#include<bits/stdc++.h>
#include<ext/pb_ds/tree_policy.hpp>
#include<ext/pb_ds/assoc_container.hpp>
#define ll long long
#define int long long
using namespace std;

const int maxn = 210000;
const int inf = 1e9+5;

int n,m;
vector< pair<int,int> >E[maxn];

signed main()
{
	ios_base::sync_with_stdio(false);
	
	int Tcase; cin>>Tcase;
	while(Tcase--)
	{
		cin>>n>>m;
		for(int i=1;i<=n;i++)
		{
			vector< pair<int,int> >_;
			E[i].swap(_);
		}
		int spu,spv,spw;
		for(int i=1;i<=m;i++)
		{
			int u,v,w; cin>>u>>v>>w;
			E[v].emplace_back(u,w);
			if(u>v) spu=u,spv=v,spw=w;
		}
		
		vector<int>go(n+5),goc(n+5);
		int ans=0;
		go[1]=0,goc[1]=0;
		for(int i=2;i<=n;i++)
		{
			goc[i]=inf;
			for(auto [j,c]:E[i]) 
			{
				if(goc[i]>c) go[i]=j,goc[i]=c;
			}
			ans+=goc[i];
		}
		
		vector<int>V,vis(n+5);
		int ok=1;
		for(int i=spu;i;i=go[i])
		{
			if(vis[i]) { ok=0; break; }
			vis[i]=1;
			V.push_back(i);
		}
		int temp=inf;
		if(ok) temp=0;
		for(auto i:V)
		{
			for(auto [j,c]:E[i]) if(!vis[j])
			{
				temp=min(temp, c-goc[i]);
			}
		}
		cout<<ans+temp<<'\n';
	}
	
	return 0;
}