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;
struct fast_ios { fast_ios(){ cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
#define FOR(i, begin, end) for(int i=(begin);i<(end);i++)
#define REP(i, n) FOR(i,0,n)
#define IFOR(i, begin, end) for(int i=(end)-1;i>=(begin);i--)
#define IREP(i, n) IFOR(i,0,n)
#define Sort(v) sort(v.begin(), v.end())
#define Reverse(v) reverse(v.begin(), v.end())
#define all(v) v.begin(),v.end()
#define SZ(v) ((int)v.size())
#define Lower_bound(v, x) distance(v.begin(), lower_bound(v.begin(), v.end(), x))
#define Upper_bound(v, x) distance(v.begin(), upper_bound(v.begin(), v.end(), x))
#define Max(a, b) a = max(a, b)
#define Min(a, b) a = min(a, b)
#define bit(n) (1LL<<(n))
#define bit_exist(x, n) ((x >> n) & 1)
#define debug(x) cout << #x << "=" << x << endl;
#define vdebug(v) cout << #v << "=" << endl; REP(i_debug, v.size()){ cout << v[i_debug] << ","; } cout << endl;
#define mdebug(m) cout << #m << "=" << endl; REP(i_debug, m.size()){ REP(j_debug, m[i_debug].size()){ cout << m[i_debug][j_debug] << ","; } cout << endl;}
#define pb push_back
#define f first
#define s second
#define int long long
#define INF 1000000000000000000
template<typename T> istream &operator>>(istream &is, vector<T> &v){ for (auto &x : v) is >> x; return is; }
template<typename T> ostream &operator<<(ostream &os, vector<T> &v){ for(int i = 0; i < v.size(); i++) { cout << v[i]; if(i != v.size() - 1) cout << endl; }; return os; }
template<typename T> void Out(T x) { cout << x << endl; }
template<typename T1, typename T2> void Ans(bool f, T1 y, T2 n) { if(f) Out(y); else Out(n); }

using vec = vector<int>;
using mat = vector<vec>;
using Pii = pair<int, int>;
using PiP = pair<int, Pii>;
using PPi = pair<Pii, int>;
using bools = vector<bool>;
using pairs = vector<Pii>;

//int dx[4] = {1,0,-1,0};
//int dy[4] = {0,1,0,-1};
//char d[4] = {'D','R','U','L'};

const int mod = 1000000007;
//const int mod = 998244353;
#define Add(x, y) x = (x + (y)) % mod
#define Mult(x, y) x = (x * (y)) % mod

class UnionFind
{
public:
    vector<int> par;
    vector<int> sz;
    mat ls;

    UnionFind(int N){
        par = vector<int>(N);
        REP(i, N) par[i] = i;
        sz = vector<int>(N, 1);
        ls.resize(N);
        REP(i, N) ls[i].pb(i);
    }

    int find(int x){
        if(par[x] == x) return x;
        else return par[x] = find(par[x]);
    }

    void unite(int x, int y){
        x = find(x);
        y = find(y);
        if(x == y) return;

        if(sz[x] < sz[y]) swap(x, y);

        par[y] = x;
        sz[x] += sz[y];
        for(int v: ls[y]) ls[x].pb(v);
    }

    bool is_union(int x, int y){
        x = find(x);
        y = find(y);
        return x == y;
    }

    int union_size(int x){
        return sz[find(x)];
    }

};

struct LazySegmentTree
{
    //A: data, B: 作用素
    using T_A = int;
    using T_B = int;
    T_A id_A = 0;
    T_B id_B = 0;
    int N;
    vector<T_A> dat;
    vector<T_B> ope;

    T_A F_AA(T_A &u, T_A &v){
        return u + v;
    }

    T_A F_AB(T_A &u, T_B &v, int sz){
        return u + v * sz;
    }

    T_B F_BB(T_B &u, T_B &v){
        return u + v;
    }

    LazySegmentTree(int n){
        N = 1;
        while(n > N) N = N << 1;
        dat = vector<T_A>(2 * N - 1, id_A);
        ope = vector<T_B>(2 * N - 1, id_B);
    }

