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;  
using ll = long long;  
using PII = pair<ll, ll>;  
#define FOR(i, a, n) for (ll i = (ll)a; i < (ll)n; ++i)  
#define REP(i, n) FOR(i, 0, n)  
#define ALL(x) x.begin(), x.end()  
template<typename T> void chmin(T &a, const T &b) { a = min(a, b); }  
template<typename T> void chmax(T &a, const T &b) { a = max(a, b); }  
struct FastIO {FastIO() { cin.tie(0); ios::sync_with_stdio(0); }}fastiofastio;  
#ifdef DEBUG_   
#include "../program_contest_library/memo/dump.hpp"  
#else  
#define dump(...)  
#endif  
const ll INF = 1LL<<60;

struct RBST {
    struct node {
        node *l, *r, *p;
        ll val;
        ll lazy;
        int sz;
        node(ll v, ll lz) : l(nullptr), r(nullptr), p(nullptr), val(v), lazy(lz), sz(1) {}
    };

    int size(node *a) { return !a ? 0 : a->sz; }
    node* fix(node *a) {
        a->sz = size(a->l) + 1 + size(a->r);
        return a;
    }
    void eval(node *a) {
        if(a->lazy != 0) {
            a->val += a->lazy;
            if(a->l) a->l->lazy += a->lazy;
            if(a->r) a->r->lazy += a->lazy;
            a->lazy = 0;
        }
    }

    inline int xor128() {
        static int x = 123456789, y = 362436069, z = 521288629, w = 88675123;
        int t;
        t = x ^ (x << 11); x = y; y = z; z = w;
        return w = (w ^ (w >> 19)) ^ (t ^ (t >> 8));
    }

    node* getroot(node *a) {
        if(!a->p) return a;
        return getroot(a->p);
    }

    node* merge(node *a, node *b) {
        if(a == nullptr) return b;
        if(b == nullptr) return a;
        eval(a); eval(b);
        if(xor128() % (size(a) + size(b)) < size(a)) {
            a->r = merge(a->r, b);
            if(a->r) a->r->p = a;
            return fix(a);
        } else {
            b->l = merge(a, b->l);
            if(b->l) b->l->p = b;
            return fix(b);
        }
    }

    void dfs(node *a) {
        eval(a);
        if(a->l) dfs(a->l);
        if(a->r) dfs(a->r);
    }
};

struct UnionFind {
    vector<int> par, s;
    UnionFind(int n=2e5) { init(n); }
    void init(int n) { 
        s.assign(n, 1); par.resize(n); 
        iota(par.begin(), par.end(), 0);
    }
    int find(int x) {
        if(par[x] == x) return x;
        return par[x] = find(par[x]);
    }
    void unite(int x, int y) {
        x = find(x);
        y = find(y);
        if(x == y) return;
        if(s[x] < s[y]) par[x] = y, s[y] = s[x] + s[y];
        else par[y] = x, s[x] = s[x] + s[y];
    }
    bool same(int x, int y) { return find(x) == find(y); }
    int size(int x) { return s[find(x)]; }
};

signed main() {
    ll n;
    cin >> n;
    vector<ll> a(n-1), b(n-1), c(n-1);
    REP(i, n-1) {
        cin >> a[i] >> b[i] >> c[i];
        a[i]--, b[i]--;
    }

    RBST tree;
    vector<RBST::node*> nodes(n);
    REP(i, n) nodes[i] = new RBST::node(0, 0);

    vector<ll> ord(n-1);
    iota(ALL(ord), 0);
    sort(ALL(ord), [&](ll l, ll r){
        return c[l] > c[r];
    });

    UnionFind uf(n);
    for(auto i: ord) {
        // b[i] と連結なやつには a[i]の連結成分のサイズ*c[i] を足す
        {
            auto r = tree.getroot(nodes[b[i]]);
            r->lazy += uf.size(a[i]) * c[i];
        }
        // a[i] と連結なやつ
        {
            auto r = tree.getroot(nodes[a[i]]);
            r->lazy += uf.size(b[i]) * c[i];
        }
        // a[i] と b[i] をつなぐ
        {
            auto u = tree.getroot(nodes[a[i]]), v = tree.getroot(nodes[b[i]]);
            tree.merge(u, v);
            uf.unite(a[i], b[i]);
        }
    }

    auto root = tree.getroot(nodes[0]);
    tree.dfs(root);

    vector<ll> ans(n);
    REP(i, n) ans[i] = nodes[i]->val;
    REP(i, n) cout << ans[i] << "\n";
    cout << flush;

    return 0;
}
