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 VARNAME(x) #x
#define show(x) cerr << #x << " = " << x << endl

using namespace std;
using ll = long long;

template <typename T>
ostream& operator<<(ostream& os, const vector<T>& v)
{
    os << "sz:" << v.size() << "\n[";
    for (const auto& p : v) {
        os << p << ",";
    }
    os << "]\n";
    return os;
}

template <typename S, typename T>
ostream& operator<<(ostream& os, const pair<S, T>& p)
{
    os << "(" << p.first << "," << p.second
       << ")";
    return os;
}


constexpr ll MOD = (ll)1e9 + 7LL;

template <typename T>
constexpr T INF = numeric_limits<T>::max() / 10;


class DisjointSets
{
public:
    DisjointSets(const int v)
    {
        m_parent.resize(v);
        m_rank.resize(v);
        m_size.resize(v);
        for (int i = 0; i < v; i++) {
            m_parent[i] = i;
            m_rank[i] = 0;
            m_size[i] = 1;
        }
    }

    bool same(const int a, const int b)
    {
        return find(a) == find(b);
    }


    int find(const int a)
    {
        if (m_parent[a] == a) {
            return a;
        } else {
            return m_parent[a] = find(m_parent[a]);
        }
    }

    void unite(const int a_, const int b_)
    {
        const int a = find(a_);
        const int b = find(b_);
        if (a == b) {
            return;
        }
        if (m_rank[a] > m_rank[b]) {
            m_parent[b] = a;
            m_size[a] += m_size[b];
        } else {
            m_parent[a] = b;
            m_size[b] += m_size[a];
        }
        if (m_rank[a] == m_rank[b]) {
            m_rank[b]++;
        }
    }

    int getSize(const int a)
    {
        return m_size[m_parent[a]];
    }

private:
    vector<int> m_parent;
    vector<int> m_rank;
    vector<int> m_size;
};

struct Edge {
    int from;
    int to;
    ll cost;
    bool operator<(const Edge& e) const
    {
        return cost > e.cost;
    }
};

struct Graph {
    Graph(const int n)
    {
        edge.resize(n);
    }
    void addEdge(const int from, const int to)
    {
        edge[from].push_back(to);
    }
    vector<vector<int>> edge;
};

void dfs(const Graph& g, const int s, vector<ll>& cost)
{
    for (const int to : g.edge[s]) {
        cost[to] += cost[s];
        dfs(g, to, cost);
    }
}

int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);
    int N;
    cin >> N;

    vector<Edge> edge;
    for (int i = 0; i < N - 1; i++) {
        int u, v;
        cin >> u >> v;
        u--, v--;
        ll c;
        cin >> c;
        edge.push_back(Edge{u, v, c});
    }
    sort(edge.begin(), edge.end());
    DisjointSets uf(N);
    vector<ll> cost(2 * N - 1, 0);
    Graph g(2 * N - 1);
    vector<int> par(N, 0);
    for (int i = 0; i < edge.size(); i++) {
        const Edge& e = edge[i];
        const int u = e.from;
        const int v = e.to;
        const ll c = e.cost;
        const int dummy = N + i;
        const int upar = uf.find(u);
        const int vpar = uf.find(v);
        if (par[upar] == 0) {
            g.addEdge(dummy, u);
            cost[u] += c * uf.getSize(v);
        } else {
            g.addEdge(dummy, par[upar]);
            cost[par[upar]] += c * uf.getSize(v);
        }
        if (par[vpar] == 0) {
            g.addEdge(dummy, v);
            cost[v] += c * uf.getSize(u);
        } else {
            g.addEdge(dummy, par[vpar]);
            cost[par[vpar]] += c * uf.getSize(u);
        }

        uf.unite(u, v);
        par[uf.find(u)] = i + N;
    }
    const int root = 2 * N - 2;
    dfs(g, root, cost);

    for (int i = 0; i < N; i++) {
        cout << cost[i] << endl;
    }

    return 0;
}
