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;
const int maxn = 100100;
vector<int> t[maxn];
int p[maxn];
long long lazy[maxn], ans[maxn];
void init(){
    for(int e = 0; e < maxn; e++){
        p[e] = e;
        lazy[e] = 0;
        t[e].push_back(e);
    }
}
int find(int x){
    if(p[x] == x) return x;
    return p[x] = find(p[x]);
}
void join(int u, int v, int w){
    u = find(u);
    v = find(v);
    assert(u != v);
    if(t[u].size() < t[v].size()) swap(u, v);
    for(int x : t[v]){
        ans[x] -= 1ll * t[v].size() * w;
        ans[x] += 1ll * t[u].size() * w;
        ans[x] += lazy[v];
        ans[x] -= lazy[u];
    }
    lazy[u] += 1ll * t[v].size() * w;
    for(int x : t[v]) t[u].push_back(x);
    p[v] = u;
    lazy[v] = 0;
    t[v].clear();
}
int uu[maxn], vv[maxn], ww[maxn], od[maxn];
int main(){
    int n;
    scanf("%d", &n);
    for(int e = 0; e < n - 1; e++) scanf("%d %d %d", uu + e, vv + e, ww + e), uu[e]--, vv[e]--;
    for(int e = 0; e < n - 1; e++) od[e] = e;
    sort(od, od + n - 1, [&](int a, int b){
        return ww[a] > ww[b];
    });
    init();
    for(int e = 0; e < n - 1; e++) join(uu[od[e]], vv[od[e]], ww[od[e]]);
    for(int e = 0; e < n; e++) ans[e] += lazy[find(e)];
    for(int e = 0; e < n; e++) printf("%lld\n", ans[e]);
    return 0;
}
