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>
#define ll          long long
#define pb          push_back
#define endl        '\n'
#define pii         pair<ll int,ll int>
#define vi          vector<ll int>
#define all(a)      (a).begin(),(a).end()
#define F           first
#define S           second
#define sz(x)       (ll int)x.size()
#define hell        1000000001
#define r(i,a,b)    for(i=a;i<b;i++)
#define ra(i,a,b)   for(i=a;i<=b;i++)
#define lbnd        lower_bound
#define ubnd        upper_bound
#define bs          binary_search
#define mp          make_pair
#define ss          set<ll int>
using namespace std;
 
#define N 1000000
#define M 100000000

struct unit {
  ll int a[N];  
};

ll fact (ll int x)
{if(x==1 || x==0)return 1;
else return x*fact(x-1);}

ll power(ll int x,ll int n)
{if(n==0)return 1;
else if(n%2 == 0)return power(x*x,n/2);
else return x*power(x*x,(n-1)/2);}

bool cmp (const pii&a,const pii&b)
{ return((a.F-a.S) > (b.F-b.S));
/*if(a.S<=b.S){if(a.S==b.S)return a.F<b.F;else return a.S<b.S;}
else return a.S<b.S;*/}


int main()
{
    cin.tie(0), cin.sync_with_stdio(0), cout.tie(0), cout.sync_with_stdio(0);
    ll i,j,k,l,m,n,a=0,b=0;
    cin>>n>>m;
    vector<pii> v;
    r(i,0,m)
    {
        cin>>k>>l;
        v.pb(mp(k,l));
    }
    ll dp[n+1];
    memset(dp,0,sizeof(dp));
    r(j,0,m)
    dp[v[j].S]=1;
    r(j,0,m)
    dp[v[j].S]=max(dp[v[j].S],dp[v[j].F]+1);
    cout<<*max_element(dp,dp+n+1);
}