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<cstring>
#include<cmath>
#include<algorithm>
#include<cstdlib>
#include<cstdio>
#include<vector>
#define ll long long
using namespace std;

const int N=100005;

struct E{
	int x,y,w;
	E(){}
	E(int x,int y,int w):x(x),y(y),w(w){}
}mem[N];
int n,x,y,w;
int sz[N],f[N];
ll tag[N],ans[N];
vector<int> lev[N];

bool cmp(E a,E b){
	return a.w>b.w;
}

int find(int k){
	if (f[k]!=k) f[k]=find(f[k]);
	return f[k];
}

void merge(int x,int y,int w){
	int k;
	if (sz[x]>sz[y]) swap(x,y);
	tag[y]+=1ll*sz[x]*w;
	for (int j=0;j<lev[x].size();j++){
		k=lev[x][j];
		ans[k]+=1ll*sz[y]*w+tag[x];
		ans[k]-=tag[y];
		lev[y].push_back(k);
	}
	sz[y]+=sz[x]; f[x]=y;
}

int main(){
	int i;
	scanf("%d",&n);
	for (i=1;i<n;i++){
		scanf("%d%d%d",&x,&y,&w);
		mem[i]=E(x,y,w);
	}
	sort(mem+1,mem+n,cmp);
	for (i=1;i<=n;i++){
		sz[i]=1; f[i]=i;
		lev[i].push_back(i);
	}
	for (i=1;i<n;i++){
		x=find(mem[i].x); y=find(mem[i].y);
		w=mem[i].w;
		merge(x,y,w);
	}
	ans[0]=tag[find(1)];
	for (i=1;i<=n;i++) printf("%lld\n",ans[i]+ans[0]);
	return 0;
}