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)

var dp = Array(100001) { -1L }
val g = mutableMapOf<Int, MutableList<Int>>()

fun main(args: Array<String>) {
    val (n, m) = readLine()!!.split(' ').map(String::toInt)
    for (i in 1..m) {
        val (x, y) = readLine()!!.split(' ').map(String::toInt)
        if (g.containsKey(x)) g[x]!!.add(y) else g[x] = mutableListOf(y)
    }
    var temp = 0L
    g.keys.forEach { temp = Math.max(temp, rec(it)) }
    println(dp.max())

}

fun rec(cur: Int): Long {
    if (dp[cur] != -1L) return dp[cur]
    var temp = 0L
    g[cur]?.forEach {
        temp = Math.max(temp, rec(it) + 1)
    }
    dp[cur] = temp
    return temp
}