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;

const int MAXN = 100010;

int n;
int f[MAXN];
int child[MAXN];
int visit[MAXN];
vector<pair<int, int>> g[MAXN];

vector<long long> weights;

void dfs_model(int v, int p) {
  for(auto e : g[v]) {
    int s = e.first, w = e.second;
    if(s == p || visit[s]) continue;
  }
}

void dfs_prepare(int v, int p) {
  child[v] = 1;
  for(auto e : g[v]) {
    int s = e.first, w = e.second;
    if(s == p || visit[s]) continue;
    dfs_prepare(s, v);
    child[v] += child[s];
  }
}

int dfs_centroid(int v, int p, int root) {
  for(auto e : g[v]) {
    int s = e.first, w = e.second;
    if(s == p || visit[s]) continue;
    if(child[s] * 2 >= child[root]) return dfs_centroid(s, v, root);
  }
  return v;
}

/// sum of edges smaller than x, count of edges greater than x
long long fwt[MAXN], fwt2[MAXN], answer[MAXN];

void add(int y, int sign) {
  for(int x = y; x < MAXN; x += x & -x) fwt[x] += sign * weights[y];
  for(int x = y - 1; x > 0; x -= x & -x) fwt2[x] += sign;
}

long long calc(int y) {
  long long ret = 0;
  for(int x = y; x < MAXN; x += x & -x) ret += fwt2[x] * weights[y];
  for(int x = y; x > 0; x -= x & -x) ret += fwt[x];
  return ret;
}

void dfs_calc(int v, int p, int W) {
  answer[v] += calc(W);
  for(auto e : g[v]) {
    int s = e.first, w = e.second;
    if(s == p || visit[s]) continue;
    dfs_calc(s, v, min(W, w));
  }
}

void dfs_add(int v, int p, int W, int sign) {
  add(W, sign);
  for(auto e : g[v]) {
    int s = e.first, w = e.second;
    if(s == p || visit[s]) continue;
    dfs_add(s, v, min(W, w), sign);
  }
}

void go(int v) {
  dfs_prepare(v, -1);
  v = dfs_centroid(v, -1, v);
  visit[v] = 1;

  add(weights.size() - 1, 1);
  for(auto e : g[v]) {
    int s = e.first, w = e.second;
    if(visit[s]) continue;
    dfs_calc(s, v, w);
    dfs_add(s, v, w, 1);
  }

  add(weights.size() - 1, -1);
  answer[v] += calc(weights.size() - 1);

  for(auto e : g[v]) {
    int s = e.first, w = e.second;
    if(visit[s]) continue;
    dfs_add(s, v, w, -1);
    dfs_calc(s, v, w);
  }

  for(auto e : g[v]) {
    int s = e.first, w = e.second;
    if(visit[s]) continue;
    go(s);
  }
}

int main() {
  ios_base::sync_with_stdio(false); cin.tie(NULL);

  weights = {-1, 0, (int)1e9 + 7};

  cin >> n;
  for(int i = 0; i < n - 1; ++i) {
    int u, v, w;
    cin >> u >> v >> w;
    g[--u].emplace_back(--v, w);
    g[v].emplace_back(u, w);
    weights.push_back(w);
  }

  sort(weights.begin(), weights.end());

  for(int u = 0; u < n; ++u) {
    for(auto &e : g[u]) {
      e.second = lower_bound(weights.begin(), weights.end(), e.second) - weights.begin();
    }
  }
  go(0);

  for(int i = 0; i < n; ++i) cout << answer[i] << "\n";

  return 0;
}
