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;

int rt(vector<int> &uf,int i)
{
  return uf[i]<0?i:uf[i]=rt(uf,uf[i]);
}

int con(vector<int> &uf,int a,int b)
{
  int ret;
  if(-uf[a]<-uf[b]){
    uf[a]=b;
    ret=b;
  }
  else if(-uf[a]>-uf[b]){
    uf[b]=a;
    ret=a;
  }
  else{
    uf[a]=b;
    uf[b]--;
    ret=b;
  }
 return ret;
}

int main()
{
  int n;
  scanf("%d",&n);
  vector<int> pr(2*n,-1);
  vector<int> uf(n,-1);
  vector<int> X(n);
  for(int i=0;i<n;i++)X[i]=i;
  int N=n;
  vector<long long> S(2*n,0);
  vector<pair<long long,pair<int,int> > > E(n-1);
  for(int i=0;i<n-1;i++){
    int a,b;
    long long c;
    scanf("%d%d%lld",&a,&b,&c);
    a--,b--;
    E[i]=make_pair(c,make_pair(a,b));
  }
  sort(E.begin(),E.end());
  for(int t=n-2;t>=0;t--){
    long long c=E[t].first;
    int a=E[t].second.first,b=E[t].second.second;
    int Ra=rt(uf,a),Rb=rt(uf,b);
    int ra=X[Ra],rb=X[Rb];
    int Rc=con(uf,Ra,Rb);
    //printf("%d %d %d\n",rt(uf,a),rt(uf,b),Rc);
    //printf("%d %d %d %d\n",a+1,b+1,ra,rb);
    X[Rc]=N;
    pr[N]=pr[ra]+pr[rb];
    S[ra]+=-pr[rb]*c;
    S[rb]+=-pr[ra]*c;
    pr[ra]=N;
    pr[rb]=N;
    N++;
  }
  for(int i=N-1;i>=0;i--){
    //printf("%d %d\n",i,pr[i]);
    if(pr[i]>=0){
      S[i]+=S[pr[i]];
    }
  }
  for(int i=0;i<n;i++){
    printf("%lld\n",S[i]);
  }
  return 0;
}
