1 #include <bits/stdc++.h>
  2 using namespace std;
  3 #define X first
  4 #define Y second
  5 #define pii pair<int, int>
  6 #define mp make_pair
  7 typedef long long ll;
  8 const int N = 1e5+5;
  9 void gmax(int& a, int b){ if(a < b) a = b;}
 10 int n;
 11 ll ans;
 12 int down[N][2], up[N], dis[N], dis2[N];
 13
 14 int head[N], nex[N*2], tot;
 15 pii edge[N*2];
 16 void init(){
 17     tot = 0;
 18     memset(head, -1, sizeof(head));
 19     memset(down, 0, sizeof(down));
 20     memset(up, 0, sizeof(up));
 21     memset(dis, 0, sizeof(dis));
 22     memset(dis2, 0, sizeof(dis2));
 23 }
 24 void add(int u, int v, int w){
 25     edge[tot] = mp(v, w);
 26     nex[tot] = head[u];
 27     head[u] = tot++;
 28 }
 29 //down[][0]:从i结点向下的最大距离
 30 //down[][1]:与down[][0]无交集的向下次大距离
 31 //dis:以i为根的子树的直径
 32 void dfs(int fa, int x){
 33 //    printf("dfs x %d, fa %d\n", x, fa);
 34 //down[x][0] = down[x][1] = dis[x] = dis2[x] = up[x] = 0;
 35     for(int i = head[x]; ~i; i = nex[i]){
 36         int y = edge[i].X, w = edge[i].Y;
 37         if(y == fa) continue ;
 38         dfs(x, y);
 39         if(down[y][0]+w > down[x][0])
 40             down[x][1] = down[x][0], down[x][0] = down[y][0]+w;
 41         else if(down[y][0]+w > down[x][1])
 42             down[x][1] = down[y][0]+w;
 43         gmax(dis[x], dis[y]);
 44     }
 45     gmax(dis[x], down[x][0]+down[x][1]);
 46 }
 47 //up:从i结点向上的最远距离
 48 //dis2:切掉以i为根的子树后的直径
 49 multiset<int>::iterator it;
 50 void dfs2(int fa, int x){
 51     if(fa != -1) ans += max(dis[x], dis2[x]);
 52 //    printf("fa %d, x %d\n", fa, x);
 53     multiset<int> se, se2;//兄弟树的直径, x往各个兄弟树的最长路
 54     for(int i = head[x]; ~i; i = nex[i]){
 55         int y = edge[i].X, w = edge[i].Y;
 56         if(y == fa) continue ;
 57         se.insert( dis[y] );
 58         se2.insert( down[y][0]+w );
 59     }
 60     for(int i = head[x]; ~i; i = nex[i]){
 61         int y = edge[i].X, w = edge[i].Y;
 62         if(y == fa) continue ;
 63         up[y] = up[x]+w;
 64         if(down[y][0]+w == down[x][0])
 65             gmax(up[y], down[x][1]+w);
 66         else gmax(up[y], down[x][0]+w);
 67         it = se.find( dis[y] ), se.erase(it);
 68         it = se2.find( down[y][0]+w ), se2.erase(it);
 69         dis2[y] = dis2[x];
 70         if(!se.empty())
 71             gmax(dis2[y], *se.rbegin());
 72         if(se2.empty()) gmax(dis2[y], up[x]);
 73         else gmax(dis2[y], up[x]+*se2.rbegin());
 74         if(se2.size() >= 2){
 75             int tmp = 0;
 76             it = se2.end();
 77             tmp += *--it;
 78             tmp += *--it;
 79             gmax(dis2[y], tmp);
 80         }
 81         dfs2(x, y);
 82         se.insert( dis[y] );
 83         se2.insert( down[y][0]+w );
 84     }
 85 }
 86 void debug(int n){
 87     for(int i = 1; i <= n; i++)
 88         printf("%d: down0 %d, down1 %d, dis %d, dis2 %d, up %d\n", i, down[i][0], down[i][1], dis[i], dis2[i], up[i]);
 89 }
 90 int main(){
 91     int t, u, v, w; scanf("%d", &t);
 92     while(t--) {
 93         init();
 94         scanf("%d", &n);
 95         for(int i = 1; i < n; i++){
 96             scanf("%d%d%d", &u, &v, &w);
 97             add(u, v, w), add(v, u, w);
 98         }
 99         ans = 0;
100         dfs(-1, 1);
101         dfs2(-1, 1);
102         printf("%lld\n", ans);
103     }
104     return 0;
105 }