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;

typedef long long ll;
typedef pair<ll, ll> P;

#define each(i,a) for (auto&& i : a)
#define FOR(i,a,b) for (ll i=(a),__last_##i=(b);i<__last_##i;i++)
#define RFOR(i,a,b) for (ll i=(b)-1,__last_##i=(a);i>=__last_##i;i--)
#define REP(i,n) FOR(i,0,n)
#define RREP(i,n) RFOR(i,0,n)
#define __GET_MACRO3(_1, _2, _3, NAME, ...) NAME
#define rep(...) __GET_MACRO3(__VA_ARGS__, FOR, REP)(__VA_ARGS__)
#define rrep(...) __GET_MACRO3(__VA_ARGS__, RFOR, RREP)(__VA_ARGS__)
#define pb push_back
#define all(a) (a).begin(),(a).end()
#define chmin(x,v) x = min(x, v)
#define chmax(x,v) x = max(x, v)

const ll linf = 1e18;
const double eps = 1e-12;
const double pi = acos(-1);

template<typename T>
istream& operator>>(istream& is, vector<T>& vec) {
    each(x,vec) is >> x;
    return is;
}
template<typename T>
ostream& operator<<(ostream& os, const vector<T>& vec) {
    rep(i,vec.size()) {
        if (i) os << " ";
        os << vec[i];
    }
    return os;
}
template<typename T>
ostream& operator<<(ostream& os, const vector< vector<T> >& vec) {
    rep(i,vec.size()) {
        if (i) os << endl;
        os << vec[i];
    }
    return os;
}
struct Edge {
    ll a, b, c;
};
class UnionFind {
    vector<ll> par, h, sz;
public:
    UnionFind(ll size) : par(size, 0), h(size, 0), sz(size, 1) {
        rep(i, size) par[i] = i;
    }
    void unite(ll u, ll v) {
        u = root(u), v = root(v);
        if (u == v) return;
        if (h[u] < h[v]) {
            par[u] = v;
            sz[v] += sz[u];
        }
        else {
            par[v] = u;
            sz[u] += sz[v];
        }
        if (h[u] == h[v]) ++h[u];
    }
    ll size(ll v) {
        return sz[root(v)];
    }
    bool isUnited(ll u, ll v) {
        return root(u) == root(v);
    }
    ll root(ll v) {
        if (par[v] == v) return v;
        return par[v] = root(par[v]);
    }
};
bool operator>(const Edge& e1, const Edge& e2) {
    return e1.c > e2.c;
}
int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    ll n; cin >> n;
    ll maxC = 0;
    vector<Edge> edges;
    rep(i, n-1) {
        ll a, b, c; cin >> a >> b >> c; --a, --b;
        chmax(maxC, c);
        edges.pb({a, b, c});
    }
    sort(all(edges), greater<Edge>());
    vector<Edge> nedges;
    vector<ll> root(n, 0);
    vector<ll> w(n, 0);
    vector<vector<ll>> G(2*n);
    UnionFind uf(n);
    rep(i, n) root[i] = i;
    each(e, edges) {
        if (uf.isUnited(e.a, e.b)) continue;
        ll u = root[uf.root(e.a)];
        ll v = root[uf.root(e.b)];
        uf.unite(e.a, e.b);
        ll vid = w.size();
        root[uf.root(e.a)] = vid;
        w.pb(e.c);
        G[vid].pb(u);
        G[vid].pb(v);
        // cout << vid << " " << u << endl;
        // cout << vid << " " << v << endl;
    }
    ll r = root[uf.root(0)];
    vector<ll> ans(n, 0);
    vector<ll> size(2*n, 0);
    rep(i, n) size[i] = 1;
    function<ll(ll)> dfs = [&](ll v) {
        each(to, G[v]) {
            size[v] += dfs(to);
        }
        return size[v];
    };
    dfs(r);
    function<void(ll,ll)> dfs2 = [&](ll v, ll val) {
        if (v < n) ans[v] = val;
        ll sum = size[v];
        each(to, G[v]) {
            dfs2(to, val + (sum-size[to]) * w[v]);
        }
    };
    dfs2(r, 0);
    each(a, ans) cout << a << endl;
}
