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<cassert>
#include<stdexcept>
#include<utility>
#include<functional>
#include<numeric>
#include<cmath>
#include<algorithm>
#include<cstdio>
#include<cstdlib>
#include<array>
#include<stack>
#include<queue>
#include<deque>
#include<vector>
#include<complex>
#include<set>
#include<map>
#include<unordered_map>
#include<unordered_set>
#include<string>
#include<bitset>
#include<memory>
using namespace std;
using ll=long long;


namespace ProconLib{
    class UnionFind{
        int N;
        std::vector<int> par;
        std::vector<int> rank;
        std::vector<int> dat;
        public:
        UnionFind(int N):N(N),par(N),rank(N,0){std::iota(par.begin(),par.end(),0);dat=par;}
        int find(int x);
        void unite(int x,int y);
        void set(int v,int val){dat[find(v)]=val;}
        int get(int v){return dat[find(v)];}
        bool same(int x,int y){return find(x)==find(y);}
    };

    int UnionFind::find(int x){
        if(par[x]==x) return x;
        return par[x]=find(par[x]);
    }
    void UnionFind::unite(int x,int y){
        x=find(x),y=find(y);
        if(x==y) return;
        if(rank[x]>=rank[y]){
            if(rank[x]==rank[y]) rank[x]++;
            par[y]=x;
        }else{
            par[x]=y;
        }
    }
}
using namespace ProconLib;
struct Edge{
    int a,b;
    ll c;
};

bool operator<(Edge lhs,Edge rhs){
    return lhs.c>rhs.c;
}

using Graph=vector<vector<int>>;

vector<int> sz;
int setSZ(int v,const Graph& g){
    if(g[v].size()==0) return sz[v]=1;
    for(auto to:g[v]) sz[v]+=setSZ(to,g);
    return sz[v];
}
int n;
vector<Edge> edges;
vector<ll> res;
void solve(int v,Graph& g,ll sum){
    if(g[v].size()==0){
        res[v]=sum;
        return;
    }
    for(auto to:g[v]){
        solve(to,g,sum+(sz[v]-sz[to])*edges[v-n].c);
    }
}
int main(){
    
    cin>>n;
    edges.resize(n-1);
    for(int i=0;i<n-1;i++){
        int a,b;
        ll c;
        cin>>a>>b>>c;
        a--,b--;
        edges[i]=Edge{a,b,c};
    }

    sort(edges.begin(),edges.end());

    Graph g(2*n-1);
    UnionFind u(n);

    for(int i=0;i<edges.size();i++){
        Edge e=edges[i];
        int l=u.get(e.a);
        int r=u.get(e.b);
        int p=i+n;
        g[p].push_back(l);
        g[p].push_back(r);
        u.unite(e.a,e.b);
        u.set(e.a,p);
    }

    sz.assign(2*n-1,0);
    setSZ(2*n-2,g);
    res.assign(n,-1);
    solve(2*n-2,g,0);
    
    for(int i=0;i<n;i++){
        cout<<res[i]<<endl;
    }
    return 0;
}
