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

const int N=1e5+5;
int n,pset[N],lazy[N],ans[N];
vector<int> child[N];
vector< pair<int, pair<int,int> > > edge;

void joinset(int u, int v, int w){
    if(child[ pset[u] ].size() > child[ pset[v] ].size()) swap(u, v);
    int pau = pset[u];
    lazy[ pset[v] ] += w * (child[ pset[u] ].size());
    for(int cu : child[ pset[u] ]){
        ans[cu] += lazy[ pset[u] ] + w * child[ pset[v] ].size() - lazy[ pset[v] ];
    }
    for(int cu : child[ pset[u] ]) child[ pset[v] ].push_back(cu), pset[cu] = pset[v];
    child[ pau ].clear();
}

signed main(){
    ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
    cin>>n;
    for(int i=1;i<n;++i){
        int u,v,w; cin>>u>>v>>w;
        edge.push_back(make_pair(w,make_pair(u,v)));
    }
    sort(edge.begin(), edge.end());

    for(int i=1;i<=n; ++i) pset[i] = i, child[i].push_back(i);

    for(int i = edge.size()-1; i >= 0; --i){
        joinset(edge[i].second.first, edge[i].second.second, edge[i].first);
    }

    for(int i = 1; i <= n; ++i) cout << ans[i] + lazy[ pset[i] ] << "\n";

    return 0;
}
