#pragma GCC optimize(2)
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define int ll
#define pii pair<int,int>
#define fi first
#define se second
#define mk make_pair
#define pb emplace_back
const int N=5e5+7;
struct edge
{
	int to,w,nxt;
	bool ex;
}e[N<<1];
int h[N],etot=1;
inline void EADD(int x,int y,int w)
{
	e[++etot].to=y;
	e[etot].w=w;e[etot].ex=1;
	e[etot].nxt=h[x];
	h[x]=etot;
}
vector<pii>G1[N],G2[N];
int fa[N],ww[N],son[N],Siz[N];
void dfs1(int x)
{
	Siz[x]=1;int mx=-1;
	for(auto P:G2[x])
	{
		int y=P.fi,w=P.se;
		if(y==fa[x])continue;
		ww[y]=ww[x]+w,fa[y]=x;
		dfs1(y),Siz[x]+=Siz[y];
		if(Siz[y]>mx)mx=Siz[y],son[x]=y;
	}
}
int Top[N],dfn[N],dcnt;
void dfs2(int x,int topn)
{
	dfn[x]=++dcnt;Top[x]=topn;
	if(!son[x])return;
	dfs2(son[x],topn);
	for(auto P:G2[x])
	{
		int y=P.fi,w=P.se;
		if(y==fa[x]||y==son[x])continue;
		dfs2(y,y);
	}
}
int lca(int x,int y)
{
	while(Top[x]!=Top[y])
	{
		if(dfn[Top[x]]<dfn[Top[y]])swap(x,y);
		x=fa[Top[x]];
	//cout<<x<<" "<<y<<endl;
	}
	return dfn[x]<dfn[y]?x:y;
}
int val(int x,int y)
{
	return ww[x]-ww[y];
}
void eadd(int x,int y,int w)
{
	EADD(x,y,w),EADD(y,x,w);
}
int ans[N];
int tot,nd[N],re[N];bool cs[N];
void redfs(int x,int fa)
{
	if(!nd[x])nd[x]=++tot;
	for(auto P:G1[x])
	{
		int y=P.fi,w=P.se;
		if(y==fa)continue;
		if(cs[x])
		{
			eadd(nd[x],++tot,0);
			nd[x]=tot;
		}
		nd[y]=++tot;cs[x]=1;
		eadd(nd[x],nd[y],w);
		redfs(y,x);
	}
	re[nd[x]]=x;
}
#define FOR(x) for(int i=h[x],y,w;y=e[i].to,w=e[i].w,i;i=e[i].nxt)
int siz[N],eid[N],W[N];
void szdfs(int x,int fa)
{
	siz[x]=1;
	FOR(x)if(e[i].ex&&y!=fa)W[y]=W[x]+w,eid[y]=i,szdfs(y,x),siz[x]+=siz[y];
}
inline void cmax(int &x,int y){x=max(x,y);}
inline void cmin(int &x,int y){x=min(x,y);}
inline void ban(int x){e[x].ex=e[x^1].ex=0;}
pii core(int x,int fa,int T)
{
	int mx=-1,bst;//cout<<x<<"??"<<fa<<"??"<<T<<endl;
	FOR(x)if(e[i].ex&&y!=fa)if(siz[y]>mx)bst=y,mx=siz[y];
	//cout<<bst<<" "<<mx<<endl;
	if(2*mx<=T)return siz[x]<T-mx?mk(x,fa):mk(bst,x);
	return core(bst,x,T);
}
int col[N];
void getv(int x,int fa,vector<int>&v)
{
	v.pb(x);
	FOR(x)if(e[i].ex&&y!=fa)getv(y,x,v);
}
vector<pii>G[N];
vector<int>vx,vy,v;
int stc[N],top;
inline void Gadd(int x,int y,int w)
{
	//cout<<"Edge "<<x<<" "<<y<<" "<<w<<endl;
	G[x].pb(y,w),G[y].pb(x,w);
}
void vbuild(vector<int>&a)
{
	if(!a.size())return;
	//for(auto x:a)cout<<x<<" ";cout<<endl;
	sort(a.begin(),a.end(),[](int x,int y){return dfn[x]<dfn[y];});
	vector<int>v;
	int n=a.size(),rt=lca(a[0],a[n-1]);
	stc[++top]=rt;
	for(int i=(a[0]==rt);i<n;i++)
	{
		int x=a[i],y=lca(x,stc[top]);//cout<<x<<" "<<y<<" "<<top<<endl;
		if(y==stc[top]){stc[++top]=x;continue;}
		while(dfn[stc[top]]>dfn[y])
		{
			Gadd(stc[top],stc[top-1],val(stc[top],stc[top-1]));
			v.pb(stc[top]);//cout<<v.back()<<endl;
			top--;
		}
		if(y==stc[top]){stc[++top]=x;continue;}
		G[v.back()].pop_back(),G[stc[top]].pop_back();//cout<<"BACK\n";
		Gadd(v.back(),y,val(v.back(),y));
		stc[++top]=y,stc[++top]=x;
	}
	while(top)
	{
		if(top-1)Gadd(stc[top],stc[top-1],val(stc[top],stc[top-1]));
		v.pb(stc[top]);
		top--;
	}
	swap(v,a);
}

