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
/*input
3
1 2 10
2 3 20
*/
#ifdef UncleGrandpa
#include <prettyprint.hpp>
#endif
#include <bits/stdc++.h>
using namespace std;
#define sp ' '
#define endl '\n'
#define fi first
#define se second
#define int long long
#define loop(i,l,r) for(int i=(l); i<=(r); i++)
#define rloop(i,l,r) for(int i=(l); i>=(r); i--)
#define debug(x...) {cout << "[" << #x << "] ="; _co(x);}
void _co() {cout << endl;}
template<typename T, typename... Ts> void _co(const T& value, const Ts&... values) {cout << ' ' << value; _co(values...);}
template<typename T, typename... Ts> void co(const T& value, const Ts&... values) {cout << "deb: " << value; _co(values...);}
// change cout to cerr for debug in crash
const int N = 1e5 + 5;

struct Edge {
	int u, v, c;
};

int lazy[N];
struct dsu {
	vector<int> par, sz;
	void init(int n) {
		par.assign(n + 5, 0); sz.assign(n + 5, 1);
		iota(par.begin(), par.end(), 0);
	}
	int find(int x) {
		return par[x] == x ? x : find(par[x]);
	}
	void uni(int x, int y) {
		x = find(x); y = find(y);
		if (x != y) {
			if (sz[x] > sz[y]) swap(x, y);
			sz[y] += sz[x]; sz[x] = 0;
			par[x] = y;
		}
	}
} d;


int n;
vector<Edge> e;
signed main() {
	ios_base::sync_with_stdio(false); cin.tie(0);
	cin >> n; d.init(n);
	loop(i, 1, n - 1) {
		int u, v, c; cin >> u >> v >> c;
		e.push_back({u, v, c});
	}
	sort(e.begin(), e.end(), [&](Edge & X, Edge & Y) {
		return X.c > Y.c;
	});

	for (auto &cur : e) {
		int u = d.find(cur.u); int v = d.find(cur.v);
		int szu = d.sz[u]; int szv = d.sz[v];
		lazy[u] += cur.c * szv; lazy[v] += cur.c * szu;
		d.uni(u, v);
		if (d.par[u] == v) {
			lazy[u] -= lazy[v];
		}
		else {
			lazy[v] -= lazy[u];
		}
		// co(u, v, lazy[u], lazy[v]);
	}
	// loop(i, 1, n) cout << d.par[i] << sp;
	// cout << endl;
	loop(i, 1, n) {
		int res = lazy[i];
		int u = i;
		while (d.par[u] != u) {
			u = d.par[u];
			res += lazy[u];
		}
		cout << res << endl;
	}
}