#include <iostream>
#include <cstdio>
#include <algorithm>
using namespace std;
const int N=2e4+10;
struct Edge {
    int u,v,w;
}g[N];
int f[N],sz[N];
int T,n;

int Get_F(int x) {return f[x]==x?x:f[x]=Get_F(f[x]);}

bool CMP(Edge a,Edge b) {
    return a.w<b.w;
}

int main() {
    for (scanf("%d",&T);T;T--) {
        scanf("%d",&n);
        for (int i=1;i<n;i++) scanf("%d%d%d",&g[i].u,&g[i].v,&g[i].w),sz[i]=1,f[i]=i;
        f[n]=n;sz[n]=1;long long ans=0;
        sort(g+1,g+n,CMP);
        for (int i=1;i<n;i++) {
            int fu=Get_F(g[i].u),fv=Get_F(g[i].v);
            if (fu!=fv) {
                ans+=1ll*(sz[fu]*sz[fv]-1ll)*(g[i].w+1ll);
                sz[fu]+=sz[fv];
                f[fv]=fu;
                ans+=g[i].w;
            }
        }
        printf("%lld\n",ans);
    }
}