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>

#define int long long

using namespace std;

const int N = 100005;
vector <pair <int, int> > g[N];
vector <int> all, temp[N], pref_all, pref_temp[N];
int dp[N], ans[N], dist[N];
bool visited[N];

void dfs (int u, int p) {
    dp[u] = 1;
    for (int i = 0; i < g[u].size(); i++) {
        int v = g[u][i].first;
        if (v != p && !visited[v]) {
            dfs(v, u);
            dp[u] += dp[v];
        }
    }
}

int find_centroid (int u, int p, int sz) {
    for (int i = 0; i < g[u].size(); i++) {
        int v = g[u][i].first;
        if (v != p && !visited[v] && dp[v] > sz/2) return find_centroid(v, u, sz);
    }

    return u;
}

void redfs (int u, int p, int val, int branch) {
    all.push_back(val);
    temp[branch].push_back(val);

    dist[u] = val;
    for (int i = 0; i < g[u].size(); i++) {
        int v = g[u][i].first;
        if (v == p || visited[v]) continue;

        redfs(v, u, min(val,g[u][i].second), branch);
    }
}

void cal (int u, int p, int branch) {
    int pos_all = upper_bound(all.begin(), all.end(), dist[u]) - all.begin();
    int pos_temp = upper_bound(temp[branch].begin(), temp[branch].end(), dist[u]) - temp[branch].begin();
    ans[u] = ans[u] + pref_all[pos_all - 1] - pref_temp[branch][pos_temp - 1];

    pos_all = (int)all.size() - pos_all;
    pos_temp = (int)temp[branch].size() - pos_temp;
    ans[u] = ans[u] + (pos_all - pos_temp + 1) * dist[u];

    for (int i = 0; i < g[u].size(); i++) {
        int v = g[u][i].first;
        if (visited[v] || v == p) continue;

        cal(v, u, branch);
    }
}

void centroid (int root) {
    dfs(root, root);

    if(dp[root] == 1) return;
    int cen = find_centroid(root, root, dp[root]);
    visited[cen] = true;

    all.clear();
    pref_all.clear();
    for (int i = 0; i < g[cen].size(); i++) {
        int v = g[cen][i].first;
        if (visited[v]) continue;

        temp[v].clear();
        pref_temp[v].clear();
        redfs(v, cen, g[cen][i].second, v);
    }

    sort(all.begin(), all.end());
    pref_all.push_back(all[0]);
    for (int i = 1; i < all.size(); i++) pref_all.push_back(all[i] + pref_all[pref_all.size() - 1]);
    for (int i = 0; i < g[cen].size(); i++) {
        int v = g[cen][i].first;
        if (visited[v]) continue;

        sort(temp[v].begin(), temp[v].end());
        for (int j = 0; j < temp[v].size(); j++) {
            if (j == 0) pref_temp[v].push_back(temp[v][0]);
            else pref_temp[v].push_back(temp[v][j] + pref_temp[v][pref_temp[v].size() - 1]);
        }

        cal(v, cen, v);
    }

    ans[cen] += pref_all[pref_all.size() - 1];
    for (int i = 0; i < g[cen].size(); i++) {
        int v = g[cen][i].first;
        if (!visited[v]) centroid(v);
    }
}

signed main(){
    int n;
    scanf("%lld", &n);
    for (int i = 1; i <= n - 1; i++) {
        int u, v, w;
        scanf("%lld %lld %lld", &u, &v, &w);
        g[u].push_back(make_pair(v, w));
        g[v].push_back(make_pair(u, w));
    }

    memset(visited, 0, sizeof(visited));
    memset(ans, 0, sizeof(ans));
    centroid(1);

    for (int i = 1; i <= n; i++) printf("%lld\n", ans[i]);

    //cout << "dist " << dist[2] << "\n";
    //for (int i = 0; i < all.size(); i++) cout << all[i] << " ";
    //for (int i = 0; i < temp[2].size(); i++) cout << temp[2][i] << " ";
    //cout << dist[1] << " " << dist[2] << " " << dist[3];
    return 0;
}

/*
4
1 2 10
2 3 20
1 4 10
*/
