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>

#define MAXN 100000

typedef struct LIST {
	int cnt;
	int p[500];
} IT;

IT A[MAXN+1];
int  S[MAXN+1];

int longestpath ( int n )
{
	if ( S[n] != -1 ) return S[n];

	int max, tmp,i;

	max = longestpath(A[n].p[0]);
	for ( i = 1; i < A[n].cnt; i++ ) {
		tmp = longestpath(A[n].p[i]);
		if ( max < tmp ) max = tmp;
	}

	return S[n] = max+1;
}


int main(void)
{
	int n,m,i,tmp1,tmp2,max = -1;

	scanf("%d%d", &n,&m);

	for ( i = 0; i <= n; i++ ) A[i].cnt = 0,S[i] = -1;

	for ( i = 0; i < m; i++ ) {
		scanf("%d%d", &tmp1, &tmp2);
		A[tmp2].p[A[tmp2].cnt] = tmp1;
		A[tmp2].cnt++;
	}

	for ( i = 1; i <= n; i++ ) if ( A[i].cnt == 0 ) S[i] = 0;

	for ( i = 1; i <= n; i++ ) {
		tmp1 = longestpath(i);
		if ( max < tmp1 ) max = tmp1;
	}

	printf("%d\n", max);

	return 0;
}