//vanitas vanitatum et omnia vanitas
#include<bits/stdc++.h>
#define fi first
#define se second
#define eb emplace_back
#define mp make_pair
using namespace std;
typedef long double ld;
typedef long long ll;
typedef unsigned long long ull;
typedef __int128 i128;
template<typename T,typename U>
T ceil(T x, U y) {return (x>0?(x+y-1)/y:x/y);}
template<typename T,typename U>
T floor(T x, U y) {return (x>0?x/y:(x-y+1)/y);}
template<class T,class S>
bool chmax(T &a,const S b) {return (a<b?a=b,1:0);}
template<class T,class S>
bool chmin(T &a,const S b) {return (a>b?a=b,1:0);}
int popcnt(int x) {return __builtin_popcount(x);}
int popcnt(ll x)  {return __builtin_popcountll(x);}
int topbit(int x) {return (x==0?-1:31-__builtin_clz(x));}
int topbit(ll x)  {return (x==0?-1:63-__builtin_clzll(x));}
int lowbit(int x) {return (x==0?-1:__builtin_ctz(x));}
int lowbit(ll x)  {return (x==0?-1:__builtin_ctzll(x));}

#define int long long
#define rep(i,a,b) for(int i=(a);i<=(b);i++)
#define per(i,a,b) for(int i=(a);i>=(b);i--)
typedef pair<int,int> pii;
typedef vector<int> vi;
typedef vector<pii> vp;
typedef tuple<int,int,int> tiii;
int read() {
  int x=0,w=1; char c=getchar(); 
  while(!isdigit(c)) {if(c=='-') w=-1; c=getchar();}
  while(isdigit(c)) {x=x*10+(c-'0'); c=getchar();}
  return x*w;
}

const int N=2.5e5+5,inf=0x3f3f3f3f3f3f3f3f;
int n,dfn[N],son[N],sz1[N],sz2[N],pa[N],tick,top[N],ans[N],d[N],b[N],
    vst[N],rt,m,msz[N],p[N],pk,q[N],qk,r1[N],r2[N],fm[N],fs[N],fp[N],g[N];
vp e1[N],e2[N]; vi t2[N];

void dfs21(int u,int fa) {
  for(auto [v,w]:e2[u]) if(v!=fa) {
    d[v]=d[u]+1, r2[v]=r2[u]+w;
    dfs21(v,u); sz2[u]+=sz2[v]; pa[v]=u;
    if(sz2[v]>sz2[son[u]]) son[u]=v;
  } sz2[u]++;
}
void dfs22(int u,int tp) {
  top[u]=tp; dfn[u]=++tick; if(son[u]) dfs22(son[u],tp);
  for(auto [v,w]:e2[u]) if(v!=pa[u]&&v!=son[u]) dfs22(v,v);
}
void dfs23(int u) {
  fm[u]=fs[u]=inf, fp[u]=0;
  for(int v:t2[u]) {
    dfs23(v);
    if(g[v]<fm[u]) fs[u]=fm[u], fp[u]=v, fm[u]=g[v];
    else if(g[v]<fs[u]) fs[u]=g[v];
  }
  chmin(g[u],fm[u]);
  //cout<<u<<" "<<g[u]<<" "<<fm[u]<<' '<<fp[u]<<" "<<fs[u]<<endl;
}
void dfs24(int u,int mn) {
  if(b[u]) {
    chmin(ans[u],r1[u]+mn+r2[u]);
    chmin(ans[u],r1[u]+fm[u]-r2[u]);
  }
  for(int v:t2[u]) {
    int vm=mn; if(b[u]) chmin(vm,r1[u]-r2[u]);
    if(v==fp[u]) chmin(vm,fs[u]-2*r2[u]);
    else chmin(vm,fm[u]-2*r2[u]);
    dfs24(v,vm);
  }
}
int lca(int u,int v) {
  for(;top[u]!=top[v];u=pa[top[u]])
    if(d[top[u]]<d[top[v]]) swap(u,v);
  return d[u]<d[v]?u:v;
}
bool cmp(const int &x,const int &y) {
  return dfn[x]<dfn[y];
}
void work1() {
  //cout<<"WORK: "; rep(i,1,pk) cout<<p[i]<<" "; puts("");
  sort(p+1,p+pk+1,cmp); static int st[N];
  qk=1, q[qk]=1; int top=1; st[1]=1;
  rep(i,1,pk) if(p[i]!=1) {
    int x=p[i], y=lca(x,st[top]);
    if(y==st[top]) st[++top]=x, q[++qk]=x;
    else {
      while(top>1&&d[st[top-1]]>d[y]) t2[st[top-1]].eb(st[top]), top--;
      t2[y].eb(st[top]), top--;
      if(st[top]!=y) st[++top]=y, q[++qk]=y;
      st[++top]=x, q[++qk]=x;
    }
  } while(top>1) t2[st[top-1]].eb(st[top]), top--;
  //cout<<"Q: "; rep(i,1,qk) cout<<q[i]<<" "; puts("");
  rep(i,1,qk) g[q[i]]=inf, b[q[i]]=0;
  rep(i,1,pk) g[p[i]]=r2[p[i]]+r1[p[i]], b[p[i]]=1;
  //rep(i,1,n) cout<<g[i]<<" "; puts("");
  //rep(i,1,n) cout<<b[i]<<" "; puts("");
  dfs23(1); dfs24(1,inf);
  rep(i,1,qk) {vi emp; t2[q[i]].swap(emp);}
}

void dfs11(int u,int fa) {
  sz1[u]=1;
  for(auto [v,w]:e1[u]) if(v!=fa&&!vst[v]) {
    dfs11(v,u); sz1[u]+=sz1[v];
    chmax(msz[u],sz1[v]);
  } chmax(msz[u],m-sz1[u]);
  if(msz[u]<msz[rt]) rt=u;
}
void dfs12(int u,int fa) {
  p[++pk]=u; sz1[u]=1;
  for(auto [v,w]:e1[u]) if(v!=fa&&!vst[v]) {
    r1[v]=r1[u]+w; dfs12(v,u); sz1[u]+=sz1[v];
  }
}
void dfs13(int u,int tm) {
  rt=0, msz[0]=n+1, m=tm, dfs11(u,0), u=rt;
  r1[u]=0, pk=0, vst[u]=1, dfs12(u,0), work1();
  for(auto [v,w]:e1[u]) if(!vst[v]) dfs13(v,sz1[v]);
}

signed main() {
  n=read(); rep(i,1,n) ans[i]=inf;
  rep(i,2,n) {
    int u=read(), v=read(), w=read();
    e1[u].eb(v,w), e1[v].eb(u,w);
  }
  rep(i,2,n) {
    int u=read(), v=read(), w=read();
    e2[u].eb(v,w), e2[v].eb(u,w);
  }
  dfs21(1,0); dfs22(1,0); dfs13(1,n);
  rep(i,1,n) printf("%lld\n",ans[i]);
  return 0;
}