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;

int main() {
   ios_base::sync_with_stdio(false);
   int N;
   cin >> N;
   vector<tuple<int, int, int>> edges;
   for (int i = 0; i < N - 1; ++i) {
      int v, u, w;
      cin >> v >> u >> w;
      --v, --u;
      edges.emplace_back(w, v, u);
   }
   sort(edges.begin(), edges.end());
   reverse(edges.begin(), edges.end());
   vector<int> par(N);
   vector<int> sz(N);
   vector<ll> add(N);
   iota(par.begin(), par.end(), 0);
   fill(sz.begin(), sz.end(), 1);
   function<int(int)> getPar = [&](int v) {
      if (v == par[v]) {
         return v;
      } else {
         return getPar(par[v]);
      }
   };
   function<ll(int)> getSum = [&](int v) {
      ll ans = add[v];
      if (v != par[v]) {
         ans += getSum(par[v]);
      }
      return ans;
   };
   for (auto e : edges) {
      int w, v, u;
      tie(w, v, u) = e;
      v = getPar(v), u = getPar(u);
      add[v] += ll(sz[u]) * w;
      add[u] += ll(sz[v]) * w;
      if (sz[v] < sz[u]) swap(v, u);
      par[u] = v;
      sz[v] += sz[u];
      add[u] -= add[v];
   }
   for (int i = 0; i < N; ++i) {
      cout << getSum(i) << "\n";
   }
}
