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 <bits/stdc++.h>
using namespace std;
typedef long long int ll;
#define fastio ios_base:: sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
#define INF LLONG_MAX

int main()
{
    fastio;

    ll n , m, x, y, maxlength;
    vector<ll> indegree(100005);
    vector<ll> adj[100005];
    priority_queue<pair<ll,ll>> q;
    vector<ll> dp(100005);

    cin >> n >> m;

    for(ll i = 1 ; i <= m ; i++)
    {
        cin >> x >> y;
        indegree[y]++;
        adj[x].push_back(y);
    }

    for( ll i = 1 ; i <= n ; i++)
    {
        q.push(make_pair(-indegree[i] , i));
    }

    while(!q.empty())
    {
        auto h = q.top();
        ll ind = h.first;
        ll v = h.second;
        q.pop();

        for( auto u:adj[v])
        {
            dp[u] = max(dp[u] , dp[v]+1);
            h.first++;
        }

    }

    maxlength = *max_element(dp.begin()+1 , dp.begin()+n+1);
    cout << maxlength;

    return 0;
}