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 <vector>
#include <algorithm>
#include <utility>
#define llint long long

using namespace std;

struct Node{
	int left, right;
	llint val;
	Node(){
		left = right = -1;
	}
	Node(int a, int b, llint c){
		left = a, right = b, val = c;
	}
};

int N;
int id[100005];
vector< pair< int, pair<int, int> > > edge;
vector<Node> tree;
int num[200005];
llint ans[100005];

int parent[100005];
void init()
{
	for(int i = 1; i <= N; i++) parent[i] = i;
}
int root(int i)
{
	if(parent[i] == i) return i;
	return parent[i] = root(parent[i]);
}
bool same(int i, int j)
{
	return root(i) == root(j);
}
void unite(int i, int j)
{
	int root_i = root(i), root_j = root(j);
	if(root_i == root_j) return;
	parent[root_i] = root_j;
}

int dfs(int v)
{
	int ret = 0;
	if(tree[v].left != -1){
		ret += dfs(tree[v].left);
		ret += dfs(tree[v].right);
	}
	else ret = 1;
	return num[v] = ret;
}

void dfs2(int v, llint sum)
{
	if(tree[v].left != -1){
		dfs2(tree[v].left, sum + num[tree[v].right] * tree[v].val);
		dfs2(tree[v].right, sum + num[tree[v].left] * tree[v].val);
	}
	else{
		ans[v+1] = sum;
	}
}

int main(void)
{
	cin >> N;
	init();
	
	for(int i = 1; i <= N; i++) id[i] = i-1;
	for(int i = 0; i < N; i++) tree.push_back( Node() );
	
	int a, b;
	llint c;
	for(int i = 0; i < N-1; i++){
		cin >> a >> b >> c;
		edge.push_back(make_pair(c, make_pair(a, b)));
	}
	sort(edge.begin(), edge.end());
	reverse(edge.begin(), edge.end());
	
	for(int i = 0; i < edge.size(); i++){
		a = edge[i].second.first, b = edge[i].second.second, c = edge[i].first;
		tree.push_back(Node());
		tree.back().left = id[root(a)];
		tree.back().right = id[root(b)];
		tree.back().val = c;
		unite(a, b);
		id[root(a)] = tree.size()-1;
	}
	
	int s = id[root(1)];
	dfs(s);
	dfs2(s, 0);
	
	for(int i = 1; i <= N; i++){
		cout << ans[i] << endl;
	}
	return 0;
}