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 rep(i,n) for(int i=0;i<(int)(n);i++)
#define rep1(i,n) for(int i=1;i<=(int)(n);i++)
#define all(c) c.begin(),c.end()
#define pb push_back
#define fs first
#define sc second
#define show(x) cout << #x << " = " << x << endl
#define chmin(x,y) x=min(x,y)
#define chmax(x,y) x=max(x,y)
using namespace std;
template<class S,class T> ostream& operator<<(ostream& o,const pair<S,T> &p){return o<<"("<<p.fs<<","<<p.sc<<")";}
template<class T> ostream& operator<<(ostream& o,const vector<T> &vc){o<<"sz = "<<vc.size()<<endl<<"[";for(const T& v:vc) o<<v<<",";o<<"]";return o;}

struct UnionFind{
	vector<int> par,rank,r;
	UnionFind(int N){
		par.assign(N,0);
		rank.assign(N,0);
		r.assign(N,0);
		rep(i,N) par[i]=i,r[i]=i;
	}
	int find(int x){
		if(par[x]==x) return x;
		return par[x]=find(par[x]);
	}
	bool same(int x,int y){
		return find(x)==find(y);
	}
	void unite(int x,int y){
		x=find(x),y=find(y);
		if(x==y) return;
		if(rank[x]<rank[y]){
			par[x]=y;
			chmax(r[y],r[x]);
		}else{
			par[y]=x;
			chmax(r[x],r[y]);
			if(rank[x]==rank[y]) rank[x]++;
		}
	}
};

using ll = long long;
using P = pair<int,int>;
using PP = pair<ll,P>;
int N;
vector<vector<int>> G;
vector<ll> cs;
vector<int> sz;
vector<ll> ans;

void dfs(int v,ll d){
	if(v<N){
		ans[v] = d;
		return;
	}
	int x = G[v][0], y = G[v][1];
	ll c = cs[v];
	dfs(x,d+c*sz[y]);
	dfs(y,d+c*sz[x]);
}
int main(){
	cin>>N;
	vector<PP> es;
	rep(i,N-1){
		int a,b,c;
		cin>>a>>b>>c;
		a--,b--;
		es.pb(PP(c,P(a,b)));
	}
	sort(all(es),greater<PP>());
	cs.resize(N*2-1);
	sz.resize(N*2-1);
	G.resize(N*2-1);
	UnionFind UF(N*2-1);

	rep(i,N) sz[i] = 1;

	int I = N;
	for(auto e:es){
		ll c = e.fs;
		int x = e.sc.fs, y = e.sc.sc;
		x = UF.r[UF.find(x)], y = UF.r[UF.find(y)];
		UF.unite(I,x);
		UF.unite(I,y);
		G[I].pb(x);
		G[I].pb(y);
		cs[I] = c;
		sz[I] = sz[x]+sz[y];
		I++;
	}
	ans.resize(N);
	dfs(I-1,0);
	rep(i,N) cout<<ans[i]<<endl;
}