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
#ifndef LOCAL
#pragma GCC optimize "-O3"
#endif
#include <bits/stdc++.h>

typedef long long ll;
typedef long long llong;
typedef long double ld;
typedef unsigned long long ull;

using namespace std;

/*
ll pw(ll a, ll b) {
	ll ans = 1; while (b) {
		while (!(b & 1)) b >>= 1, a = (a * a) % MOD;
		ans = (ans * a) % MOD, --b;
	} return ans;
}
*/
const int MAXN = 120000;

int n;

vector<tuple<ll, int, int> > ed;
int p[MAXN];

int sz[MAXN];
ll dd[MAXN];

int get(int a) {
	if (p[a] == a)
		return a;
	return get(p[a]);
}

ll get2(int a) {
	if (p[a] == a)
		return dd[a];
	return dd[a] + get2(p[a]);
}

int main() {
	cin >> n;
	for (int i = 0; i < n - 1; ++i) {
		int a, b;
		ll c;
		cin >> a >> b >> c;
		--a, --b;
		ed.push_back(make_tuple(c, a, b));
	}
	sort(ed.begin(), ed.end());
	reverse(ed.begin(), ed.end());
	for (int i = 0; i < n; ++i) {
		p[i] = i, sz[i] = 1, dd[i] = 0;
	}
	for (int i = 0; i < ed.size(); ++i) {
		int a, b;
		ll c;
		tie(c, a, b) = ed[i];
		a = get(a);
		b = get(b);
		dd[a] += sz[b] * c;
		dd[b] += sz[a] * c;
		if (sz[a] > sz[b])
			swap(a, b);
		dd[a] -= dd[b];
		sz[b] += sz[a];
		p[a] = b;
	}
	for (int i = 0; i < n; ++i) {
		cout << get2(i) << "\n";
	}
	return 0;
}


