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;

#define int long long
#define pb push_back

struct data{
	int x , y , val;
};
const int N = 1e5 + 1;

int n , pa[N] , ans[N] ,lazy[N];
vector<data> inp;
vector<int> par[N];

bool how_sort(data a , data b){
	return a.val > b.val;
}
signed main(){
	cin >> n;
	pa[n] = n; par[n].pb(n);
	for(int i = 1 ; i < n ; ++ i){
		pa[i] = i ; par[i].pb(i);
		int u , v , w;
		cin >> u >> v >> w;
		inp.pb( data{ u , v , w });
	}	
	sort(inp.begin() , inp.end() , how_sort);
	for(int i = 0 ; i < inp.size() ; ++ i){
		int u = inp[i].x , v = inp[i].y , w = inp[i].val; 
		if(par[pa[u]].size() > par[pa[v]].size()) swap(u,v);
		int z = pa[u];
		lazy[pa[v]] += w * par[z].size();
		int add = w * par[pa[v]].size();
		for(int i = 0 ;i < par[z].size() ; ++ i){
			int k = par[z][i];
			pa[k] = pa[v];
			par[pa[v]].pb(k);
			ans[k] += lazy[z] - lazy[pa[v]] + add;
		}
	}
	for(int i = 0 ;i < par[pa[1]].size() ; ++ i){
		int k = par[pa[1]][i];
		ans[k] += lazy[pa[1]];
	}
	for(int i = 1 ; i <= n ; ++ i)
		cout << ans[i] << "\n";
}