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<stdio.h>
#include<math.h>
#include<algorithm>
#include<queue>
#include<deque>
#include<stack>
#include<string>
#include<string.h>
#include<vector>
#include<set>
#include<map>
#include<bitset>
#include<stdlib.h>
#include<cassert>
#include<time.h>
#include<bitset>
using namespace std;
const long long mod=1000000007;
const long long inf=mod*mod;
const long long d2=(mod+1)/2;
const long double EPS=1e-9;
const long double PI=acos(-1.0);
int ABS(int a){return max(a,-a);}
long long ABS(long long a){return max(a,-a);}
long double ABS(long double a){return max(a,-a);}
vector<pair<int,int> > g[110000];
int UF[110000];
vector<pair<int,int> >G[210000];
int num[210000];
int FIND(int a){
	if(UF[a]<0)return a;
	return UF[a]=FIND(UF[a]);
}
void UNION(int a,int b){
	a=FIND(a);b=FIND(b);if(a==b)return;
	//if(UF[a]>UF[b])swap(a,b);
	UF[a]+=UF[b];
	UF[b]=a;
}
pair<int,pair<int,int> > edge[110000];
long long ans[110000];
int sz[210000];
int n;
int calc(int a){
	if(a<n){
		sz[a]++;
	}
	for(int i=0;i<G[a].size();i++){
		sz[a]+=calc(G[a][i].first);
	}
	return sz[a];
}
void dfs(int a,long long b){
	if(G[a].size()==2){
		dfs(G[a][0].first,b+(long long)sz[G[a][1].first]*G[a][0].second);
		dfs(G[a][1].first,b+(long long)sz[G[a][0].first]*G[a][1].second);
	}else{
		ans[a]=b;
	}
}
int main(){
	int a;scanf("%d",&a);n=a;
	for(int i=0;i<a;i++){
		num[i]=i;
	}

	for(int i=0;i<a;i++)UF[i]=-1;
	for(int i=0;i<a-1;i++){
		int p,q,r;scanf("%d%d%d",&p,&q,&r);p--;q--;
		edge[i]=make_pair(r,make_pair(p,q));
		g[p].push_back(make_pair(q,r));
		g[q].push_back(make_pair(p,r));
	}
	std::sort(edge,edge+a-1);
	reverse(edge,edge+a-1);
	for(int i=0;i<a-1;i++){
		int L=edge[i].second.first;
		int R=edge[i].second.second;
		if(UF[FIND(L)]>UF[FIND(R)])swap(L,R);
		
		G[a+i].push_back(make_pair(num[FIND(L)],edge[i].first));
		G[a+i].push_back(make_pair(num[FIND(R)],edge[i].first));
		UNION(L,R);
		num[FIND(L)]=a+i;
	}
	calc(a+a-2);
	dfs(a+a-2,0LL);
	for(int i=0;i<a;i++)printf("%lld\n",ans[i]);
}
