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>
using namespace std;

typedef pair<int, int> pii;
typedef long long ll;
typedef vector<int> vi;

#define pb push_back
#define eb emplace_back
#define mp make_pair
#define fi first
#define se second
#define rep(i,n) rep2(i,0,n)
#define rep2(i,m,n) for(int i=m;i<(n);i++)
#define ALL(c) (c).begin(),(c).end()

vector<int> i2g;          // i2g[i] := アイテム i の所属するグループの番号
vector<vector<int>> g2i;  // g2i[g] := グループ g に所属するアイテムたち

void init(int n) {
	i2g.resize(n);
	g2i.resize(n);
	for (int i = 0; i < n; ++i) {
    // 最初はアイテム i はグループ i に所属
		i2g[i] = i;
		g2i[i].assign(1, i);
	}
}

ll all[100010];
ll ans[100010];
int N;
vector<pair<int,pii>> vec;

void merge(int ia, int ib, ll ct) {
	if (g2i[i2g[ia]].size() < g2i[i2g[ib]].size()) {
		swap(ia, ib);
	}

	int ga = i2g[ia], gb = i2g[ib];

	ll sa = g2i[ga].size(), sb = g2i[gb].size();
	for (int j : g2i[gb]) {
		i2g[j] = ga;
		ans[j] += all[gb];
		ans[j] -= (sb-sa) * ct;
		ans[j] -= all[ga];
	}

	all[ga] += sb * ct; 
	all[gb] = 0;

	g2i[ga].insert(g2i[ga].end(), g2i[gb].begin(), g2i[gb].end());
	g2i[gb].clear();
}

int main() {
	cin >> N;

	rep(i, N-1) {
		int a, b, c;
		cin >> a >> b >> c;
		--a; --b;
		vec.eb(c, mp(a, b));
	}

	sort(ALL(vec));
	reverse(ALL(vec));

	init(N);

	for (auto t:vec) {
		int a = t.se.fi, b = t.se.se, c = t.fi;
		merge(a, b, c);
	}

	rep(i, N) {
		cout << ans[i] + all[i2g[i]] << endl;
	}

	return 0;
}