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 <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <string>
#include <sstream>
#include <complex>
#include <vector>
#include <list>
#include <queue>
#include <deque>
#include <stack>
#include <map>
#include <set>
using namespace std;
 
#define mod 1000000007
#define FOR(x,to) for(int x=0;x<(to);x++)
#define FORR(x,arr) for(auto& x:arr)
#define ALL(a) (a.begin()),(a.end())
#define ZERO(a) memset(a,0,sizeof(a))
#define MINUS(a) memset(a,0xff,sizeof(a))
#define long long long
inline int rei(){int x;cin>>x;return x;}
inline long rel(){long x;cin>>x;return x;}
inline string res(){string x;cin>>x;return x;}
//------------------------------------------------------- 
struct UnionFind{
    vector<int> par;
    UnionFind(int N){
        par.resize(N);
        for(int i=0;i<N;i++){
            par[i] = i;
        }
    }
    void Union(int x,int y){
        par[Get(x)] = Get(y); 
    }
    bool Same(int x,int y){
        return Get(x) == Get(y);
    }
    int Get(int x){
        if(x != par[x]){
            par[x] = Get(par[x]);
        }
        return par[x];
    }
};
vector<tuple<long,int,int>> Edge;
pair<int,int> G[199999];
int To[100000];
long ans[100000];
int child[199999];
long cost[199999];
void Calc(){
	int N = rei();
	for(int i=0;i<N-1;i++){
		To[i] = i;
		int a = rei()-1;
		int b = rei()-1;
		long c = rel();
		Edge.push_back({c,a,b});
	}
	To[N-1] = N-1;
	sort(Edge.begin(),Edge.end());
	UnionFind U(N);
	int d = N;
	for(int i=N-2;i>=0;i--){
		G[d].first = To[U.Get(get<1>(Edge[i]))];
		G[d].second = To[U.Get(get<2>(Edge[i]))];
		U.Union(get<1>(Edge[i]),get<2>(Edge[i]));
		cost[d] = get<0>(Edge[i]);
		To[U.Get(get<1>(Edge[i]))] = d++;
	}
	stack<int> sp;
	sp.push(d-1);
	while(!sp.empty()){
		int v = sp.top();
		sp.pop();
		if(v >= d){
			v -= d;
			child[v] = 1;
			if(v >= N){
				child[v] += child[G[v].first] + child[G[v].second];
			}
		}
		else{
			sp.push(v+d);
			if(v >= N){
				sp.push(G[v].first);
				sp.push(G[v].second);
			}
		}
	}
	for(int i=0;i<d;i++){
		child[i] = (child[i]+1) / 2;
	}
	stack<pair<int,long>> sp2;
	sp2.push({d-1,0});
	while(!sp2.empty()){
		int v = sp2.top().first;
		long c = sp2.top().second;
		sp2.pop();
		if(v < N){
			ans[v] = c;
		}
		else{
			sp2.push({G[v].first,c + child[G[v].second]*cost[v]});
			sp2.push({G[v].second,c + child[G[v].first]*cost[v]});
		}
	}
	for(int i=0;i<N;i++){
		cout << ans[i] << endl;
	}
}
int main(int argc,char** argv){
	ios::sync_with_stdio(false), cin.tie(0);
	cout.tie(0); Calc(); return 0;
}