#include<cstdio>
#include<vector>
#include<queue>
#include<cstring>
#include<iostream>
#include<algorithm>
#include<ctime>
#include<random>
#include<assert.h>
#define pb emplace_back
#define mp make_pair
#define fi first
#define se second
#define dbg(x) cerr<<"In Line "<< __LINE__<<" the "<<#x<<" = "<<x<<'\n';
#define dpi(x,y) cerr<<"In Line "<<__LINE__<<" the "<<#x<<" = "<<x<<" ; "<<"the "<<#y<<" = "<<y<<'\n';
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int>pii;
typedef pair<ll,int>pli;
typedef pair<ll,ll>pll;
typedef pair<int,ll>pil;
typedef vector<int>vi;
typedef vector<ll>vll;
typedef vector<pii>vpii;
typedef vector<pil>vpil;
template<typename T>T cmax(T &x, T y){return x=x>y?x:y;}
template<typename T>T cmin(T &x, T y){return x=x<y?x:y;}
template<typename T>
T &read(T &r){
	r=0;bool w=0;char ch=getchar();
	while(ch<'0'||ch>'9')w=ch=='-'?1:0,ch=getchar();
	while(ch>='0'&&ch<='9')r=r*10+(ch^48),ch=getchar();
	return r=w?-r:r;
}
template<typename T1,typename... T2>
void read(T1 &x,T2& ...y){read(x);read(y...);}
const int mod=998244353;
inline void cadd(int &x,int y){x=(x+y>=mod)?(x+y-mod):(x+y);}
inline void cdel(int &x,int y){x=(x-y<0)?(x-y+mod):(x-y);}
inline int add(int x,int y){return (x+y>=mod)?(x+y-mod):(x+y);}
inline int del(int x,int y){return (x-y<0)?(x-y+mod):(x-y);}
const int N=250010;
const ll inf=0x7fffffffffffffff;
int n;
vpii eg1[N],eg2[N];
int siz[N],rt,mx[N],vis[N],all;
int dfn[N],dft,sd[N],tp[N],si[N],son[N],fa[N];
ll dep[N],sum[N],ans[N];
void dfs2(int x,int f){
	dfn[x]=++dft;sd[x]=sd[f]+1;si[x]=1;fa[x]=f;
	for(auto i:eg2[x]){
		int v=i.fi,w=i.se;
		if(v==f)continue;
		sum[v]=sum[x]+w;
		dfs2(v,x);
		si[x]+=si[v];
		if(si[v]>si[son[x]])son[x]=v;
	}
}
void rdfs(int x,int t){
	tp[x]=t;
	if(son[x])rdfs(son[x],t);
	for(auto i:eg2[x]){
		int v=i.fi;
		if(v==fa[x]||v==son[x])continue;
		rdfs(v,v);
	}
}
int LCA(int x,int y){
	while(tp[x]!=tp[y]){
		if(sd[tp[x]]>sd[tp[y]])x=fa[tp[x]];
		else y=fa[tp[y]];
	}
	return dfn[x]<dfn[y]?x:y;
}
ll dis(int x,int y){
	return sum[x]+sum[y]-2*sum[LCA(x,y)];
}
void find(int x,int f){
	siz[x]=1;mx[x]=0;
	for(auto i:eg1[x]){
		int v=i.fi;
		if(v==f||vis[v])continue;
		find(v,x);
		siz[x]+=siz[v];
		mx[x]=max(mx[x],siz[v]);
	}
	mx[x]=max(mx[x],all-siz[x]);
	if(mx[x]<mx[rt])rt=x;
}
vi pos;
void dfs1(int x,int f,ll h){
	dep[x]=h;pos.pb(x);
	for(auto i:eg1[x]){
		int v=i.fi,w=i.se;
		if(v==f||vis[v])continue;
