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
// In the name of God

#include <iostream>
#include <algorithm>
#include <fstream>
#include <vector>
#include <deque>
#include <assert.h>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <stdio.h>
#include <string.h>
#include <utility>
#include <math.h>
#include <bitset>
#include <iomanip>
#include <complex>

using namespace std;

#define rep(i, a, b) for (int i = (a), i##_end_ = (b); i < i##_end_; ++i)
#define debug(...) fprintf(stderr, __VA_ARGS__)
#define mp make_pair
#define x first
#define y second
#define pb push_back
#define SZ(x) (int((x).size()))
#define ALL(x) (x).begin(), (x).end()

template<typename T> inline bool chkmin(T &a, const T &b) { return a > b ? a = b, 1 : 0; }
template<typename T> inline bool chkmax(T &a, const T &b) { return a < b ? a = b, 1 : 0; }
template<typename T> inline bool smin(T &a, const T &b)   { return a > b ? a = b : a;    }
template<typename T> inline bool smax(T &a, const T &b)   { return a < b ? a = b : a;    }

typedef long long LL;
#define int long long
const int N = (int) 1e6 + 6, mod = (int) 0;
int add[N], res[N], sz[N], par[N];
vector<int> all[N];
pair<int, pair<int, int>> em[N];
void unite(int u, int v, int w) {
	u = par[u];
	v = par[v];
	if (u == v) return;
	if (sz[u] > sz[v]) swap(u, v);
	add[v] += w * sz[u];
	for (int x : all[u]) {
		par[x] = v;
		res[x] += add[u];
		res[x] -= add[v];
		res[x] += w * sz[v];
		all[v].pb(x);
	}
	sz[v] += sz[u];
}
int32_t main() {
	int n;
	cin >> n;
	for (int j = 0; j < n - 1; ++j) {
		int u, v, w;
		cin >> u >> v >> w;
		--u, --v;
		em[j] = mp(w, mp(u, v));
	}
	for (int j = 0; j < n; ++j) par[j] = j, sz[j] = 1, all[j].pb(j);
	sort(em, em + n - 1);
	reverse(em, em + n - 1);
	for (int j = 0; j < n - 1; ++j) {
		int w = em[j].x, u = em[j].y.x, v = em[j].y.y;
		unite(u, v, w);
	}
	for (int j = 0; j < n; ++j)
		cout << res[j] + add[par[j]] << '\n';
}







