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<iostream>
#include<vector>
#include<algorithm>
using namespace std;
int N;
int pr[1<<17],sz[1<<17];
long sum[1<<17];
int main()
{
	cin>>N;
	vector<pair<int,pair<int,int> > >E(N-1);
	for(int i=0;i<N-1;i++)
	{
		int a,b,c;cin>>a>>b>>c;
		a--,b--;
		E[i]=make_pair(c,make_pair(a,b));
	}
	for(int i=0;i<N;i++)
	{
		pr[i]=i;
		sz[i]=1;
	}
	sort(E.begin(),E.end());
	reverse(E.begin(),E.end());
	for(pair<int,pair<int,int> >e:E)
	{
		int a=e.second.first,b=e.second.second;
		while(pr[a]!=a)a=pr[a];
		while(pr[b]!=b)b=pr[b];
		if(sz[a]<sz[b])swap(a,b);
		sum[a]+=(long)e.first*sz[b];
		sum[b]+=(long)e.first*sz[a];
		sum[b]-=sum[a];
		sz[a]+=sz[b];
		pr[b]=a;
	}
	for(int i=0;i<N;i++)
	{
		int t=i;
		long ans=sum[t];
		while(pr[t]!=t)
		{
			t=pr[t];
			ans+=sum[t];
		}
		cout<<ans<<endl;
	}
}
