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 FIO "race"
#define mset(a,b) memset(a,b,sizeof a)
#define mcpy(a,b) memcpy(a,b,sizeof b)
#define xx first
#define yy second
#define pb push_back
#define mp make_pair
#define pii pair<int,int> 
#define lb(x) ((x)&(-(x)))
#define dalao 1000000007
#define inf 0x3f3f3f3f
#define N 200010
using namespace std;
typedef long long ll;
struct edge{int a,b,c;bool operator <(const edge& t)const{return c>t.c;};}e[N];
int n,cnt,fa[N],siz[N],v[N],G[N][2];
ll ans[N];
inline int find(int x){while(x^fa[x])x=fa[x]=fa[fa[x]];return x;}
inline void dfs(int x,ll t){
	if(x<=n){ans[x]=t;return;}
	dfs(G[x][0],t+1ll*v[x]*siz[G[x][1]]),dfs(G[x][1],t+1ll*v[x]*siz[G[x][0]]);
}
int main(){
	cin>>n,cnt=n;
	for(int i=1;i<=n;i++)fa[i]=i,siz[i]=1;
	for(int i=1;i<n;i++)scanf("%d%d%d",&e[i].a,&e[i].b,&e[i].c);
	sort(e+1,e+n);
	for(int i=1;i<n;i++){
		int x=find(e[i].a),y=find(e[i].b);
		cnt++,fa[cnt]=cnt,v[cnt]=e[i].c,siz[cnt]=siz[x]+siz[y],fa[x]=fa[y]=cnt;
		G[cnt][0]=x,G[cnt][1]=y;
	}
	dfs(cnt,0);
	for(int i=1;i<=n;i++)printf("%lld\n",ans[i]);
	return 0;
}