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;
#define GET_MACRO(_1, _2, _3, NAME, ...) NAME
#define _repl(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define _rep(i,n) _repl(i,0,n)
#define rep(...) GET_MACRO(__VA_ARGS__, _repl, _rep)(__VA_ARGS__)
#define mp(a,b) make_pair((a),(b))
#define pb(a) push_back((a))
#define all(x) (x).begin(),(x).end()
#define uniq(x) sort(all(x)),(x).erase(unique(all(x)),end(x))
#define fi first
#define se second
#define dbg(...) _dbg(#__VA_ARGS__, __VA_ARGS__)
void _dbg(string){cout<<endl;}
template<class H,class... T> void _dbg(string s,H h,T... t){int l=s.find(',');cout<<s.substr(0,l)<<" = "<<h<<", ";_dbg(s.substr(l+1),t...);}
template<class T,class U> ostream& operator<<(ostream &o, const pair<T,U> &p){o<<"("<<p.fi<<","<<p.se<<")";return o;}
template<class T> ostream& operator<<(ostream &o, const vector<T> &v){o<<"[";for(T t:v){o<<t<<",";}o<<"]";return o;}

#define INF 1120000000

class UnionFind {
public:
  vector<int> par, rank;
  // if par is negative, it is a root, of which tree size is the abs-value.
  // rank represents depth
  UnionFind(int sz) : par(sz, -1), rank(sz, 0){}
  int find(int x){
    if(par[x]<0) return x;
    else return par[x] = find(par[x]);
  }
  void unite(int x, int y){
    x=find(x); y=find(y);
    if(x==y) return;
    if(rank[x] < rank[y]) swap(x,y);
    par[x] += par[y];
    par[y] = x;
    if(rank[x]==rank[y]) rank[x]++;
  }
  inline bool same(int x, int y){ return find(x) == find(y); }
  inline int size(int x){ return -par[find(x)]; }
};

vector<long> val;
vector<int> tree[200005];

long ans[100005];

void dfs(int v, long p_val){
  p_val += val[v];
  if(tree[v].size()==0) ans[v] = p_val;
  for(auto to : tree[v]) dfs(to, p_val);
}

int main(){
  int n;
  cin>>n;
  vector<pair<int,pair<int,int>>> g;
  rep(i,n-1){
    int a,b,c;
    cin>>a>>b>>c;
    a--;b--;
    g.pb(mp(c,mp(a,b)));
  }

  sort(all(g));
  reverse(all(g));

  UnionFind uf(n);

  vector<int> pnode(n,0);
  rep(i,n) pnode[i] = i;
  int nodes = n;

  val.resize(n,0);

  for(auto &pp : g){
    int a = pp.se.fi;
    int b = pp.se.se;
    long c = pp.fi;
    if(uf.same(a,b)) continue;
    int pa = pnode[uf.find(a)];
    int pb = pnode[uf.find(b)];
    tree[nodes].pb(pa);
    tree[nodes].pb(pb);
    val[pa] += uf.size(b) * c;
    val[pb] += uf.size(a) * c;

    uf.unite(a,b);
    pnode[uf.find(a)] = nodes;
    nodes++;
    val.pb(0);
  }

  dfs(nodes-1, 0);

  rep(i,n) cout << ans[i] << "\n";

  return 0;
}
