#include <bits/stdc++.h>

using namespace std;

long long inf = numeric_limits<long long>::max()/3;
int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    long long t;
    cin>>t;
    while (t--){
        long long n,m;
        cin>>n>>m;
        long long left = -1;
        long long right = -1;
        long long weight = -1;
        vector<vector<pair<long long,long long>>> adj_matrix(n+1);
        for (int i=0;i<m;i++){
            long long u,v,w;
            cin>>u>>v>>w;
            if (u>v){
                left = v;
                right = u;
                weight = w;
            }else{
                adj_matrix[v].push_back({u,w});
            }
        }
        vector<long long> best(n+1,inf);
        vector<long long> best2(n+1,inf);
        
        for (int i=0;i<adj_matrix.size();i++){
            for (pair<long long,long long> p:adj_matrix[i]){
                best[i] = min(best[i],p.second);
                if (p.first!=left){
                    best2[i] = min(best2[i],p.second);
                }
            }
        }

        long long answer1 = 0;
        for (int i=2;i<best.size();i++){
            if (best[i]==inf){
                answer1 = inf;
                break;
            }
            answer1 += best[i];
        }

        long long answer2 = 0;
        for (int i=2;i<best2.size();i++){
            if (i==left){
                continue;
            }else if (i==right){
                if (best2[i]==inf){
                    answer2 = inf;
                    break;
                }
                answer2 += weight + best2[i];
            }else{
                if (best2[i]==inf){
                    answer2 = inf;
                    break;
                }
                answer2 += best2[i];
            }
        }

        cout<<min(answer1,answer2)<<"\n";
    }
    return 0;
}
/*
1
3 2
1 3 10
3 2 10
*/