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;

struct Unionfind {
  // tree number
  vector<int> par;
  // constructor
  Unionfind(int n = 1) : par(n, -1) {}
  // search root
  int root(int x) {
    if (par[x] < 0) return x;
    return par[x] = root(par[x]);
  }
  // is same?
  bool issame(int x, int y) { return root(x) == root(y); }

  // add
  // already added, return 0
  bool uni(int x, int y) {
    x = root(x);
    y = root(y);
    if (x == y) return 0;
    if (par[x] > par[y]) swap(x, y);
    par[x] += par[y];
    par[y] = x;
    return 1;
  }
  int size(int x) { return -par[root(x)]; }
};

struct edge {
  int x, y;
  long long cos;
  bool operator<(const edge &r) const {
    if (cos != r.cos) return cos > r.cos;
    if (x != r.x) return x > r.x;
    return y > r.y;
  }
};

long long n;
vector<edge> edges;
vector<long long> res, memo, sum;
vector<set<int>> g;
Unionfind uf;

void solve();

int main() {
  cin >> n;
  for (int i = 1; i < n; ++i) {
    int x, y, c;
    cin >> x >> y >> c;
    edges.push_back({--x, --y, c});
  }
  solve();
  for (auto p : res) cout << p << endl;
  return 0;
}

void solve() {
  uf = Unionfind(n);
  res.assign(n, 0);
  sum.assign(n, 0);
  g.resize(n);
  for (int i = 0; i < n; ++i) g[i].insert(i);
  sort(edges.begin(), edges.end());
  for (auto e : edges) {
    long long x = uf.root(e.x), y = uf.root(e.y), c = e.cos, sx, sy;
    sx = uf.size(x);
    sy = uf.size(y);
    if (sx < sy) {
      swap(x, y);
      swap(sx, sy);
    }
    sum[x] += sy * c;
    for (auto p : g[y]) {
      res[p] += sx * c - sum[x] + sum[y];
      g[x].insert(p);
    }
    uf.uni(x, y);
  }
  for (int i = 0; i < n; ++i) res[i] += sum[uf.root(i)];
}