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>
using namespace std;
const int N = 1e5 + 5;
struct edge{
	int u,v;
	long long w;
	edge(int a,int b,long long c):u(a),v(b),w(c){}
};
long long lazy[N],res[N];
int n,p[N];
vector<vector<int> > sets;
vector<edge> E;
bool cmp(edge &a,edge &b){
	return a.w<b.w;
}
void dsu(int i,int j,long long w){
	for(int k=0;k<sets[i].size();k++){
		res[sets[i][k]]+=lazy[i]-lazy[j]+w*sets[j].size();
		p[sets[i][k]]=j;
	}
	for(int k=0;k<sets[i].size();k++){
		sets[j].push_back(sets[i][k]);
	}
	sets[i].clear();
}
int main(){
	scanf("%d",&n);
	sets.assign(n+1,vector<int>());
	for(int i=1;i<=n;i++){
		p[i]=i;
		sets[i].push_back(i);
	}
	for(int i=1;i<n;i++){
		int u,v;
		long long w;
		cin>>u>>v>>w;
		E.push_back(edge(u,v,w));
	}
	sort(E.begin(),E.end(),cmp);
	reverse(E.begin(),E.end());
	for(int i=0;i<E.size();i++){
		int u=p[E[i].u];
		int v=p[E[i].v];
		int w=E[i].w;
		if(sets[u].size()>sets[v].size()){
			swap(u,v);
		}
		lazy[v]+=w*sets[u].size();
		dsu(u,v,w);
	}
	for(int i=1;i<=n;i++){
		cout<<res[i]+lazy[p[i]]<<"\n";
	}
}