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;

#define fi first
#define se second
#define pb push_back
#define ii pair<int, int>
#define mp make_pair
#define iii pair< int, pair<int, ii> >
#define int long long
#define FOR(a, b, c) for(int a = b; a <= c; ++a)
const int N = 1e5 + 10;
const int oo = 1e8;
const int mod = 1e9 + 7;
const double PI = acos(-1);
int n;
int res[N], la[N], pr[N];
vector<int> dsu[N];
struct book{
	int u, v, val;
} eg[N];
bool cmp(const book x, const book y)	{
	return x.val < y.val;
}
void join(int u, int v, int val)	{
	int pru = pr[u], prv = pr[v];
	if(dsu[pru].size() < dsu[prv].size()) swap(pru, prv);
	int tmp = dsu[pru].size();
	la[pru] += dsu[prv].size()*val;
	for(int j = 0; j < dsu[prv].size(); ++j)	{
		int cur = dsu[prv][j];
		pr[cur] = pru; dsu[pru].pb(cur);
		res[cur] += tmp*val; res[cur] += la[prv];
		res[cur] -= la[pru];
	}
	dsu[prv].clear();
}
signed main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(0); cout.tie(0);
    cin >> n;
    for(int i = 1; i <= n; ++i) {
    	pr[i] = i;
    	dsu[i].pb(i);
	}
    for(int i = 1; i < n; ++i)	{
    	cin >> eg[i].u >> eg[i].v >> eg[i].val;
	}
	sort(eg + 1, eg + n, cmp);
	for(int i = n - 1; i >= 1; --i)	{
		int u1 = eg[i].u, v1 = eg[i].v, val1 = eg[i].val;
		join(u1, v1, val1);
	}
	for(int i = 1; i <= n; ++i) cout << res[i] + la[pr[i]] << '\n';
}