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 <cstdio>
#include <cstring>
#include <string>
#include <iostream>
#include <cmath>
#include <bitset>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <deque>
#include <algorithm>
#include <complex>
#define MOD 1000000007LL

using namespace std;
typedef long long int ll;
typedef pair<ll, int> Pl;
typedef pair<int, int> P;
typedef pair<ll, P> Pll;
typedef pair<P, P> PP;

int par[100002];
int rk[100002];
int size[100002];
vector<PP> g[100002];
vector<Pll> cab;
 
void init(int n){
	for(int i=0; i<n; i++){
		par[i]=i;
		size[i]=1;
	}
}
 
int find(int x){
	if(par[x]==x){
		return x;
	}else{
		return find(par[x]);
	}
}
 
void unite(int x, int y, int i){
	x=find(x);
	y=find(y);
	if(x==y) return;
	if(rk[x]<rk[y]){
		par[x]=y;
		g[y].push_back(PP(P(i, x), P(size[x], size[y])));
		size[y]+=size[x];
	}else{
		par[y]=x;
		g[x].push_back(PP(P(i, y), P(size[y], size[x])));
		size[x]+=size[y];
		if(rk[x]==rk[y]) rk[x]++;
	}
}
 
bool same(int x, int y){
	return find(x)==find(y);
}

int num[100002];
ll ans[100002];
int ct;

void eulertour(int x){
	ct++;
	num[x]=ct;
	for(int i=0; i<g[x].size(); i++){
		int y=g[x][i].first.second;
		eulertour(y);
	}
}

bool used[100002];

void add(int x){
	used[x]=1;
	for(int i=0; i<g[x].size(); i++){
		int y=g[x][i].first.second;
		ll s1=(ll)g[x][i].second.first, s2=(ll)g[x][i].second.second;
		ll c=cab[g[x][i].first.first].first;
		ans[num[x]]+=(s1*c);
		ans[num[x]+s2]-=(s1*c);
		ans[num[y]]+=(s2*c);
		ans[num[y]+s1]-=(s2*c);
		add(y);
	}
}


int main()
{
	int n;
	cin>>n;
	init(n);
	for(int i=0; i<n-1; i++){
		int a, b; ll c;
		cin>>a>>b>>c;
		a--; b--;
		cab.push_back(Pll(c, P(a, b)));
	}
	sort(cab.begin(), cab.end(), greater<Pll>());
	for(int i=0; i<n-1; i++){
		ll c=cab[i].first;
		int a=cab[i].second.first, b=cab[i].second.second;
		unite(a, b, i);
	}
	fill(num, num+n, -1);
	ct=-1;
	for(int i=0; i<n; i++){
		if(num[i]>=0) continue;
		i=find(i);
		eulertour(i);
	}
	for(int i=0; i<n; i++){
		if(used[i]) continue;
		i=find(i);
		add(i);
	}
	for(int i=1; i<n; i++){
		ans[i]+=ans[i-1];
	}
	for(int i=0; i<n; i++){
		cout<<ans[num[i]]<<endl;
	}
	return 0;
}