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 ll;
typedef unsigned long long ull;
typedef pair<ll, ll> P;

#define fi first
#define se second
#define repl(i,a,b) for(ll i=(ll)(a);i<(ll)(b);i++)
#define rep(i,n) repl(i,0,n)
#define each(itr,v) for(auto itr:v)
#define pb push_back
#define all(x) (x).begin(),(x).end()
#define dbg(x) cout<<#x"="<<x<<endl
#define mmax(x,y) (x>y?x:y)
#define mmin(x,y) (x<y?x:y)
#define maxch(x,y) x=mmax(x,y)
#define minch(x,y) x=mmin(x,y)
#define uni(x) x.erase(unique(all(x)),x.end())
#define exist(x,y) (find(all(x),y)!=x.end())
#define bcnt __builtin_popcount

#define INF INT_MAX/3

struct edge
{
  ll w,s,t;
};
bool sorter(const edge& a,const edge& b){
  return a.w > b.w;
}

struct UnionFind{
  vector<int> v;
  UnionFind(int n) : v(n, -1) {}
  void init(){ for(int i = 0;i < v.size();i++)v[i]=-1; }
  int find(int x) { return v[x] < 0 ? x : v[x] = find(v[x]); }
  bool unite(int x, int y) {
    x = find(x); y = find(y);
    if (x == y) return false;
    if (-v[x] < -v[y]) swap(x, y);
    v[x] += v[y]; v[y] = x;
    return true;
  }
  bool root(int x) { return v[x] < 0; }
  bool same(int x, int y) { return find(x) == find(y); }
  int size(int x) { return -v[find(x)]; }
};

ll n;
vector<edge> es;
ll sum[200020];
vector<ll> g[200020];
ll par[200020];
ll res[200020];

void dfs(ll v,ll par,ll nsum){
  if(v<n){
    res[v]=nsum+sum[v];
    return;
  }
  for(ll nv : g[v]){
    if(par==nv)continue;
    dfs(nv,v,nsum+sum[v]);
  }
}

int main(){
  cin>>n;
  UnionFind uf(n);
  rep(i,n-1){
    ll a,b,c;
    cin>>a>>b>>c;
    a--; b--;
    es.push_back((edge){c,a,b});
  }
  sort(all(es),sorter);
  ll V=n;
  rep(i,n)par[uf.find(i)]=i;
  rep(i,n-1){
    ll sx=uf.size(es[i].s);
    ll sy=uf.size(es[i].t);
    //dbg(sx); dbg(sy);
    ll px=par[uf.find(es[i].s)];
    ll py=par[uf.find(es[i].t)];
    //dbg(px); dbg(py);
    sum[px]+=es[i].w*sy;
    sum[py]+=es[i].w*sx;
    g[px].push_back(V); g[V].push_back(px);
    g[py].push_back(V); g[V].push_back(py);
    uf.unite(es[i].s,es[i].t);
    par[uf.find(es[i].s)]=V++;
  }
  //rep(i,V)dbg(sum[i]);
  dfs(V-1,-1,0);
  rep(i,n)cout<<res[i]<<endl;
	return 0;
}
