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
int n;
vector<pair<int, pair<int, int> > > d;

int par[100005];
long long res[100005];
int lazy[100005];

vector<int> child[100005];

void Union(int u, int v, int w)
{
    if (child[par[u]].size() > child[par[v]].size())
    {
        swap(u, v);
    }
    int k = par[u];
    lazy[par[v]] += w*child[k].size();
    for (int i = 0; i < child[k].size(); i++)
    {
        par[child[k][i]] = par[v];
        res[child[k][i]] += w*child[par[v]].size() - lazy[par[v]] + lazy[k];
    }
    for (int i = 0; i < child[k].size(); i++)
    {
        child[par[v]].push_back(child[k][i]);
    }
    lazy[k] = 0;
    child[k].clear();
}

signed main()
{
    ios::sync_with_stdio(false); cin.tie(0);
    cin >> n;
    for (int i = 1; i < n; i++)
    {
        int x, y, l; cin >> x >> y >> l;
        d.push_back({l,{x,y}});
    }
    for (int i = 1; i <= n; i++)
    {
        child[i].push_back(i);
        par[i] = i;
        lazy[i] = 0;
    }
    sort(d.begin(), d.end());
    memset(res, 0, sizeof res);
    memset(lazy, 0, sizeof lazy);
    reverse(d.begin(), d.end());
    for (int i = 0; i < n-1; i++)
    {
        Union(d[i].second.first, d[i].second.second, d[i].first);
    }
    for (int i = 1; i <= n; i++)
    {
        cout << res[i] + lazy[par[i]] << endl;
    }
}
