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 int long long

#define rep(i,n) for(int i=0;i<(n);i++)
#define pb push_back
#define all(v) (v).begin(),(v).end()
#define fi first
#define se second
typedef vector<int>vint;
typedef pair<int,int>pint;
typedef vector<pint>vpint;

template<typename A,typename B>inline void chmin(A &a,B b){if(a>b)a=b;}
template<typename A,typename B>inline void chmax(A &a,B b){if(a<b)a=b;}


int N;

int par[111111];
set<pint>s[111111];
int ev[111111];
int find(int x){
    return x==par[x]?x:par[x]=find(par[x]);
}

signed main(){
    cin>>N;
    vector<tuple<int,int,int>>es;
    rep(i,N-1){
        int a,b,c;
        cin>>a>>b>>c;
        a--;b--;
        es.pb(make_tuple(c,a,b));
    }
    sort(all(es));
    reverse(all(es));

    rep(i,N){
        par[i]=i;
        s[i].insert({i,0});
    }

    for(auto &w:es){
        int a,b,c;
        tie(c,a,b)=w;
        a=find(a);b=find(b);

        ev[a]+=s[b].size()*c;
        ev[b]+=s[a].size()*c;

        if(s[a].size()<s[b].size())swap(a,b);

        for(auto &p:s[b]){
            pint q=p;
            q.se+=ev[b];
            q.se-=ev[a];
            s[a].insert(q);
        }

        par[b]=a;
    }

    for(auto &p:s[find(0)]){
        cout<<p.se+ev[find(0)]<<endl;
    }
    return 0;
}
