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;
typedef long long lint;
typedef long double llf;
typedef pair<int, int> pi;
const int mod = 1e9 + 7;
const int MAXN = 100005;

lint dap[MAXN];

struct disj{
	int pa[MAXN], sz[MAXN];
	lint offset[MAXN];
	vector<int> nd[MAXN];
	void init(int n){
		for(int i=1; i<=n; i++){
			pa[i] = i;
			sz[i] = 1;
			nd[i].push_back(i);
		}
	}
	int find(int x){
		return pa[x] = (pa[x] == x ? x : find(pa[x]));
	}
	bool uni(int p, int q, lint x){
		p = find(p);
		q = find(q);
		if(sz[p] < sz[q]) swap(p, q);
		pa[q] = p;
		offset[p] += sz[q] * x;
		for(auto &i : nd[q]){
			dap[i] += sz[p] * x + offset[q];
			dap[i] -= offset[p];
			nd[p].push_back(i);
		}
		sz[p] += sz[q];
		return 1;
	}
}disj;

struct edg{
	int s, e, x;
	bool operator<(const edg &e)const{
		return x > e.x;
	}
}v[MAXN];

int main(){
	int n;
	scanf("%d",&n);
	for(int i=1; i<n; i++){
		int s, e, x;
		scanf("%d %d %d",&s,&e,&x);
		v[i] = {s, e, x};
	}
	sort(v+1, v+n);
	disj.init(n);
	for(int i=1; i<n; i++){
		disj.uni(v[i].s, v[i].e, v[i].x);
	}
	lint f = disj.offset[disj.find(1)];
	for(int i=1; i<=n; i++) printf("%lld\n",f +  dap[i]);
}