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"
	"flag"
	"fmt"
	"io"
	"math/big"
	"os"
)

var reader *bufio.Reader
var writer *bufio.Writer

var inputFile = flag.String("input", "", "")

func init() {
	flag.Parse()
	var i io.Reader
	if *inputFile != "" {
		i, _ = os.Open(*inputFile)
	} else {
		i = os.Stdin
	}
	reader = bufio.NewReaderSize(i, 1<<20)
	writer = bufio.NewWriterSize(os.Stdout, 1<<20)
}

func println(a ...interface{}) {
	_, _ = fmt.Fprintln(writer, a...)
}

func printf(format string, a ...interface{}) {
	_, _ = fmt.Fprintf(writer, format, a...)
}

func scanf(format string, a ...interface{}) {
	_, _ = fmt.Fscanf(reader, format, a...)
}

func scan(a interface{}) {
	_, _ = fmt.Fscan(reader, a)
}

func NextInt64() int64 {
	var res int64
	scan(&res)
	return res
}

func NextInt() int {
	var res int
	scan(&res)
	return res
}

func NextIntArray(n int) []int {
	res := make([]int, n)
	for i := range res {
		scan(&res[i])
	}
	return res
}

func NextInt64Array(n int) []int64 {
	res := make([]int64, n)
	for i := range res {
		scan(&res[i])
	}
	return res
}

func NextString() string {
	var res string
	scan(&res)
	return res
}

func NextBigInt() *big.Int {
	n := new(big.Int)
	n, _ = n.SetString(NextString(), 10)
	return n
}

func AbsInt64(x int64) int64 {
	if x < 0 {
		return -x
	}
	return x
}

func MinInt64(x, y int64) int64 {
	if x < y {
		return x
	}
	return y
}

func MaxInt64(x, y int64) int64 {
	if x > y {
		return x
	}
	return y
}

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

func main() {
	defer writer.Flush()

	n := NextInt()
	m := NextInt()

	g := make([][]int, n)

	for i := 0; i < m; i++ {
		u := NextInt() - 1
		v := NextInt() - 1

		g[u] = append(g[u], v)
	}

	cache := make([]int, n)
	var solve func(x int ) int

	solve = func(x int ) int {
		if cache[x] != 0 {
			return cache[x]
		}
		for _, to := range g[x] {
			t := solve(to) + 1
			if t > cache[x] {
				cache[x] = t
			}
		}
		return cache[x]
	}

	answer := 0

	for i := 0; i < n; i++ {
		t := solve(i)
		if t > answer {
			answer = t
		}
	}

	println(answer)
}