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 "climits"
#include "list"
#include "queue"
#include "stack"
#include "set"
#include "functional"
#include "algorithm"
#include "string"
#include "map"
#include "unordered_map"
#include "unordered_set"
#include "iomanip"
#include "cmath"
#include "random"
#include "bitset"
#include "cstdio"
#include "numeric"
#include "cassert"
#include "ctime"

using namespace std;

constexpr long long int MOD = 1000000007;
//constexpr int MOD = 1000000007;
//constexpr int MOD = 998244353;
//constexpr long long int MOD = 998244353;
constexpr long double EPS = 1e-8;

long long int N, M, K, L, R, H, W;
//int N, M, K, L, R, H, W;

class UnionFind {
	vector<int>parent;
public:
	vector<int>sz;
	UnionFind(int num) {
		num++;
		parent.resize(num);
		sz.resize(num);
		for (int i = 0; i < N; i++)sz[i] = 1;
		for (int i = 0; i < num; i++) {
			parent[i] = i;
		}
	}
	int Find(int node) {
		if (parent[node] == node)return node;
		else return parent[node] = Find(parent[node]);
	}
	void Unite(int u, int v) {
		u = Find(u);
		v = Find(v);
		if (u == v)return;
		if (u < v)swap(u, v);
		parent[v] = u;
		sz[u] += sz[v];
	}
	bool Check_Same(int u, int v) {
		return Find(u) == Find(v);
	}
};

struct Edge {
	int a, b, cost;
	bool operator<(const Edge&n)const {
		return cost < n.cost;
	}
	Edge(const int aa, const int bb, const int cc) {
		a = aa, b = bb, cost = cc;
	}
};

void Search(vector<long long int>&ans, vector<vector<pair<int, long long int>>>&edge, int node = N * 2 - 2) {
	ans[node] = M;
	for (auto i : edge[node]) {
		M += i.second;
		Search(ans, edge, i.first);
		M -= i.second;
	}
}

int main() {
	ios::sync_with_stdio(false);
	cin.tie(0);

	cin >> N;
	vector<Edge>edge;
	for (int i = 1; i < N; i++) {
		cin >> L >> R >> K;
		L--, R--;
		edge.emplace_back(L, R, K);
	}
	sort(edge.begin(), edge.end());
	reverse(edge.begin(), edge.end());
	vector<vector<pair<int, long long int>>>t_edge(N * 2 - 1);
	int cnt = N;
	UnionFind uf(N * 2 - 1);
	for (auto i : edge) {
		int a = uf.Find(i.a);
		int b = uf.Find(i.b);
		t_edge[cnt].emplace_back(a, 1LL * uf.sz[uf.Find(i.b)] * i.cost);
		t_edge[cnt].emplace_back(b, 1LL * uf.sz[uf.Find(i.a)] * i.cost);
		uf.Unite(cnt, i.b);
		uf.Unite(cnt, i.a);
		cnt++;
	}
	vector<long long int>ans(N*2-1);
	Search(ans, t_edge);
	for (int i = 0; i < N; i++)cout << ans[i] << endl;
}