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 <vector>
#include <iostream>
#include <algorithm>
using namespace std;
int n, a[100009], b[100009], c[100009], p[100009], id[100009]; long long ans[100009], pot[100009]; vector<int> g[100009];
int main() {
	ios::sync_with_stdio(false);
	cin >> n;
	for (int i = 0; i < n - 1; i++) cin >> a[i] >> b[i] >> c[i], a[i]--, b[i]--, p[i] = i;
	sort(p, p + n - 1, [](int i, int j) { return c[i] > c[j]; });
	for (int i = 0; i < n; i++) id[i] = i, g[i] = { i };
	for (int i = 0; i < n - 1; i++) {
		int va = a[p[i]], vb = b[p[i]], vc = c[p[i]], ga = id[va], gb = id[vb];
		int sza = g[ga].size(), szb = g[gb].size();
		if (sza < szb) swap(sza, szb), swap(va, vb), swap(ga, gb);
		pot[ga] += 1LL * szb * vc;
		for (int j : g[gb]) {
			ans[j] += pot[gb] + 1LL * sza * vc - pot[id[va]];
			g[ga].push_back(j);
		}
		pot[gb] = 0;
		for (int j : g[gb]) id[j] = ga;
		g[gb].clear();
	}
	for (int i = 0; i < n; i++) {
		cout << ans[i] + pot[id[0]] << endl;
	}
	return 0;
}