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<string>
#include<algorithm>
#include<vector>
#include<iomanip>
#include<math.h>
#include<complex>
#include<queue>
#include<deque>
#include<map>
#include<set>
#include<bitset>
using namespace std;
#define REP(i,m,n) for(int i=(int)m ; i < (int) n ; ++i )
#define rep(i,n) REP(i,0,n)
typedef long long ll;
typedef pair<int,int> pint;
typedef pair<ll,int> pli;
const int inf=1<<30;
const ll longinf=1LL<<60 ;
const ll mod=1e9+7 ;
int dx[8]={1,0,-1,0,1,1,-1,-1} , dy[8]={0,1,0,-1,1,-1,1,-1} ;

struct UnionFind{
   vector<int> par;
   vector<ll> ran;
   UnionFind(int n):par(n,-1),ran(n){}
   int find(int x){
       if(par[x]<0)return x;
       int y = find(par[x]);
      ran[x] += ran[par[x]];
      return par[x] = y;
   }
   bool unite(int x,int y,ll z,int k){
       x=find(x);
       y=find(y);
       if(x==y)return false;
       ran[x]-=z*par[y];
       ran[y]-=z*par[x];
       par[k]=par[x]+par[y];
       par[x]=k;
       par[y]=k;
       return true;
   }

   bool same(int x,int y){
       return find(x)==find(y);
   }
};


int main(){
    int n;
    cin>>n;
    vector<pair<ll,pint>> v;
    rep(i,n-1){
        int x,y,z;
        cin>>x>>y>>z;
        v.push_back({z,{x-1,y-1}});
    }
    UnionFind uf(2*n);
    sort(v.begin(),v.end());
    reverse(v.begin(),v.end());
    rep(i,n-1){
        uf.unite(v[i].second.first, v[i].second.second, v[i].first,n+i);
    }
    rep(i,n){
        uf.find(i);
        cout<<uf.ran[i]<<endl;
    }
}