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 Kotlin (1.0.0) (judge verdict: Accepted)

class Graph<T : List<Int>> constructor(private val graph: Array<T>) {
    private val dp = IntArray(100000) { -1 }

    fun rec(v: Int): Int {
        if (dp[v] != -1) return dp[v]

        var res = 0
        graph[v].forEach {
            res = Math.max(res, rec(it) + 1)
        }
        dp[v] = res
        return res
    }

}

fun main(args: Array<String>) {
    val (n, m) = readLine()!!.split(' ').map { it.toInt() }

    val graph = Array(n) { mutableListOf<Int>() }
    repeat(m) {
        val (x, y) = readLine()!!.split(' ').map { it.toInt() }
        graph[x - 1].add(y - 1)
    }

    val g = Graph(graph)
    var res = 0
    (0 until n).forEach {
        res = Math.max(res, g.rec(it))
    }
    println(res)
}