Snuke Festival 2017 will be held in a tree with N vertices numbered 1,2, ...,N. The i-th edge connects Vertex a_i and b_i, and has joyfulness c_i.

The staff is Snuke and N-1 black cats. Snuke will set up the headquarters in some vertex, and from there he will deploy a cat to each of the other N-1 vertices.

For each vertex, calculate the niceness when the headquarters are set up in that vertex. The niceness when the headquarters are set up in Vertex i is calculated as follows:

* Let X=0.
* For each integer j between 1 and N (inclusive) except i, do the following:
* Add c to X, where c is the smallest joyfulness of an edge on the path from Vertex i to Vertex j.
* The niceness is the final value of X.

Constraints

* 1 \leq N \leq 10^{5}
* 1 \leq a_i,b_i \leq N
* 1 \leq c_i \leq 10^{9}
* The given graph is a tree.
* All input values are integers.

Input

Input is given from Standard Input in the following format:


N
a_1 b_1 c_1
:
a_{N-1} b_{N-1} c_{N-1}


Output

Print N lines. The i-th line must contain the niceness when the headquarters are set up in Vertex i.

Examples

Input

3
1 2 10
2 3 20


Output

20
30
30


Input

15
6 3 2
13 3 1
1 13 2
7 1 2
8 1 1
2 8 2
2 12 2
5 2 2
2 11 2
10 2 2
10 9 1
9 14 2
4 14 1
11 15 2


Output

16
20
15
14
20
15
16
20
15
20
20
20
16
15
20


Input

19
19 14 48
11 19 23
17 14 30
7 11 15
2 19 15
2 18 21
19 10 43
12 11 25
3 11 4
5 19 50
4 11 19
9 12 29
14 13 3
14 6 12
14 15 14
5 1 6
8 18 13
7 16 14


Output

103
237
71
263
370
193
231
207
299
358
295
299
54
368
220
220
319
237
370
#include <bits/stdc++.h>
#define syosu(x) fixed<<setprecision(x)
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> P;
typedef pair<double,double> pdd;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<string> vs;
typedef vector<P> vp;
typedef vector<vp> vvp;
typedef vector<pll> vpll;
typedef pair<int,P> pip;
typedef vector<pip> vip;
const int inf=1<<30;
const ll INF=1ll<<60;
const double pi=acos(-1);
const double eps=1e-10;
const ll mod=1e9+7;
const int dx[4]={0,1,0,-1},dy[4]={1,0,-1,0};

int n;
vvp g;
vi vis,s;
vl a;

int Cdfs(int v,int p){
	s[v]=1;
	for(auto i:g[v]){
		int u=i.first;
		if(!vis[u]&&u!=p) s[v]+=Cdfs(u,v);
	}
	return s[v];
}

P Cdfs1(int v,int p,int S){
	P q={inf,0};
	int M=0,S_=S-1;
	for(auto i:g[v]){
		int u=i.first;
		if(!vis[u]&&u!=p){
			q=min(q,Cdfs1(u,v,S));
			M=max(M,s[u]);
			S_-=s[u];
		}
	}
	return min(q,{max(M,S_),v});
}

int Cent(int v){
	Cdfs(v,-1);
	return Cdfs1(v,-1,s[v]).second;
}

void dfs(int v,int p,ll e,vp& b){
	b.push_back({e,v});
	a[v]+=e;
	for(auto i:g[v]){
		int u=i.first;
		if(!vis[u]&&u!=p) dfs(u,v,min(e,(ll)i.second),b);
	}
}

void f(vp b,ll t){
	sort(b.begin(),b.end());
	ll S=b.size(),sum=0;
	for(int i=0;i<S;i++){
		ll e=b[i].first,v=b[i].second;
		a[v]+=(sum+e*(S-i-1))*t;
		sum+=e;
	}
}

void Rec(int v){
	int C=Cent(v);
	vp b;
	for(auto i:g[C]) if(!vis[i.first]){
		vp b_;
		dfs(i.first,C,i.second,b_);
		for(auto j:b_){
			a[C]+=j.first;
			b.push_back(j);
		}
		f(b_,-1);
	}
	f(b,1);
	vis[C]++;
	for(auto i:g[C]){
		int u=i.first;
		if(!vis[u]) Rec(u);
	}
}

int main(){
	cin>>n;
	g=vvp(n);
	a=vl(n);
	vis=s=vi(n);
	for(int i=1;i<n;i++){
		int u,v,c;
		cin>>u>>v>>c;
		u--;v--;
		g[u].push_back({v,c});
		g[v].push_back({u,c});
	}
	Rec(0);
	for(auto i:a) cout<<i<<endl;
}