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 Int = long long;


struct QuickFind{
  Int n;
  vector<Int> r,p,dat,laz;
  vector<vector<Int> > v;
  QuickFind(){}
  QuickFind(Int sz):n(sz),r(sz),p(sz),dat(n,0),laz(n,0),v(sz){
    for(Int i=0;i<n;i++){
      r[i]=1,p[i]=i;
      v[i].resize(1,i);
    }
  }
  bool same(Int x,Int y){
    return p[x]==p[y];
  }
  void unite(Int x,Int y,Int w){
    x=p[x];y=p[y];
    if(x==y) return;
    if(r[x]<r[y]) swap(x,y);
    //cout<<x<<" "<<r[x]<<":"<<y<<" "<<r[y]<<":"<<w<<endl;
    for(Int i=0;i<(Int)v[y].size();i++){
      p[v[y][i]]=x;
      v[x].push_back(v[y][i]);
      dat[v[y][i]]-=laz[x];
      dat[v[y][i]]+=laz[y];
      dat[v[y][i]]+=(r[x]-r[y])*w;
    }
    laz[x]+=r[y]*w;
    r[x]+=r[y];
    v[y].clear();
    laz[y]=0;
  }
  Int get(Int x){
    //cout<<x<<" "<<dat[x]<<" "<<laz[p[x]]<<endl;
    return dat[x]+laz[p[x]];
  }
};

//INSERT ABOVE HERE
signed main(){
  Int n;
  cin>>n;
  using T = tuple<Int, Int, Int>;
  vector<T> v;
  for(Int i=1;i<n;i++){
    Int a,b,c;
    cin>>a>>b>>c;
    v.emplace_back(c,--a,--b);
  }
  sort(v.rbegin(),v.rend());
  QuickFind uf(n);
  for(Int i=1;i<n;i++){
    Int c,a,b;
    tie(c,a,b)=v[i-1];
    uf.unite(a,b,c);
  }
  for(Int i=0;i<n;i++) cout<<uf.get(i)<<endl;
  return 0;
}
