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>

#define fi first
#define se second
#define mp make_pair
#define pb push_back

using namespace std;
typedef long long ll;

const int maxn = 2e5 + 5;

array<int, 3> edge[maxn];
int N, lab[maxn]; ll res[maxn];
int info[maxn], par[maxn], sz[maxn];

int finds(int u)
{
  if (lab[u] == u) return u;
  return lab[u] = finds(lab[u]);
}

signed main(void)
{
  ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
  if (fopen("A.INP", "r")){
    freopen("A.INP", "r", stdin);
    freopen("A.OUT", "w", stdout);
  }
  cin >> N;
  for (int i = 1; i < N; ++i){
    cin >> edge[i][1] >> edge[i][2] >> edge[i][0];
  }
  sort(edge + 1, edge + N);
  for (int i = 1; i <= N; ++i){
    lab[i] = info[i] = i; sz[i] = 1;
  }
  int cnt = N + 1;
  for (int i = N - 1; i >= 1; --i){
    int u = edge[i][1], v = edge[i][2], w = edge[i][0];
    u = finds(u); v = finds(v);
    par[info[u]] = cnt;
    par[info[v]] = cnt;
    res[info[u]] = 1ll * sz[v] * w;
    res[info[v]] = 1ll * sz[u] * w;
    info[v] = cnt;
    sz[v] += sz[u];
    lab[u] = v;
    ++cnt;
  }
  for (int i = cnt; i >= 1; --i){
    res[i] += res[par[i]];
  }
  for (int i = 1; i <= N; ++i){
    cout << res[i] << '\n';
  }
}
