for _, j := range list[i] {
		memo[i] = max(memo[i], f(j)+1)
	}
	return memo[i]
}

func main() {
	var v, e int
	fmt.Scan(&v, &e)

	list = make([][]int, v+1)
	var x, y int
	for i := 0; i < e; i++ {
		fmt.Scan(&x, &y)
		list[x] = append(list[x], y)
	}

	memo = make([]int, v+1)
	for i := 1; i < v+1; i++ {
		memo[i] = -1
		if len(list[i]) == 0 {
			memo[i] = 0
		}
	}

	var result int
	for i := 1; i < v+1; i++ {
		result = max(result, f(i))
	}
	fmt.Println(result)
}