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<cstdio>
#include<algorithm>
#include<vector>
using namespace std;
#define pii pair<int,int>
#define pil pair<int, long long>
int n, UF[101000];
vector<int>G[101000];
vector<pii>H[101000];
vector<pil>U[101000];
vector<long long>S[101000];
struct point {
	int a, b, c;
	bool operator<(const point &p)const {
		return c < p.c;
	}
}w[101000];
int cnt = 0;
int Find(int a) {
	if (a == UF[a])return a;
	return Find(UF[a]);
}
void Merge(int a, int b, int c) {
	a = Find(a), b = Find(b);
	cnt++;
	if (G[a].size() < G[b].size())swap(a, b);
	int i;
	for (i = 0; i < G[b].size(); i++) {
		int x = G[b][i];
		H[x].push_back({ a,cnt });
	}
	U[a].push_back({ cnt, 1ll * G[b].size() * c });
	U[b].push_back({ cnt, 1ll * G[a].size() * c });
	for (i = 0; i < G[b].size(); i++)G[a].push_back(G[b][i]);
	UF[b] = a;
}
int main() {
	int i, j;
	scanf("%d", &n);
	for (i = 1; i <= n; i++) {
		UF[i] = i;
		G[i].push_back(i);
		H[i].push_back({ i,0 });
	}
	for (i = 1; i < n; i++) {
		scanf("%d%d%d", &w[i].a, &w[i].b, &w[i].c);
	}
	sort(w + 1, w + n);
	for (i = n-1; i >=1; i--){

		Merge(w[i].a, w[i].b, w[i].c);
	}
	for (i = 1; i <= n; i++) {
		S[i].resize(U[i].size() + 1);
		for (j = 0; j < U[i].size(); j++) {
			S[i][j + 1] = S[i][j] + U[i][j].second;
		}
	}
	for (i = 1; i <= n; i++) {
		long long r = 0;
		for (j = 0; j < H[i].size(); j++) {
			int x = H[i][j].first, t = H[i][j].second;
			pil tp = { t + 1, 0ll };
			int p = lower_bound(U[x].begin(), U[x].end(), tp) - U[x].begin(), sz = U[x].size();
			r += S[x][sz] - S[x][p];
		}
		printf("%lld\n", r);
	}
}