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

template<class T>
struct ICAdd {
  std::vector<T> val;
  std::vector<int> l;
  std::vector<int> r;
  std::vector<int> uf;
  std::vector<int> uf2;

  ICAdd(int n) : l(n, -1), r(n, -1), val(n), uf(n, -1), uf2(n) {
    for (int i = 0; i < n; i++) {
      uf2[i] = i;
    }
  }

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

  void merge(int u, int v) {
    u = find(u);
    v = find(v);
    if (u == v) return;
    if (-uf[u] < -uf[v]) std::swap(u, v);
    uf[u] += uf[v];
    uf[v] = u;
    val.push_back(T());
    l.push_back(uf2[u]);
    r.push_back(uf2[v]);
    uf2[u] = l.size() - 1;
  }

  void add(int u, T x) {
    val[uf2[find(u)]] += x;
  }

  int size(int u) {
    return -uf[find(u)];
  }

  void dfs(int u, T x) {
    if (u == -1) return;
    val[u] += x;
    dfs(l[u], val[u]);
    dfs(r[u], val[u]);
  }

  void build() {
    std::vector<bool> used(l.size());
    for (int i = l.size() - 1; i >= 0; i--) {
      if (l[i] != -1) used[l[i]] = true;
      if (r[i] != -1) used[r[i]] = true;
      if (!used[i]) {
        dfs(i, T());
      }
    }
  }
};

int main() {
  using namespace std;

  cin.tie(0);
  ios::sync_with_stdio(false);

  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());
 
  ICAdd<long long> ic(n);
  for (auto e : es) {
    int w, u, v;
    tie(w, u, v) = e;
    long long x = ic.size(u);
    long long y = ic.size(v);
    ic.add(u, y*w);
    ic.add(v, x*w);
    ic.merge(u, v);
  }
 
  ic.build();
 
  for (int i = 0; i < n; i++) {
    cout << ic.val[i] << endl;
  }
}

### Prompt

Construct a CPP code solution to the problem outlined:

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

### Response

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

template<class T>
struct ICAdd {
  std::vector<T> val;
  std::vector<int> l;
  std::vector<int> r;
  std::vector<int> uf;
  std::vector<int> uf2;

  ICAdd(int n) : l(n, -1), r(n, -1), val(n), uf(n, -1), uf2(n) {
    for (int i = 0; i < n; i++) {
      uf2[i] = i;
    }
  }

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

  void merge(int u, int v) {
    u = find(u);
    v = find(v);
    if (u == v) return;
    if (-uf[u] < -uf[v]) std::swap(u, v);
    uf[u] += uf[v];
    uf[v] = u;
    val.push_back(T());
    l.push_back(uf2[u]);
    r.push_back(uf2[v]);
    uf2[u] = l.size() - 1;
  }

  void add(int u, T x) {
    val[uf2[find(u)]] += x;
  }

  int size(int u) {
    return -uf[find(u)];
  }

  void dfs(int u, T x) {
    if (u == -1) return;
    val[u] += x;
    dfs(l[u], val[u]);
    dfs(r[u], val[u]);
  }

  void build() {
    std::vector<bool> used(l.size());
    for (int i = l.size() - 1; i >= 0; i--) {
      if (l[i] != -1) used[l[i]] = true;
      if (r[i] != -1) used[r[i]] = true;
      if (!used[i]) {
        dfs(i, T());
      }
    }
  }
};

int main() {
  using namespace std;

  cin.tie(0);
  ios::sync_with_stdio(false);

  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());
 
  ICAdd<long long> ic(n);
  for (auto e : es) {
    int w, u, v;
    tie(w, u, v) = e;
    long long x = ic.size(u);
    long long y = ic.size(v);
    ic.add(u, y*w);
    ic.add(v, x*w);
    ic.merge(u, v);
  }
 
  ic.build();
 
  for (int i = 0; i < n; i++) {
    cout << ic.val[i] << endl;
  }
}

```