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;
typedef long long int uli;
const int mx=1e5+10;
int idx[mx];
uli sz[mx];
uli val[mx];
uli inc[mx];
vector<int>bag[mx];
int main(){
  int n;
  scanf("%d",&n);
  vector<tuple<uli,int,int> >edges;
  for(int i=0;i<n-1;i++){
    int u,v;
    uli c;
    scanf("%d %d %lld",&u,&v,&c);  
    edges.push_back(make_tuple(c,--u,--v));
  }
  sort(edges.begin(),edges.end(),greater<tuple<uli,int,int> >());
  for(int i=0;i<n;i++){
    idx[i]=i;
    sz[i]=1;
    inc[i]=0;
    bag[i]={i};
  }
  for(auto e:edges){
    int u,v;
    uli w;
    tie(w,u,v)=e;
    int x=idx[u],y=idx[v];
    if(sz[x]<sz[y])swap(x,y);
    inc[x]+=w*sz[y];
    inc[y]+=w*sz[x];
    for(int z:bag[y]){
      bag[x].push_back(z);
      idx[z]=x;
      val[z]+=inc[y]-inc[x];
    }
    sz[x]+=sz[y];
  }
  int x=idx[0];
  for(int i=0;i<n;i++)val[i]+=inc[x];
  for(int i=0;i<n;i++){
    printf("%lld\n",val[i]);
  }
  return 0;
}
