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 ll = long long;
using ld = long double;

struct DSU {
  vector<int> col, rk;
  vector<ll> add;
  vector<int> cnt;

  DSU(int n): col(n), rk(n), add(n), cnt(n, 1) {
    iota(col.begin(), col.end(), 0);
  }

  int get(int u) {
    if (u == col[u]) {
      return u;
    }
    return get(col[u]);
  }

  bool join(int u, int v) {
    u = get(u), v = get(v);
    if (u == v) {
      return false;
    }
    if (rk[u] > rk[v]) {
      swap(u, v);
    }
    if (rk[u] == rk[v]) {
      ++rk[v];
    }
    add[u] -= add[v];
    col[u] = v;
    cnt[v] += cnt[u];
    return true;
  }

  void inc(int u, ll delta) {
    add[get(u)] += delta;
  }

  ll get_val(int u) {
    if (u == col[u]) {
      return add[u];
    }
    return add[u] + get_val(col[u]);
  }

  int get_cnt(int u) {
    return cnt[get(u)];
  }
};

struct Edge {
  int u, v, w;
  bool operator<(const Edge& e) const {
    return w < e.w;
  }
};

signed main() {
#ifdef LOCAL
  assert(freopen("a.in", "r", stdin));
#endif
  vector<Edge> es;
  int n;
  cin >> n;
  for (int i = 0; i < n - 1; ++i) {
    int u, v, w;
    cin >> u >> v >> w;
    --u, --v;
    es.push_back(Edge{u, v, w});
  }
  sort(es.begin(), es.end());
  reverse(es.begin(), es.end());
  DSU dsu(n);
  for (auto e : es) {
    dsu.inc(e.u, e.w * 1ll * dsu.get_cnt(e.v));
    dsu.inc(e.v, e.w * 1ll * dsu.get_cnt(e.u));
    assert(dsu.join(e.u, e.v));
  }
  for (int i = 0; i < n; ++i) {
    cout << dsu.get_val(i) << '\n';
  }
}