    LazySegmentTree(int n, vector<T_A> &v){
        N = 1;
        while(n > N) N = N << 1;
        dat = vector<T_A>(2 * N - 1, id_A);
        ope = vector<T_B>(2 * N - 1, id_B);
        REP(i, n) dat[i + N - 1] = v[i];
        IREP(i, N - 1) dat[i] = F_AA(dat[i * 2 + 1], dat[i * 2 + 2]); 
    }

    //遅延評価
    void eval(int k, int l, int r){
        if(ope[k] != id_B){
            dat[k] = F_AB(dat[k], ope[k], r - l);
            if(r - l > 1){
                ope[k * 2 + 1] = F_BB(ope[k * 2 + 1], ope[k]);
                ope[k * 2 + 2] = F_BB(ope[k * 2 + 2], ope[k]);
            }
            ope[k] = id_B;
        }
    }

    void update(int a, int b, T_B x, int k, int l, int r){

        eval(k, l, r);
        if(b <= l || r <= a) return;

        if(a <= l && r <= b){
            ope[k] = F_BB(ope[k], x);
            eval(k, l, r);
        }else{
            update(a, b, x, k * 2 + 1, l, (l + r) / 2);
            update(a, b, x, k * 2 + 2, (l + r) / 2, r);
            dat[k] = F_AA(dat[k * 2 + 1], dat[k * 2 + 2]);
        }

    }

    T_A get(int a, int b, int k, int l, int r){
        if(r <= a || b <= l) return id_A;

        eval(k, l, r);
        if(a <= l && r <= b) return dat[k];
        else{
            T_A vl = get(a, b, k * 2 + 1, l, (l + r) / 2);
            T_A vr = get(a, b, k * 2 + 2, (l + r) / 2, r);
            return F_AA(vl, vr);
        }
    }

    //[a,b)の区間更新
    void update(int a, int b, T_B x){ update(a, b, x, 0, 0, N); }

    //[a, b)の演算結果
    T_A get(int a, int b){ return get(a, b, 0, 0, N); }

    T_A val(int k){ return get(k, k + 1); }
};

signed main(){

    int N; cin >> N;
    vector<PiP> p(N - 1);
    REP(i, N - 1){
        int a, b, c; cin >> a >> b >> c;
        p[i] = PiP(c, Pii(a - 1, b - 1));
    }
    Sort(p); Reverse(p);

    UnionFind UF(N);
    REP(i, N - 1){
        int a = p[i].s.f, b = p[i].s.s;
        UF.unite(a, b);
    }
    vec v = UF.ls[UF.find(0)];
    //vdebug(v);
    vec inv(N);
    REP(i, N) inv[v[i]] = i;

    UF = UnionFind(N);
    LazySegmentTree ST(N);
    REP(i, N - 1){
        int a = p[i].s.f, b = p[i].s.s, c = p[i].f;

        int a0 = UF.find(a), b0 = UF.find(b);
        int ia = inv[UF.ls[a0][0]], ib = inv[UF.ls[b0][0]];
        int sa = SZ(UF.ls[a0]), sb = SZ(UF.ls[b0]);

        ST.update(ia, ia + sa, c * sb);
        ST.update(ib, ib + sb, c * sa);

        UF.unite(a, b);
        /*
        UF.unite(a, b);
        a = UF.find(a);
        int i0 = inv[UF.ls[a][0]];
        int sz = SZ(UF.ls[a]);
        ST.update(i0, i0 + sz, c);*/
    }
    vec ans(N);
    REP(i, N){
        ans[v[i]] = ST.val(i);
    }
    REP(i, N){
        Out(ans[i]);
    }

    return 0;
}
