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 debug(x) cerr << #x << ": " << x << endl
#define debugArray(x, n)                                                       \
    for(long long hoge = 0; (hoge) < (n); ++(hoge))                            \
    cerr << #x << "[" << hoge << "]: " << x[hoge] << endl
using namespace std;

using ll = long long;
const ll INF = LLONG_MAX / 2;

struct UnionFind {
    vector<int> par;
    UnionFind(int size) : par(size, -1) {}
    bool unionSet(int x, int y) {
        x = root(x);
        y = root(y);
        if(x != y) {
            if(par[y] < par[x])
                swap(x, y);
            par[x] += par[y];
            par[y] = x;
        }
        return x != y;
    }
    bool same(int x, int y) { return root(x) == root(y); }
    int root(int x) { return par[x] < 0 ? x : par[x] = root(par[x]); }
    int size(int x) { return -par[root(x)]; }
};

signed main() {
    int N;
    cin >> N;
    tuple<int, int, int> edge[N - 1];
    for(int i = 0; i < N - 1; i++) {
        int a, b, c;
        cin >> a >> b >> c;
        edge[i] = make_tuple(-c, a - 1, b - 1);
    }
    sort(edge, edge + (N - 1));
    UnionFind uf(N);
    int id[N];
    for(int i = 0; i < N; i++) {
        id[i] = i;
    }
    vector<pair<int, ll>> G[2 * N - 1];
    for(int i = 0; i < N - 1; i++) {
        int a, b;
        ll w;
        tie(w, a, b) = edge[i];
        w = -w;
        G[N + i].emplace_back(id[uf.root(a)], w * uf.size(b));
        G[N + i].emplace_back(id[uf.root(b)], w * uf.size(a));
        uf.unionSet(a, b);
        id[uf.root(a)] = N + i;
    }
    ll ans[N];
    stack<pair<int, ll>> st;
    st.push({2 * N - 2, 0});
    while(!st.empty()) {
        int v;
        ll w;
        tie(v, w) = st.top();
        st.pop();
        if(v < N) {
            ans[v] = w;
            continue;
        }
        for(auto e : G[v]) {
            int u;
            ll cost;
            tie(u, cost) = e;
            st.push({u, cost + w});
        }
    }
    for(int i = 0; i < N; i++) {
        cout << ans[i] << endl;
    }
    return 0;
}
