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: Runtime Error)

package main

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

func out(x ...interface{}) {
	fmt.Println(x...)
}

var sc = bufio.NewScanner(os.Stdin)

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

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

func max(a, b int) int {
	if a > b {
		return a
	}
	return b
}

func main() {
	sc.Split(bufio.ScanWords)

	N, M := getInt(), getInt()

	dp := make([][]int, N)
	for i := 0; i < N; i++ {
		dp[i] = make([]int, N)
	}

	for i := 0; i < M; i++ {
		from, to := getInt()-1, getInt()-1
		dp[from][to] = 1
	}

	for k := 0; k < N; k++ {
		for i := 0; i < N; i++ {
			for j := 0; j < N; j++ {
				if dp[i][k] != 0 && dp[k][j] != 0 {
					//					out(i+1, j+1, k+1, "cost", dp[i][j], "kcost", dp[i][k]+dp[k][j])
					dp[i][j] = max(dp[i][j], dp[i][k]+dp[k][j])
				}
			}
		}
	}

	max := 0

	for i := 0; i < N; i++ {
		for j := 0; j < N; j++ {
			if dp[i][j] > max {
				max = dp[i][j]
			}
		}
	}

	out(max)

}