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 <iostream>
#include <algorithm>
#include <vector>
#include <tuple>

using namespace std;

struct node {
  long long lazy = 0;
  node *l = nullptr;
  node *r = nullptr;
  int label = -1;
};

struct DSU {
  std::vector<int> dat;
  std::vector<node *> dat2;

  DSU(int n) : dat(n, -1), dat2(n) {
    for (int i = 0; i < n; i++) {
      dat2[i] = new node();
      dat2[i]->label = i;
    }
  }

  int find(int u) {
    if (dat[u] < 0) return u;
    return dat[u] = find(dat[u]);
  }

  void unite(int u, int v) {
    u = find(u);
    v = find(v);
    if (u == v) {
      cout << "ng" << endl;
    }
    if (-dat[u] < -dat[v]) std::swap(u, v);
    node *pu = dat2[u];
    node *pv = dat2[v];
    dat2[u] = new node();
    dat2[u]->l = pu;
    dat2[u]->r = pv;
    dat[u] += dat[v];
    dat[v] = u;
  }

  node *find_parent(int u) {
    u = find(u);
    return dat2[u];
  }

  int find_size(int u) {
    return -dat[find(u)];
  }
};

long long ans[202020];

void dfs(node *x, long long lz) {
  if (!x) return;
  lz += x->lazy;
  if (x->label != -1) {
    ans[x->label] = lz;
  }

  dfs(x->l, lz);
  dfs(x->r, lz);
}

int main() {
  int n;
  cin >> n;

  vector<tuple<int, int, int>> es;
  for (int i = 0; i < n - 1; i++) {
    int u, v, w;
    cin >> u >> v >> w;
    u--;
    v--;
    es.emplace_back(w, u, v);
  }

  sort(es.begin(), es.end());
  reverse(es.begin(), es.end());

  DSU dsu(n);
  for (auto e : es) {
    int w, u, v;
    tie(w, u, v) = e;
    long long x = dsu.find_size(u);
    long long y = dsu.find_size(v);
    node *px = dsu.find_parent(u);
    node *py = dsu.find_parent(v);
    px->lazy += y * w;
    py->lazy += x * w;
    dsu.unite(u, v);
  }

  dfs(dsu.find_parent(0), 0);

  for (int i = 0; i < n; i++) {
    cout << ans[i] << endl;
  }
}
