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;

typedef long long int LLI;

struct UnionFind {
  vector<int> data;
  UnionFind(int size) : data(size, -1) { }
  bool unionSet(int x, int y) {
    x = root(x); y = root(y);
    if (x != y) {
      if (data[y] < data[x]) swap(x, y);
      data[x] += data[y]; data[y] = x;
    }
    return x != y;
  }
  bool findSet(int x, int y) {
    return root(x) == root(y);
  }
  int root(int x) {
    return data[x] < 0 ? x : data[x] = root(data[x]);
  }
  int size(int x) {
    return -data[root(x)];
  }
};

struct Edge {
  LLI len;
  int u;
  int v;
};

struct E {
  LLI len;
  int to;
};

bool cmp(const Edge &a, const Edge &b) {
  return a.len > b.len;
}

bool cmp2(const E &a, const E &b) {
  if (a.len != b.len) return a.len < b.len;
  return a.to < b.to;
}

int N;
LLI ans[114514];
LLI num[114514];
Edge es[114514];
vector<E> ds[114514];

LLI dfs(int v, int p, LLI conv) {
  //printf("(v, p, conv)=(%d, %d, %lld)\n", v, p, conv);
  LLI ret = 1;
  ans[v] += conv;
  for (E &e : ds[v]) {
    int u = e.to;
    if (u == p) continue;
    //ans[u] += conv;
    LLI res = dfs(u, v, conv);
    conv += res * e.len;
    ans[v] += res*e.len;
    ret += res;
  }
  return num[v] = ret;
}

void dfs2(int v, int p, LLI conv) {
  //printf("2(v, p, conv)=(%d, %d, %lld)\n", v, p, conv);
  ans[v] += conv;
  LLI t = num[v];
  for (E &e : ds[v]) {
    int u = e.to;
    if (u == p) continue;
    //ans[u] += conv;
    t -= num[u];
    dfs2(u, v, conv+e.len*t);
  }
}

int main() {
  scanf("%d", &N);
  UnionFind uf(N);
  for (int i=0; i<N-1; i++) {
    int a, b;
    LLI c;
    scanf("%d%d%lld", &a, &b, &c);
    --a;
    --b;
    es[i] = Edge{c, a, b};
  }
  sort(es, es+N-1, cmp);
  for (int i=0; i<N-1; i++) {
    auto &e = es[i];
    int a = uf.root(e.u);
    int b = uf.root(e.v);
    ds[a].emplace_back(E{e.len, b});
    ds[b].emplace_back(E{e.len, a});
    uf.unionSet(e.u, e.v);
  }

  for (int i=0; i<N; i++) {
    sort(ds[i].begin(), ds[i].end(), cmp2);
  }

  int root = uf.root(0);
  dfs(root, root, 0);
  dfs2(root, root, 0);
  /*for (auto& e: ds[root]) {
    int u = e.to;
    ans[root] += e.len*num[u];
  }*/

  for (int i=0; i<N; i++) {
    printf("%lld\n", ans[i]);
  }
}
