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;

typedef pair<int,ii> iii;

int n,par[100005];
long long lz[100005];
vector<iii> edge;
long long ans[100005];
vector<int> st[100005];

int findSet(int u){
    if(u == par[u]) return u;
    return par[u] = findSet(par[u]);
}
void UnionSet(int u,int v,int val){
    int pu = findSet(u), pv = findSet(v);
    if(st[pu].size()>st[pv].size()) swap(pu,pv);
    for(int i = 0;i<st[pu].size();i++){
        ans[st[pu][i]]+=val*st[pv].size();
        ans[st[pu][i]]+=lz[pu];
        ans[st[pu][i]]-=val*st[pu].size();
        ans[st[pu][i]]-=lz[pv];
    }
    lz[pu] = 0;
    for(int i = 0;i<st[pu].size();i++)
        st[pv].pb(st[pu][i]);
    lz[pv]+=val*st[pu].size();
    par[pu] = pv;
}

int main(){
    cin.tie(0),ios::sync_with_stdio(0);
    cin >> n;
    for(int i = 1;i<=n;i++){
        par[i] = i;
        st[i].pb(i);
    }
    int u,v,w;
    for(int i = 1;i<=n-1;i++){
        cin >> u >> v >> w;
        edge.pb(mp(w,mp(u,v)));
    }
    sort(edge.begin(),edge.end());
    for(int i = edge.size()-1;i>=0;i--){
        u = edge[i].se.fi; v = edge[i].se.se;
        w = edge[i].fi;
        UnionSet(u,v,w);
    }
    for(int i = 1;i<=n;i++)
        cout<<ans[i]+lz[findSet(i)]<<"\n";
}