bool vis[N];
const int oo=1e16;
int sz[N],dep[N];
void szdfs2(int x,int fa)
{
	sz[x]=1;//cout<<"szdfs2 "<<x<<endl;
	for(auto P:G[x])
	{
		int y=P.fi,w=P.se;
		if(vis[y]||y==fa)continue;
		dep[y]=dep[x]+w,szdfs2(y,x);
		sz[x]+=sz[y];
	}
}
int Core(int x,int fa,int T)
{
	int mx=-1,bst;
	for(auto P:G[x])
	{
		int y=P.fi,w=P.se;
		if(vis[y]||y==fa)continue;
		if(sz[y]>mx)mx=sz[y],bst=y;
	}
	//cout<<x<<" "<<sz[x]<<" "<<mx<<endl;
	if(2*mx<=T)return x;
	return Core(bst,x,T);
}

void insdfs(int x,int fa,vector<int>&mn)
{
	if(~col[x])cmin(mn[col[x]],dep[x]+W[nd[x]]);
	for(auto P:G[x])
	{
		int y=P.fi,w=P.se;
		if(vis[y]||y==fa)continue;
		insdfs(y,x,mn);
	}
}

void qrydfs(int x,int fa,vector<int>&mn)
{
	if(~col[x])
	{
		//cout<<"Q "<<x<<endl;
		cmin(ans[x],mn[col[x]^1]+dep[x]+W[nd[x]]);
	}
	for(auto P:G[x])
	{
		int y=P.fi,w=P.se;
		if(vis[y]||y==fa)continue;
		qrydfs(y,x,mn);
	}
}

void sol(int x,int T)
{
	x=Core(x,0,T);//cout<<x<<">>>>"<<T<<endl;
	dep[x]=0,szdfs2(x,0),vis[x]=1;
	vector<int>mn(2,oo);
	if(~col[x])cmin(mn[col[x]],dep[x]+W[nd[x]]);
	for(int i=0;i<G[x].size();i++)
	{
		pii P=G[x][i];
		int y=P.fi,w=P.se;
		if(vis[y])continue;
		qrydfs(y,0,mn),insdfs(y,0,mn);
	}
	mn[0]=mn[1]=oo;
	for(int i=G[x].size()-1;~i;i--)
	{
		pii P=G[x][i];
		int y=P.fi,w=P.se;
		if(vis[y])continue;
		qrydfs(y,0,mn),insdfs(y,0,mn);
	}
	if(~col[x])
	{
		//cout<<"Q "<<x<<endl;
		cmin(ans[x],mn[col[x]^1]+dep[x]+W[nd[x]]);
	}
	for(auto P:G[x])
	{
		int y=P.fi,w=P.se;
		if(vis[y])continue;
		sol(y,sz[y]);
	}
}

void solve(int rt,int T)
{
	if(T==1)return;
	pii P=core(rt,0,T);
	int x=P.fi,y=P.se,w=e[eid[x]].w;
	//cout<<x<<","<<y<<">>"<<T<<endl;
	ban(eid[x]);W[x]=0,W[y]=0;
	szdfs(x,0),szdfs(y,0);
	getv(x,0,vx),getv(y,0,vy);
	for(auto p:vx)W[p]+=w;
		//cout<<"X ";
	for(auto z:vx)if(re[z])v.pb(re[z]),col[re[z]]=0;//,cout<<re[z]<<" ";cout<<endl;
		//cout<<"Y ";
	for(auto z:vy)if(re[z])v.pb(re[z]),col[re[z]]=1;//,cout<<re[z]<<" ";cout<<endl;
	//for(auto x:v)cout<<x<<" ";cout<<endl;
	vbuild(v);
	if(v.size())
	{
		szdfs2(v[0],0);//cout<<"???"<<endl;
		sol(v[0],v.size());
		for(auto z:v)col[z]=-1,vis[z]=0,G[z].clear();	
	}
	vx.clear(),vy.clear(),v.clear();	
	solve(x,siz[x]),solve(y,siz[y]);
}

signed main()
{
	ios::sync_with_stdio(0);
	cin.tie(0);
	int n;
	cin>>n;
	memset(col,-1,sizeof(col));
	for(int i=1;i<n;i++)
	{
		int x,y,w;
		cin>>x>>y>>w;
		G1[x].pb(y,w),G1[y].pb(x,w);
	}
	for(int i=1;i<n;i++)
	{
		int x,y,w;
		cin>>x>>y>>w;
		G2[x].pb(y,w),G2[y].pb(x,w);
	}
	for(int i=1;i<=n;i++)ans[i]=oo;
	dfs1(1),dfs2(1,1);
	redfs(1,0);
	szdfs(1,0);
	solve(1,tot);
	for(int i=1;i<=n;i++)cout<<ans[i]<<"\n";
	return 0;
}