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;

using int64 = long long;
using vi = vector< int >;
using vii = vector< vi >;
const int mod = 1e9 + 7;


struct edge
{
  int u, v, cost;

  bool operator<(const edge &e) const
  {
    return (cost < e.cost);
  }
};

const int INF = 1 << 30;

struct UnionFind
{
  vector< int > data;

  UnionFind(int sz)
  {
    data.assign(sz, -1);
  }

  bool unite(int x, int y)
  {
    x = find(x), y = find(y);
    if(x == y) return (false);
    data[x] += data[y];
    data[y] = x;
    return (true);
  }

  int find(int k)
  {
    if(data[k] < 0) return (k);
    return (data[k] = find(data[k]));
  }

  int size(int k)
  {
    return (-data[find(k)]);
  }
};


int main()
{

  int N;
  cin >> N;
  vector< edge > edges;
  for(int i = 1; i < N; i++) {
    int a, b, c;
    cin >> a >> b >> c;
    --a, --b;
    edges.emplace_back((edge) {a, b, c});
  }
  sort(begin(edges), end(edges));
  reverse(begin(edges), end(edges));

  UnionFind uf(N);
  vector< int64 > cost(N);
  vector< vector< int > > dsu(N);
  for(int i = 0; i < N; i++) {
    dsu[i].emplace_back(i);
  }
  vector< int64 > lazy(N);
  for(auto &e : edges) {

    e.u = uf.find(e.u);
    e.v = uf.find(e.v);
    if(dsu[e.u].size() < dsu[e.v].size()) {
      swap(e.u, e.v);
    }

    int64 sa = lazy[e.v] - lazy[e.u]; // e.u のほうが sa だけ多い
    int64 latte = 1LL * e.cost * uf.size(e.v);
    int64 malta = 1LL * e.cost * uf.size(e.u);

    while(!dsu[e.v].empty()) {
      cost[dsu[e.v].back()] += malta + sa - latte;
      dsu[e.u].emplace_back(dsu[e.v].back());
      dsu[e.v].pop_back();
    }
    lazy[e.u] += latte;
    lazy[e.v] = 0;
    uf.unite(e.u, e.v);
  }
  for(int i = 0; i < N; i++) {
    cout << cost[i] + lazy[uf.find(i)] << endl;
  }


}
