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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
#include <cmath>
#include<cstdio>
#include <cstring>
#include <algorithm>
#define ll long long int
using namespace std;

ll arr[100030];
ll x[100030],y[100030];
ll dp[100030][1000];
ll n,m;

ll call(int i,int p)
{
    int asn1 = 0,maxi = 0;
    if(i == m)
        return 0;
    if(dp[i][p] != -1)
        return dp[i][p];
    else if(p == x[i])
    {
        asn1 = 1 + call(i+1,y[i]);
        dp[i][p] = asn1;
        return dp[i][p];
    }
    else if(p != x[i])
    {
        asn1 = call(i+1,p);
        maxi = call(i+1,y[i]);
        dp[i][p] = max(asn1,maxi);
        return dp[i][p];
    }

}

int main()
{
    cin>>n>>m;
    for(int i=0;i<m;i++)
        cin>>x[i]>>y[i];
    int max = 0;
    memset(dp,-1,sizeof(dp));

    cout<<call(0,x[0]);
}