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
// 修改自提交记录：192182
// 原记录作者：E.Space (UID: 1579)
#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<ctime>
#include<cstdlib>
#define cmin(a,b) (a>(b)?a=(b),1:0)
#define cmax(a,b) (a<(b)?a=(b),1:0)
#define dmin(a,b) ((a)<(b)?(a):(b))
#define dmax(a,b) ((a)>(b)?(a):(b))
namespace io
{
	int F()
	{
		int n=0,F=1;
		char ch;
		while((ch=getchar())!='-'&&(ch<'0'||ch>'9'));
		ch=='-'?F=0:n=ch-'0';
		while((ch=getchar())>='0'&&ch<='9')n=n*10+ch-'0';
		return F?n:-n;
	}
}
int fa[222222],siz[222222],pno,f[222222];
long long add[222222];
int gf(int u)
{
	if(fa[u]==u)return u;
	return fa[u]=gf(fa[u]);
}
struct edg
{
	int x,y,l;
}ed[555555];
bool operator <(const edg &x,const edg &y)
{
	return x.l>y.l;
}
int main()
{
//	freopen("migrate.in","r",stdin);
//	freopen("migrate.out","w",stdout);
	int n=io::F(),m=n-1;
	for(register int i=1;i<=m;++i)
		ed[i]=(edg){io::F(),io::F(),io::F()};
	std::sort(ed+1,ed+m+1);
	pno=n;
	for(register int i=1;i<=n;++i)fa[i]=i,siz[i]=1;
	for(register int i=1;i<=m;++i)
	{
		int t1=gf(ed[i].x),t2=gf(ed[i].y);
		if(t1==t2)continue;
		add[t1]=siz[t2]*(long long)ed[i].l;
		add[t2]=siz[t1]*(long long)ed[i].l;
		f[t1]=f[t2]=fa[t1]=fa[t2]=++pno;
		siz[pno]=siz[t1]+siz[t2];
		fa[pno]=pno;
	}
	for(register int i=pno-1;i;--i)
		add[i]+=add[f[i]];
	for(register int i=1;i<=n;++i)
		printf("%lld\n",add[i]);
	return 0;
}
