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
/**
 *    author:  tourist
 *    created: 26.11.2019 11:55:10       
**/
#include <bits/stdc++.h>

using namespace std;

class dsu {
 public:
  vector<int> p;
  int n;

  dsu(int _n) : n(_n) {
    p.resize(n);
    iota(p.begin(), p.end(), 0);
  }

  inline int get(int x) {
    return (x == p[x] ? x : (p[x] = get(p[x])));
  }

  inline bool unite(int x, int y) {
    x = get(x);
    y = get(y);
    if (x != y) {
      p[x] = y;
      return true;
    }
    return false;
  }
};

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n;
  cin >> n;
  vector<tuple<int, int, int>> e(n - 1);
  for (int i = 0; i < n - 1; i++) {
    int x, y, z;
    cin >> x >> y >> z;
    --x; --y;
    e[i] = make_tuple(z, x, y);
  }
  sort(e.rbegin(), e.rend());
  vector<int> info(n);
  for (int i = 0; i < n; i++) {
    info[i] = i;
  }
  vector<int> sz(n, 1);
  vector<int> pv(2 * n, -1);
  vector<long long> pe(2 * n, 0);
  dsu d(n);
  int cnt = n;
  for (auto& ee : e) {
    int z = get<0>(ee);
    int x = get<1>(ee);
    int y = get<2>(ee);
    x = d.get(x);
    y = d.get(y);
    pv[info[x]] = cnt;
    pv[info[y]] = cnt;
    pe[info[x]] = sz[y] * 1LL * z;
    pe[info[y]] = sz[x] * 1LL * z;
    info[y] = cnt;
    sz[y] += sz[x];
    d.p[x] = y;
    ++cnt;
  }
  for (int i = cnt - 2; i >= 0; i--) {
    pe[i] += pe[pv[i]];
  }
  for (int i = 0; i < n; i++) {
    cout << pe[i] << '\n';
  }
  return 0;
}
