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;

const int N = 100005;

struct Edge {
	int u, v, w;

	Edge (int u, int v, int w) :
		u(u), v(v), w(w) {}

	bool operator < (const Edge& rhs) const {
		return w > rhs.w;
	}
};

int n, par[N];
long long res[N];
long long val[N];
vector<Edge> E;
vector<int> comp[N];

int find(int u) {
	return (u == par[u]) ? u : par[u] = find(par[u]);
}

void join(int u, int v, int w) {
	u = find(u), v = find(v);
	if (comp[u].size() > comp[v].size()) swap(u, v);
	int szu = comp[u].size(), szv = comp[v].size();
	val[v] += 1LL * szu * w;
	for (auto i : comp[u]) {
		res[i] += val[u] + 1LL * szv * w - val[v], comp[v].push_back(i);
	}
	val[u] = 0, comp[u].clear(), par[u] = v;
}

int main() {
	ios::sync_with_stdio(false);
	cin >> n;
	for (int i = 1; i <= n; ++i) {
		par[i] = i, comp[i].push_back(i);
	}
	for (int i = 1; i < n; ++i) {
		int u, v, w; cin >> u >> v >> w;
		E.push_back(Edge(u, v, w));
	}
	sort(E.begin(), E.end());
	for (auto i : E) join(i.u, i.v, i.w);
	for (int i = 1; i <= n; ++i) {
		res[i] += val[find(i)]; cout << res[i] << '\n';
	}
}