		dfs1(v,x,h+w);
	}
}
int st[N],top,gd[N];
vector<pair<int,ll>> et[N];
ll g[N],h[N];
void merge(int x,int y){
	ll w=dis(x,y);
	et[x].pb(mp(y,w));
	et[y].pb(mp(x,w));
}
void dfs3(int x,int f){
	g[x]=gd[x]?dep[x]+sum[x]:inf;
	h[x]=inf;
	for(auto i:et[x]){
		int v=i.fi;
		if(v==f)continue;
		dfs3(v,x);
		g[x]=min(g[x],g[v]);
		h[x]=min(h[x],g[v]);
	}
}
void dfs4(int x,int f,ll dw){
	if(gd[x]){
		if(dw!=inf)ans[x]=min(ans[x],dep[x]+dw);
		if(h[x]!=inf)ans[x]=min(ans[x],dep[x]+h[x]-sum[x]);
	}
	ll mn=dw,cn=inf;
	int mp=0;
	for(auto i:et[x]){
		int v=i.fi;
		if(v==f)continue ;
		ll d=g[v]-sum[x];
		if(d<mn){
			cn=mn;
			mn=d;mp=v;
		}
		else if(d<cn){
			cn=d;
		}
	}
	#define vx (gd[x]?w+dep[x]:inf)
	for(auto i:et[x]){
		int v=i.fi;ll w=i.se;
		if(v==f)continue ;
		if(v==mp)
			dfs4(v,x,cn==inf?vx:min(cn+w,vx));
		else
			dfs4(v,x,mn==inf?vx:min(mn+w,vx));
	}
	#undef vx
}
void dfz(int x){
	vis[x]=1;
	vi().swap(pos);dep[x]=0;pos.pb(x);
	for(auto i:eg1[x]){
		int v=i.fi,w=i.se;
		if(vis[v])continue;
		dfs1(v,x,w);
	}
	for(auto i:pos)gd[i]=1;
	sort(pos.begin(),pos.end(),[](const int &x,const int &y){return dfn[x]<dfn[y];});
	int len=pos.size();
	st[top=1]=1;vector<pair<int,ll>>().swap(et[1]);
	for(int i=pos[0]==1,lca;i<len;i++){
		int x=pos[i];
		vector<pair<int,ll>>().swap(et[x]);
		while((lca=LCA(st[top],x))!=st[top]){
			if(LCA(st[top-1],x)==st[top-1] && lca!=st[top-1]){
				vector<pair<int,ll>>().swap(et[lca]);
				merge(lca,st[top]);
				st[top]=lca;
			}
			else merge(st[top],st[top-1]),--top;
		}
		st[++top]=x;
	}
	while(top>1){
		merge(st[top],st[top-1]);
		--top;
	}
	dfs3(1,0);
	dfs4(1,0,inf);
	for(auto i:pos)gd[i]=0;
	int tmp=all;
	for(auto i:eg1[x]){
		int v=i.fi;
		if(vis[v])continue;
		all=siz[v]>siz[x]?tmp-siz[x]:siz[v];rt=0;
		find(v,x);
		dfz(rt);
	}
}
signed main(){
	#ifdef do_while_true
//		assert(freopen("data.in","r",stdin));
//		assert(freopen("data.out","w",stdout));
	#endif
	read(n);
	for(int i=1;i<n;i++){
		int x,y,z;read(x,y,z);
		eg1[x].pb(mp(y,z));
		eg1[y].pb(mp(x,z));
	}
	for(int i=1;i<n;i++){
		int x,y,z;read(x,y,z);
		eg2[x].pb(mp(y,z));
		eg2[y].pb(mp(x,z));
	}
	for(int i=1;i<=n;i++)ans[i]=inf;
	dfs2(1,0);
	rdfs(1,1);
	all=n;mx[0]=N;
	find(1,0);
	dfz(rt);
	for(int i=1;i<=n;i++)cout << ans[i] << '\n';
    #ifdef do_while_true
		cerr<<'\n'<<"Time:"<<1.0*clock()/CLOCKS_PER_SEC*1000<<" ms"<<'\n';
	#endif
	return 0;
}