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
// {{{ by shik
#include <bits/stdc++.h>
#include <unistd.h>
#pragma GCC diagnostic ignored "-Wunused-result"
#pragma GCC diagnostic ignored "-Wunused-function"
#define SZ(x) ((int)(x).size())
#define ALL(x) begin(x), end(x)
#define REP(i, n) for (int i = 0; i < int(n); i++)
#define REP1(i, a, b) for (int i = (a); i <= int(b); i++)
#define MP make_pair
#define PB push_back
using namespace std;
typedef int64_t LL;
typedef pair<int, int> PII;
typedef vector<int> VI;

namespace { namespace shik {

template<class T> void _R(T &x) { cin >> x; }
void _R(int &x) { scanf("%d", &x); }
void _R(int64_t &x) { scanf("%" SCNd64, &x); }
void _R(double &x) { scanf("%lf", &x); }
void _R(char &x) { scanf(" %c", &x); }
void _R(char *x) { scanf("%s", x); }
void R() {}
template<class T, class... U> void R(T &head, U &... tail) { _R(head); R(tail...); }

template<class T> void _W(const T &x) { cout << x; }
void _W(const int &x) { printf("%d", x); }
void _W(const int64_t &x) { printf("%" PRId64, x); }
void _W(const double &x) { printf("%.16f", x); }
void _W(const char &x) { putchar(x); }
void _W(const char *x) { printf("%s", x); }
template<class T> void _W(const vector<T> &x) { for (auto i = x.begin(); i != x.end(); _W(*i++)) if (i != x.cbegin()) putchar(' '); }
void W() {}
template<class T, class... U> void W(const T &head, const U &... tail) { _W(head); putchar(sizeof...(tail) ? ' ' : '\n'); W(tail...); }

#ifdef SHIK
#include "dump.hpp"
#else
#define dump(...)
#endif

template<class T, class F = less<T>> void sort_uniq(vector<T> &v, F f = F()) { sort(begin(v), end(v), f); v.resize(unique(begin(v), end(v)) - begin(v)); }
template<class T> inline T bit(T x, int i) { return (x >> i) & 1; }
template<class T> inline bool chkmax(T &a, const T &b) { return b > a ? a = b, true : false; }
template<class T> inline bool chkmin(T &a, const T &b) { return b < a ? a = b, true : false; }
template<class T> using MaxHeap = priority_queue<T>;
template<class T> using MinHeap = priority_queue<T, vector<T>, greater<T>>;

// }}}

// {{{ DJS
struct DJS {
    vector<int> fa, sz;
    DJS() {}
    DJS(int n) { init(n); }
    void init(int n) {
        n++; // be nice for 1-index usage
        fa.resize(n);
        sz.resize(n);
        for (int i = 0; i < n; i++) {
            fa[i] = i;
            sz[i] = 1;
        }
    }
    int f(int x) {
        return x == fa[x] ? x : fa[x] = f(fa[x]);
    }
    void u(int a, int b) {
        a = f(a);
        b = f(b);
        if (a == b) return;
        // if (sz[a] > sz[b]) swap(a, b);
        fa[a] = b;
        sz[b] += sz[a];
    }
    bool is_root(int x) {
        return x == fa[x];
    }
    bool same(int a, int b) {
        return f(a) == f(b);
    }
};
// }}}

const int N=1e5+10;

struct E {
    int a,b,c;
} e[N];

bool operator<( const E &a, const E &b ) {
    return a.c>b.c;
}

int n;
LL sz[N+N];
VI g[N+N];
LL sol[N];

void get_sz( int p ) {
    if ( p<=n ) {
        sz[p]=1;
        return;
    }
    for ( int i:g[p] ) {
        get_sz(i);
        sz[p]+=sz[i];
    }
}

void go( int p, LL s ) {
    // dump(p,s);
    if ( p<=n ) {
        sol[p]=s;
        return;
    }
    LL c=e[p-n].c;
    s+=c*sz[p];
    for ( int i:g[p] ) {
        go(i,s-c*sz[i]);
    }
}

void main() {
    R(n);
    REP1(i,1,n-1) R(e[i].a,e[i].b,e[i].c);
    sort(e+1,e+n);
    DJS djs(n+n-1);
    REP1(i,1,n-1) {
        int a=djs.f(e[i].a);
        int b=djs.f(e[i].b);
        // dump(a,b,n+i);
        djs.u(a,n+i);
        djs.u(b,n+i);
        g[n+i].PB(a);
        g[n+i].PB(b);
    }
    get_sz(n+n-1);
    go(n+n-1,0);
    REP1(i,1,n) W(sol[i]);
}

// {{{ main
}}
int main() { shik::main(); return 0; }
// }}}
