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;

// Shortcut

#define int long long
#define endl '\n'
#define eb emplace_back
#define pb push_back
#define pob pop_back
#define mp make_pair
#define upb upper_bound
#define lwb lower_bound
#define fi first
#define se second
#define For(i, l, r) for (int i = l; i < r; i++)
#define ForE(i, l, r) for (int i = l; i <= r; i++)
#define Ford(i, r, l) for (int i = r; i > l; i--)
#define FordE(i, r, l) for (int i = r; i >= l; i--)
#define Fora(i, a) for (auto i : a)

// I/O & Debug

#define PrintV(a) for (int iiii = 0; iiii < a.size(); iiii++) cout << a[iiii] << ' ';
#define PrintVl(a) for (int iiii = 0; iiii < a.size(); iiii++) cout << a[iiii] << endl;
#define PrintA(a, n) for (int iiii = 0; iiii < n; iiii++) cout << a[iiii] << ' ';
#define PrintAl(a, n) for (int iiii = 0; iiii < n; iiii++) cout << a[iiii] << endl;
#define Ptest(x) return cout << x, 0;
#define gl(s) getline(cin, s);
#define setpre(x) fixed << setprecision(x)
/*
#define debug(args...){ string _sDEB = #args; replace(_sDEB.begin(), _sDEB.end(), ',', ' '); stringstream _ssDEB(_sDEB); istream_iterator<string> _itDEB(_ssDEB); DEB(_itDEB, args); }
void DEB(istream_iterator<string> it) {}
template<typename T, typename... Args>
void DEB(istream_iterator<string> it, T a, Args... args){
    cout << *it << " = " << a << endl;
    DEB(++it, args...);
}
*/

// Functions

//#define isvowel(a) (a == 'a' || a == 'e' || a == 'i' || a == 'o' || a == 'u')
#define bend(a) a.begin(), a.end()
#define rbend(a) a.rbegin(), a.rend()
#define mset(a) memset(a, 0, sizeof(a));
//mt19937 rando(chrono::steady_clock::now().time_since_epoch().count());

// Data Structure

#define pque priority_queue
#define mts multiset
typedef long long ll;
typedef long double ld;
typedef vector <int> vi;
typedef vector <ll> vll;
typedef vector <ld> vld;
typedef vector <string> vs;
typedef pair <int, int> pii;
typedef pair <ll, ll> pll;
typedef vector <vi > vvi;
typedef vector <vll > vvll;
typedef vector <pii > vpii;
typedef vector <pll > vpll;

const int N = 1e5 + 5, mod = 1e9 + 7, inf = 1e18 + 5;

struct edge{
    int x, y, val;
    bool operator < (const edge &aa) const{
        return val > aa.val;
    }
};

int n;
vector <edge> a;
vi g[N];
int sum[N], par[N], ans[N];

void merge(int x, int y, int val){
    x = par[x];
    y = par[y];
    if (g[x].size() < g[y].size()){
        swap(x, y);
    }
    sum[x] += val * g[y].size();
    sum[y] += val * g[x].size();
    Fora(i, g[y]){
        g[x].pb(i);
        par[i] = x;
        ans[i] -= sum[x];
        ans[i] += sum[y];
    }
    g[y].clear();
}

signed main(){
    ios_base::sync_with_stdio(0);
    cin.tie(0); cout.tie(0);
    cin >> n;
    For(i, 0, n - 1){
        int x, y, val;
        cin >> x >> y >> val;
        a.pb({x - 1, y - 1, val});
    }
    sort(bend(a));
    For(i, 0, n){
        par[i] = i;
        g[i].pb(i);
    }
    For(i, 0, n - 1){
        merge(a[i].x, a[i].y, a[i].val);
    }
    For(i, 0, n){
        cout << ans[i] + sum[par[i]] << endl;
    }
}

/*
==================================+
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
------------------------------    |
==================================+
*/