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 fi first
#define se second
#define pb push_back
#define mp make_pair

typedef pair<int,int> ii;

int n,f[100005],up[100005];
long long ans[100005],sum[100005],cnt[100005];

vector<ii> graph[100005];
bool vis[100005];
vector<int> all;
vector<ii> tree[100005];

void dfs(int u,int p){
    f[u] = 1;
    for(int i = 0;i<graph[u].size();i++){
        int v = graph[u][i].fi;
        if(!vis[v] && v!=p){
            dfs(v,u);
            f[u]+=f[v];
        }
    }
}

int fin(int u,int p,int sz){
    for(int i = 0;i<graph[u].size();i++){
        int v = graph[u][i].fi;
        if(!vis[v] && v!=p){
            if(2*f[v]>sz) return fin(v,u,sz);
        }
    }
    return u;
}

void dist(int u,int p,int id,int val){
    all.pb(val); tree[id].pb(mp(val,u)); up[u] = val;
    for(int i = 0;i<graph[u].size();i++){
        int v = graph[u][i].fi,w = graph[u][i].se;
        if(!vis[v] && v!=p)
            dist(v,u,id,min(w,val));
    }
}
void centroid(int cen){
    dfs(cen,cen);
    int u = fin(cen,cen,f[cen]);
    vis[u] = 1;
    all.clear();
    for(int i = 0;i<graph[u].size();i++){
        int v = graph[u][i].fi,w = graph[u][i].se;
        if(vis[v]) continue;
        tree[v].clear();
        dist(v,u,v,w);
        sort(tree[v].begin(),tree[v].end());
    }
    sort(all.begin(),all.end());
    for(int i = 0 ;i<all.size();i++)
        ans[u]+=all[i];
    sum[all.size()] = 0;
    for(int i = 0 ;i<all.size();i++){
        sum[i] = all[i];
        if(i == 0) continue;
        sum[i]+=sum[i-1];
    }
    for(int i = 0 ;i<graph[u].size();i++){
        int v = graph[u][i].fi;
        if(vis[v]) continue;
        cnt[tree[v].size()] = 0;
        for(int j = 0;j<tree[v].size();j++){
            cnt[j] = tree[v][j].fi;
            if(j == 0) continue;
            cnt[j]+=cnt[j-1];
        }
        for(int j = 0;j<tree[v].size();j++){
            //cout<<tree[v][j].fi<<" "<<tree[v][j].se<<"\n";
            int node = tree[v][j].se,val = up[node],it;
            ans[node]+=val;
            it = upper_bound(all.begin(),all.end(),val)-all.begin();
            if(it-1>=0)
            ans[node]+=sum[it-1];
            ans[node]+=val*(all.size()-it);
            it = lower_bound(tree[v].begin(),tree[v].end(),ii(val+1,-1))-tree[v].begin();
            if(it-1>=0)
            ans[node]-=cnt[it-1];
            ans[node]-=val*(tree[v].size()-it);
        }
    }
    for(int i = 0;i<graph[u].size();i++){
        int v = graph[u][i].fi;
        if(!vis[v])
            centroid(v);
    }
}

int main(){
    cin.tie(0),ios::sync_with_stdio(0);
    cin>>n;
    int u,v,w;
    for(int i = 1;i<=n-1;i++){
        cin>>u>>v>>w;
        graph[u].pb(mp(v,w));
        graph[v].pb(mp(u,w));
    }
    centroid(1);
    for(int i = 1;i<=n;i++)
        cout<<ans[i]<<"\n";
}
