#include <bits/stdc++.h>

using namespace std;
using ll = long long;
using pii = pair<int, int>;

const int N = 5e5 + 10;

struct Node {
    int u, v, w;
} e[N];

struct Edge {
    int id, v, w;
};

int T, n, m, to[N], cnt[N], nxt[N];
vector<Edge> g[N];
vector<pii> G;

void Solve() {
    cin >> n >> m;
    int p;
    for (int i = 1, u, v, w; i <= m; i++) {
        cin >> u >> v >> w;
        if (u < v) {
            g[v].push_back({i, u, w});
        } else p = i;
        e[i] = {u, v, w};
        if (u == 1) G.push_back({v, w});
    }
    ll ans = 0;
    for (int i = 2; i <= n; i++) {
        int mmin = 1e9, id;
        for (Edge j : g[i]) if (mmin > j.w || (mmin == j.w && j.v == 1)) mmin = j.w, id = j.id;
        ans += mmin, cnt[e[id].u]++, to[i] = id, nxt[e[id].u] = i;
    }
    if (e[p].v != 1) {
        ll sum = ans;
        if (cnt[1] == 1 && nxt[1] == e[p].v) {
            for (pii i : G) {
                if (e[p].v == i.first) continue;
                ll s = sum - e[to[e[p].v]].w + e[p].w + i.second - e[to[i.first]].w;
                ans = min(ans, s);
            }
        } else ans = min(ans, ans - e[to[e[p].v]].w + e[p].w);
    }
    cout << ans << '\n';
    for (int i = 1; i <= n; i++) g[i].clear();
}

int main() {
    ios::sync_with_stdio(0), cin.tie(0);
    cin >> T;
    while (T--) Solve();
    return 0;
}