** Childfree Time !! - Dijkstras Algo + Multisource BFS

#include <bits/stdc++.h>
#define endl "\n"
#define int long long
using namespace std;
vector<pair<int,int>>g[1000001];
int in[1000001];
int out[1000001];
int dis[10000001];
int32_t main()
{
	ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    int t=1;
    while(t--){
        
        int n,m;
        cin >> n >> m;

        for(int i=1;i<=m;i++)
        {
            int a,b;
            cin >> a >> b;
            int w;
            cin >> w;
            g[a].push_back({b,w});
            in[b]++;
            out[a]++;
        }

        queue<pair<int,int>> q;
        for(int i=1;i<=n;i++)
        {
            if(in[i] == 0)
                q.push({i,0});
        }
        int mx = 0;
        while(!q.empty())
        {
            int x = q.front().first;
            int d = q.front().second;q.pop();
            if(d!=dis[x])
            continue;
            if(out[x] == 0)
            {
                mx = max(mx,d);
                continue;
            }


            for(auto edge:g[x])
            {
                int v = edge.first;
                int cost = edge.second;
                if(dis[v] < d + cost + 2){
                    q.push({v,d + cost + 2});
                    dis[v] = d + cost + 2;
                }
            }

        }
        cout << mx << '\n';

    }
}