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 N = 100005;

int n, dsu[N];
long long f[N];
vector<int> adj[N];

struct edge {
    int u, v, c;
} e[N];

int trace(int u) {
    return dsu[u] < 0 ? u : dsu[u] = trace(dsu[u]);
}

void connect(int u, int v, int c) {
    u = trace(u); v = trace(v);
    if (dsu[u] > dsu[v]) {
        swap(u, v);
    }
    adj[u].push_back(v);
    f[u] += -1LL * dsu[v] * c;
    f[v] -= f[u]; f[v] += -1LL * dsu[u] * c;
    dsu[u] += dsu[v];
    dsu[v] = u;
}

void DFS(int u) {
    for (int &v : adj[u]) {
        f[v] += f[u];
        DFS(v);
    }
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    cin >> n;
    fill(dsu + 1, dsu + n + 1, -1);
    for (int i = 1; i < n; i++) {
        cin >> e[i].u >> e[i].v >> e[i].c;
    }   
    sort(e + 1, e + n, [](const edge &u, const edge &v) {
        return u.c > v.c;
    });
    for (int i = 1; i < n; i++) {
        connect(e[i].u, e[i].v, e[i].c);
    }
    DFS(trace(1));
    for (int i = 1; i <= n; i++) {
        cout << f[i] << '\n';
    }
}
