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;
using lint = long long int;
template<class T = int> using V = vector<T>;
template<class T = int> using VV = V< V<T> >;
template<class T> void assign(V<T>& v, int n, const T& a = T()) { v.assign(n, a); }
template<class T, class... U> void assign(V<T>& v, int n, const U&... u) { v.resize(n); for (auto&& i : v) assign(i, u...); }

struct QU {
  V<> par, rank, _size;
  V<lint> res;

  QU(int n) : par(n), rank(n), _size(n, 1), res(n) { 
    iota(par.begin(), par.end(), 0);
  }

  int find(int a) {
    if (par[a] == a) return a;
    return find(par[a]);
  }

  bool same(int a, int b) { return find(a) == find(b); }

  int size(int a) { return _size[find(a)]; }

  void unite(int a, int b, lint c) {
    a = find(a), b = find(b);
    if (a == b) return;
    if (rank[a] < rank[b]) {
      res[b] += _size[a] * c;
      res[a] += _size[b] * c - res[b];
      par[a] = b;
      _size[b] += _size[a];
    } else {
      res[a] += _size[b] * c;
      res[b] += _size[a] * c - res[a];
      par[b] = a;
      _size[a] += _size[b];
    }
    if (rank[a] == rank[b]) rank[a]++;
  }
};

int main() {
  cin.tie(NULL); ios::sync_with_stdio(false);
  int n; cin >> n;
  struct edge { int from, to; lint c; };
  V<edge> es(n - 1);
  for (int i = 0; i < n - 1; i++) {
    int a, b, c; cin >> a >> b >> c, a--, b--;
    es[i] = {a, b, c};
  }
  sort(es.begin(), es.end(), [](edge x, edge y) { return x.c > y.c; });
  QU qu(n);
  for (auto&& e : es) qu.unite(e.from, e.to, e.c);
  VV<> ch(n);
  int root = qu.find(0);
  for (int v = 0; v < n; v++) if (v != root) ch[qu.par[v]].push_back(v);
  queue<int> que;
  que.push(root);
  while (!que.empty()) {
    int v = que.front(); que.pop();
    for (int w : ch[v]) {
      qu.res[w] += qu.res[v]; que.push(w);
    }
  }
  for (int i = 0; i < n; i++) cout << qu.res[i] << '\n';
}