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 C (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
#include<stdlib.h>
#include<math.h>
int f(int** graph, int* index, int* dp, int val)
{
    if(graph[0][val] == -1)
    {
        dp[val] = 0;
        return 0;
    }
    if(dp[val] == -1)
    {
        int m;
        m = 1 + f(graph, index, dp, graph[0][val]);
        for(int i = 1; i < index[val]; i++)
        {

            int m2 = 1 + f(graph, index, dp, graph[i][val]);
            if(m2 > m)
            {
                m = m2;
            }
        }
        dp[val] = m;
        return dp[val];
    }
    else 
        return dp[val];
}
int main()
{
    int nodes  ;
    int paths;
    scanf("%d", &nodes );
    scanf("%d", &paths);
    int** graph = (int **)malloc((nodes + 1) * sizeof(int *));
    for(int i = 0; i < nodes + 1 ;i ++)
    {
        graph[i] = (int *)malloc((nodes + 1) * sizeof(int));
    }
    int* index = (int *)malloc((nodes + 1) * sizeof(int));
    int* dp = (int *)malloc((nodes + 1) * sizeof(int));
    for(int i = 0; i < (nodes + 1); i++)
    {
        graph[0][i] = -1;
        index[i] = 0;
        dp[i] = -1;
    }
    /*printf("Index : \n");
    for(int i = 0; i < nodes + 1 ; i++)
    {
        printf("%d ", index[i]);
    }*/
    for(int i = 0; i < paths; i++)
    {
        int val ;
        scanf("%d", &val);
        scanf("%d", &graph[index[val]][val]);
        index[val]++;
    }
    /*printf("Graph : \n");
    for(int i = 0 ; i < nodes + 1 ; i ++)
    {
        for(int j = 0; j < nodes + 1 ; j++)
        {
            printf("%d ", graph[i][j]);
        }
        printf("\n");
    }
    printf("Index : \n");
    for(int i = 0; i < nodes + 1 ; i++)
    {
        printf("%d ", index[i]);
    }*/
    int m = f(graph, index, dp, 1);
    for(int i = 2; i <= nodes; i ++)
    {
        int m2 = f(graph, index, dp, i);
        if(m2 > m)
            m = m2;
    }
    //printf("\n");

    printf("%d ", m);
}