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 <bits/stdc++.h>
#define mod 1000000007
#define mod998 998244353
#define sp ' '
#define intmax 2147483647
#define llmax 9223372036854775807
#define mkp make_pair
typedef long long ll;
using namespace std;

int N, a, b, c, t[100000];
ll s[100000];
priority_queue<pair<int, pair<int, int>>>q;

int par(int x) {
	if (t[x] < 0)return x;
	return par(t[x]);
}

void func(int x, int y, ll c) {
	x = par(x);
	y = par(y);
	if (t[x] < t[y]) {
		s[x] += -t[y] * c;
		s[y] += -t[x] * c - s[x];
		t[x] += t[y];
		t[y] = x;
	}
	else {
		s[y] += -t[x] * c;
		s[x] += -t[y] * c - s[y];
		t[y] += t[x];
		t[x] = y;
	}
}

ll calc(int i) {
	ll a = 0;
	while (i >= 0) {
		a += s[i];
		i = t[i];
	}
	return a;
}

int main() {
	cin >> N;
	memset(t, -1, sizeof t);
	for (int i = 1; i < N; ++i) {
		cin >> a >> b >> c;
		--a;
		--b;
		q.push(mkp(c, mkp(a, b)));
	}
	for (int i = 1; i < N; ++i) {
		func(q.top().second.first, q.top().second.second, q.top().first);
		q.pop();
	}
	for (int i = 0; i < N; ++i) {
		cout << calc(i) << endl;
	}
}