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 debug(x) cout<<#x<<"="<<x<<endl
typedef long long ll;
using namespace std;
const int maxn = 200009;

int fa[maxn],siz[maxn],son[maxn][2];
struct line{int from,to,val;}a[maxn];
int n,tot;
ll ans[maxn],val[maxn];

inline int read()
{
	int x=0,f=1;char ch=getchar();
	while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
	while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
	return x*f;
}

int find(int x){return fa[x]==x?x:fa[x]=find(fa[x]);}
bool cmp(const line &x,const line &y){return x.val>y.val;}

void dfs(int x)
{
	int L=son[x][0],R=son[x][1];
	if(L+R==0) return ;
	ans[L]=ans[R]=ans[x];
	ans[L]+=siz[R]*val[x];
	ans[R]+=siz[L]*val[x];
	dfs(L);dfs(R);
}

int main()
{
	n=read();tot=n;
	for(int i=1;i<=n;i++) siz[i]=1,fa[i]=i;
	for(int i=1;i<n;i++) a[i]=(line){read(),read(),read()};
	sort(a+1,a+n,cmp);
	for(int i=1;i<n;i++)
	{
		int x=find(a[i].from),y=find(a[i].to),z=a[i].val;
		tot++;fa[tot]=tot;siz[tot]=siz[x]+siz[y];val[tot]=z;
		fa[x]=fa[y]=tot;
		son[tot][0]=x;son[tot][1]=y;
	}
	dfs(tot);
	for(int i=1;i<=n;i++) printf("%lld\n",ans[i]);
	return 0;
}
