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 (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

var (
	dp []int
	g  [][]int
)

func rec(now int) int {
	if dp[now] != -1 {
		return dp[now]
	}

	ret := 0
	for _, next := range g[now] {
		ret = max(ret, rec(next)+1)
	}

	dp[now] = ret
	return ret
}

func solve() {
	n, m := getInt(), getInt()

	dp = make([]int, n+1)
	for i := range dp {
		dp[i] = -1
	}

	g = make([][]int, n)
	for i := range g {
		g[i] = make([]int, 0)
	}
	for i := 0; i < m; i++ {
		x, y := getInt()-1, getInt()-1
		g[x] = append(g[x], y)
	}

	for now := 0; now < n; now++ {
		rec(now)
	}

	ans := max(dp...)
	fmt.Fprintln(wr, ans)
}

func max(ns ...int) int {
	max := ns[0]
	for i := 1; i < len(ns); i++ {
		if max < ns[i] {
			max = ns[i]
		}
	}
	return max
}

// -----------------------------------------

const (
	inf = 1 << 60
	// mod = 1000000007
)

var (
	sc = bufio.NewScanner(os.Stdin)
	wr = bufio.NewWriter(os.Stdout)
)

func main() {
	// buf := 200001
	// sc.Buffer(make([]byte, buf), buf)
	sc.Split(bufio.ScanWords)
	solve()
	wr.Flush()
}

func getInt() int {
	sc.Scan()
	i, err := strconv.Atoi(sc.Text())
	if err != nil {
		panic(err)
	}
	return i
}

func getIntSlice(n int) []int {
	is := make([]int, n)
	for i := range is {
		is[i] = getInt()
	}
	return is
}

func getString() string {
	sc.Scan()
	s := sc.Text()
	return s
}

func getRunes() []rune {
	return []rune(getString())
}