#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using pii = array<int, 2>;
using e = array<int, 3>;
using graph = vector< vector<e> >;

#define all(x) (x).begin(), (x).end()

void solve() {
    int n, m;
    cin >> n >> m;
    e spec;
    graph gt(n);
    for (int i = 0; i < m; ++i) {
        int u, v, w;
        cin >> u >> v >> w;
        --u;--v;
        if (u > v) {
            spec = {w, u, v};
        } else {
            gt[v].push_back({w, v, u});
        }
    }
    ll tmp = 0;
    vector<int> prev(n, -1), mn(n, 0);
    for (int i = n - 1; i > 0; --i) {
        sort(all(gt[i]));
        e cur = gt[i][0];
        tmp += cur[0];
        mn[i] = cur[0];
        prev[i] = cur[2];
    }
    ll ans = tmp;
    int to = spec[1];
    set<int> in_cycle;
    while (to != spec[2] && prev[to] != -1) {
        in_cycle.insert(to);
        to = prev[to];
    }
    in_cycle.insert(to);
    if (to == spec[2]) {
        auto [sw, su, sv] = spec;
        tmp += sw;
        tmp -= mn[sv];
        while (su != sv) {
            for (auto [w, _, vv] : gt[su]) {
                if (in_cycle.count(vv)) {
                    continue;
                }
                ll tmp2 = tmp;
                tmp2 -= mn[su];
                tmp2 += w;
                ans = min(ans, tmp2);
            }
            su = prev[su];
        }
    }
    cout << ans << '\n';
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    int t;
    cin >> t;
    while (t--) {
        solve();
    }
}