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 pair<int,int>ii;
typedef vector<int>vi;
typedef vector<ii>vii;
vector<vii>adjlist;
const int N=1e5+5;
vi all;
vii tmp;
int n,child[N];
long long sum[N],sum1[N],ans[N];
bool  vis[N];
void dfs(int u,int p)
{
    child[u]=1;
    for(ii v:adjlist[u])
    {
        if(not vis[v.first] && v.first!=p){
            dfs(v.first,u);
            child[u]+=child[v.first];
        }
    }
}
int findcen(int u,int p,int sz)
{
    for(ii v:adjlist[u]){
        if(not vis[v.first] && v.first!=p && child[v.first]>sz/2)return findcen(v.first,u,sz);
    }
    return u;
}
void redfs(int u,int p,int dist)
{
    all.push_back(dist);
    for(ii v:adjlist[u]){
        if(not vis[v.first] && v.first!=p){
            redfs(v.first,u,min(dist,v.second));
        }
    }
}
void findans(int u,int p,int dist)
{
    tmp.push_back(ii(dist,u));
    for(ii v:adjlist[u]){
        if(v.first!=p && not vis[v.first]){
            findans(v.first,u,min(dist,v.second));
        }
    }
}
void centroid(int root)
{
    dfs(root,root);
    int cen=findcen(root,root,child[root]);
    vis[cen]=1;
    all.clear();
    for(int i=0;i<adjlist[cen].size();++i){
        int v=adjlist[cen][i].first;
        if(vis[v])continue;
        redfs(v,cen,adjlist[cen][i].second);
    }
    sort(all.begin(),all.end());
    for(int pos=0;pos<all.size();pos++){
        if(pos)sum[pos]=sum[pos-1]+all[pos];
        else sum[pos]=all[pos];
    }
    ans[cen]+=sum[all.size()-1];
    for(int i=0;i<adjlist[cen].size();++i){
        int v=adjlist[cen][i].first;
        int w=adjlist[cen][i].second;
        if(vis[v])continue;
        tmp.clear();
        findans(v,cen,w);
        sort(tmp.begin(),tmp.end());
        for(int j=0;j<tmp.size();j++){
            if(j)sum1[j]=sum1[j-1]+tmp[j].first;
            else sum1[j]=tmp[j].first;
        }
        for(int j=0;j<tmp.size();++j){
            int u=tmp[j].second;
            int len=tmp[j].first;
            int pos1=upper_bound(tmp.begin(),tmp.end(),ii(len,1e9+7))-tmp.begin();
            int pos2=upper_bound(all.begin(),all.end(),len)-all.begin();
            ans[u]+=sum[pos2-1]-sum1[pos1-1];
            ans[u]+=len*(all.size()-pos2+pos1-tmp.size()+1);
        }
    }
    for(int i=0;i<adjlist[cen].size();i++){
        int v=adjlist[cen][i].first;
        if(not vis[v])centroid(v);
    }
}
int main()
{
    scanf("%d",&n);
    adjlist.assign(n+1,vii());
    for(int i=1;i<n;++i){
        int u,v,w;
        scanf("%d%d%d",&u,&v,&w);
        adjlist[u].push_back(ii(v,w));
        adjlist[v].push_back(ii(u,w));
    }
    centroid(1);
    for(int i=1;i<=n;++i)printf("%lld\n",ans[i]);
}
