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 all(vec) vec.begin(),vec.end()
#define mp make_pair
using namespace std;
using ll=long long;
using P=pair<ll,ll>;
const ll INF=1LL<<30;
const ll LINF=1LL<<62;
const double eps=1e-5;
template<typename T>void chmin(T &a,T b){a=min(a,b);};
template<typename T>void chmax(T &a,T b){a=max(a,b);};
int dx[4]={0,1,0,-1};
int dy[4]={1,0,-1,0};
struct UnionFind{
	vector<ll> par,siz,s;
	UnionFind(int n){
		s.resize(n,0);
		par.resize(n);
		siz.resize(n,1);
		for(int i=0;i<n;i++)par[i]=i;
	}
	int find(int x){
		return (par[x]==x?x:find(par[x]));
	}
	void unite(int u,int v,ll c){
		u=find(u);v=find(v);
		if(u==v)return;
		if(siz[u]<siz[v])swap(u,v);
		par[v]=u;
		s[u]+=siz[v]*c;
		s[v]+=siz[u]*c;
		s[v]-=s[u];
		siz[u]+=siz[v];
	}
	ll ans(int x){
		return (par[x]==x?s[x]:ans(par[x])+s[x]);
	}
};
int main(){
	int n;cin>>n;
	vector<pair<ll,P>> v;
	for(int i=0;i<n-1;i++){
		int a,b,c;cin>>a>>b>>c;--a;--b;
		v.push_back(mp(c,mp(b,a)));
	}
	sort(all(v));
	reverse(all(v));
	UnionFind uf(n);
	for(int i=0;i<n-1;i++){
		ll c=v[i].first;int a=v[i].second.first,b=v[i].second.second;
		uf.unite(a,b,c);
	}
	for(int i=0;i<n;i++){
		cout<<uf.ans(i)<<endl;
	}
}
