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<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int maxn = 1e5 + 5;
typedef long long ll;
int p[maxn], n;
ll add[maxn], cnt[maxn];
struct Edge{
    int a, b;
    ll c;
}e[maxn];
bool Cmp(Edge a, Edge b){return a.c > b.c;}
int Find(int x){
    if(p[x] == x)return x;
    if(Find(p[x]) == p[x])return p[x];
    add[x] += add[p[x]];
    p[x] = p[p[x]];
    //add[x] -= add[p[x]];
    return p[x];
}
void Merge(int a, int b, ll c){
    int x = Find(a), y = Find(b);
    add[x] += c * cnt[y];
    add[y] += c * cnt[x];
    cnt[x] += cnt[y];
    add[y] -= add[x];
    p[y] = x;
}
int main(){
//    freopen("e:\\in.txt","r",stdin);
    cin>>n;
    int a, b;
    ll c;
    for(int i = 0; i < n - 1; i++)scanf("%d%d%lld", &e[i].a, &e[i].b, &e[i].c);
    sort(e, e + n - 1, Cmp);
    for(int i = 1; i <= n; i++)p[i] = i, add[i] = 0, cnt[i] = 1;
    for(int i = 0; i < n - 1; i++){
        Merge(e[i].a, e[i].b, e[i].c);
    }
//    for(int i = 1; i <= n; i++){
//        cout<<p[i]<<' '<<add[i]<<endl;
//    }
    for(int i = 1; i <= n; i++){
        Find(i);
//        cout<<p[i]<<' '<<add[i]<<endl;
        ll ans;
        if(p[i] == i)ans = add[i];
        else ans = add[i] + add[p[i]];
        printf("%lld\n", ans);
    }
    return 0;
}
