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<tuple>
#include<stdlib.h>
#include<iostream>
#include<algorithm>
#include<queue>
#include<set>
#include<map>
#include<string>
#include<vector>
 
using namespace std;
 
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll, int> pli;
typedef tuple<int,int,int> t3;
 
const int MX = 1<<19;
 
vector<int> C[MX];
int rv[MX];
int N;
ll ans[MX], add[MX];
 
int main()
{
	scanf("%d", &N);
	for(int i = 1; i <= N; i++){
		rv[i] = i;
		C[i].push_back(i);
	}
	vector<t3> E;
	for(int i = 1; i < N; i++){
		int a, b, c;
		scanf("%d%d%d", &a, &b, &c);
		E.emplace_back(c, a, b);
	}
	sort(E.begin(), E.end());
	reverse(E.begin(), E.end());
	for(t3 e : E){
		int a, b, c;
		tie(c, a, b) = e;
		int p = rv[a], q = rv[b];
		if( C[p].size() > C[q].size() ) swap(p, q);
		int x = C[p].size(), y = C[q].size();
		for(int e : C[p]){
			C[q].push_back(e);
			rv[e] = q;
			ans[e] += add[p] + (ll)c * y - (ll)c * x - add[q];
		}
		add[q] += (ll)c * x;
	}
	for(int i = 1; i <= N; i++) printf("%lld\n", ans[i] + add[rv[i]]);
}