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
#define DEB
#include<bits/stdc++.h>
#define REP(i,m) for(int i=0;i<(m);++i)
#define REPN(i,m,in) for(int i=(in);i<(m);++i)
#define ALL(t) (t).begin(),(t).end()
#define CLR(a) memset((a),0,sizeof(a))
#define pb push_back
#define mp make_pair
#define fr first
#define sc second

using namespace std;


#ifdef DEB
#define dump(x)  cerr << #x << " = " << (x) << endl
#define prl cerr<<"called:"<< __LINE__<<endl
#define dumpR(x) cerr<<"\x1b[31m"<<#x<<" = " <<(x)<<"\x1b[39m"<<endl
#define dumpY(x) cerr<<"\x1b[33m"<<#x<<" = " <<(x)<<"\x1b[39m"<<endl
#define dumpG(x) cerr<<"\x1b[32m"<<#x<<" = " <<(x)<<"\x1b[39m"<<endl
template<class T> void debug(T a,T b){ for(;a!=b;++a) cerr<<*a<<' ';cerr<<endl;}
#else
#define dump(x) ;
#define dumpR(x) ;
#define dumpY(x) ;
#define dumpG(x) ;
#define prl ;
template<class T> void debug(T a,T b){ ;}
#endif

template<class T> void chmin(T& a,const T& b) { if(a>b) a=b; }
template<class T> void chmax(T& a,const T& b) { if(a<b) a=b; }

typedef long long int lint;
typedef pair<int,int> pi;

namespace std{
  template<class S,class T>
  ostream &operator <<(ostream& out,const pair<S,T>& a){
    out<<'('<<a.fr<<','<<a.sc<<')';
    return out;
  }
}

//const int INF=5e8;


struct uf{
  static const int MAXN=200005;
  int par[MAXN];
  int size[MAXN];

  int cnt;
  lint sum[MAXN];
  void init(int n){
    memset(par,-1,sizeof(par));
    REP(i,n) size[i]=1;
    CLR(sum);
    cnt=n;
  }
  pair<int,lint> doit(int a){
    if(par[a]==-1) return {a,sum[a]};
    pair<int,lint> p=doit(par[a]);
    sum[a]+=p.sc;
    par[a]=p.fr;
    return {par[a],sum[a]};
  }
  void shrink(int a){
    doit(a);
  }
  int root(int a){
    shrink(a);
    if(par[a]==-1) return a;
    return par[a];
  }
  void unite(int a,int b,int w){
    a=root(a);b=root(b);
    if(a==b) return;
    if(size[a]<size[b]) swap(a,b);

    int A=size[a],B=size[b];

    par[a]=par[b]=cnt;
    sum[b]+=A*(lint)w;
    sum[a]+=B*(lint)w;
    size[cnt]=size[a]+size[b];
    ++cnt;
  }
  bool same(int a,int b){
    return root(a)==root(b);
  }

  lint take(int a){
    shrink(a);
    return sum[a];
  }
};

uf u;

int n;
pair<int,pi> es[100005];
int main(){
  cin>>n;
  REP(i,n-1){
    int a,b,c;scanf("%d%d%d",&a,&b,&c);--a;--b;
    es[i]={c,{a,b}};
  }
  sort(es,es+n-1);

  u.init(n);
  for(int i=n-2;i>=0;--i){
    u.unite(es[i].sc.fr,es[i].sc.sc,es[i].fr);
  }
  REP(i,n){
    printf("%lld\n",u.take(i));
  }
  return 0;
}



