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>
#define rep(i,n)for(int i=0;i<(n);i++)
using namespace std;
typedef long long ll;

ll sum[200000];
vector<int>vs[200000];
int belong[200000];
ll ans[200000];

void merge(int u,int v,ll w){
	u=belong[u];v=belong[v];
	if(vs[u].size()<vs[v].size())swap(u,v);
	sum[u]+=w*vs[v].size();
	sum[v]+=w*vs[u].size();
	for(int i:vs[v]){
		vs[u].push_back(i);
		belong[i]=u;
		ans[i]-=sum[u];
		ans[i]+=sum[v];
	}
	vs[v].clear();
}
struct st{int a,b,c;};
int main(){
	int n;scanf("%d",&n);
	vector<st>v;
	rep(i,n-1){
		int a,b,c;scanf("%d%d%d",&a,&b,&c);a--;b--;
		v.push_back({a,b,c});
	}
	sort(v.begin(),v.end(),[](st a,st b){return a.c>b.c;});
	rep(i,n){
		belong[i]=i;
		vs[i].push_back(i);
	}
	rep(i,n-1){
		merge(v[i].a,v[i].b,v[i].c);
	}
	rep(i,n){
		printf("%lld\n",ans[i]+sum[belong[i]]);
	}
}