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 long long ll;

const int N=1e5+10;
int n;
int v[N][2],w[N];

int gr[N];
bool comp(int x,int y){
        return w[x]>w[y];
}
ll f[N];
ll fcom[N];
int p[N];
vector <int> imp[N];
int main(){
        cin>>n;
        for(int i=1;i<n;i++)
                cin>>v[i][0]>>v[i][1]>>w[i];
        for(int i=1;i<n;i++) p[i]=i;
        sort(p+1,p+n,comp);
        

        for(int i=1;i<=n;i++){
                gr[i]=i;
                imp[i].push_back(i);
        }

        for(int i=1;i<n;i++){
                int use=p[i];
                int x=gr[v[use][0]],y=gr[v[use][1]];
                if (imp[x].size()>imp[y].size()) swap(x,y);
                fcom[x]+=1LL*imp[y].size()*w[use];
                fcom[y]+=1LL*imp[x].size()*w[use];
                for(auto per:imp[x]){
                        f[per]+=fcom[x]-fcom[y];
                        gr[per]=y;
                        imp[y].push_back(per);
                }
        }
        for(int i=1;i<=n;i++) cout<<f[i]+fcom[gr[i]]<<"\n";
}
