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<iostream>
#include<algorithm>
#include<vector>
using namespace std;
typedef long long ll;
typedef pair<ll,ll> P;
#define N 200010
ll n;
namespace uf{
  ll p[N],siz[N],id[N];
  ll to[N],len[N],m;
  void init(){
      for(int i=1;i<=n;i++)p[i]=i,siz[i]=1,id[i]=i;
      m=n;
  }
  ll par(ll x){return p[x]=(x==p[x]?x:par(p[x]));}
  
  void unite(ll a,ll b,ll e){
      a=par(a); b=par(b);
      to[id[a]]=to[id[b]]=++m;
      len[id[a]]=siz[b]*e,len[id[b]]=siz[a]*e;
      p[a]=b,siz[b]+=siz[a],id[b]=m;
  }
  
  vector<ll> g[N];
  ll ans[N];
  void dfs(ll x,ll d){
      ans[x]=d;
      for(auto y:g[x])dfs(y,d+len[y]);
  }
  void main(){
      for(int i=1;i<m;i++){
	  g[to[i]].push_back(i);
      }
      dfs(m,0);
      for(int i=1;i<=n;i++)cout<<ans[i]<<endl;
  }
};
struct edge{
  ll a,b,c;
  bool operator<(const edge&key)const{
      return this->c>key.c;
  } 
};
edge e[N];
int main(){
    cin>>n;
    for(int i=0;i<n-1;i++)cin>>e[i].a>>e[i].b>>e[i].c;
    sort(e,e+n-1); uf::init();
    for(int i=0;i<n-1;i++){
	uf::unite(e[i].a,e[i].b,e[i].c);
    }
    uf::main();
    return 0;
}

