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>
typedef long long ll;
#define FOR(i,a,b) for(ll i=(a);i<(b);i++)
#define REP(i,a) FOR(i,0,a)

using namespace std;
const int MAX_N=1e5;
ll N;
typedef pair<ll,ll> P;
ll par[MAX_N*2-1],sz[MAX_N*2-1];
void inituf(ll n){
	REP(i,n){
		par[i]=i;
		sz[i]=i<=n/2;
	}
}
ll fndpar(ll v){
	if(v==par[v]){
		return v;
	}
	return par[v]=fndpar(par[v]);
}
struct edge{
	ll u,v,cst,inx;
};
bool operator < (const edge &a,const edge &b){
	return a.cst<b.cst;
}
edge E[MAX_N-1];
vector<P> G[MAX_N*2-1];
ll dst[MAX_N*2-1];
void dfs(ll v,ll p,ll d){
	dst[v]=d;
	for(auto e:G[v]){
		if(e.first!=p){
			dfs(e.first,v,d+e.second);
		}
	}
}
int main(){
	ios::sync_with_stdio(false);
	cin.tie(0);
	cin>>N;
	REP(i,N-1){
		ll a,b,c;
		cin>>a>>b>>c;
		a--;
		b--;
		E[i]=(edge){a,b,c,i};
	}
	sort(E,E+N-1);
	inituf(N*2-1);
	REP(i,N-1){
		edge e=E[N-2-i];
		e.u=fndpar(e.u);
		e.v=fndpar(e.v);
		par[e.u]=e.inx+N;
		par[e.v]=e.inx+N;
		sz[e.inx+N]=sz[e.u]+sz[e.v];
		G[e.inx+N].push_back(P(e.u,sz[e.v]*e.cst));
		G[e.inx+N].push_back(P(e.v,sz[e.u]*e.cst));
	}
	ll rt=fndpar(0);
	dfs(rt,-1,0);
	REP(i,N){
		cout<<dst[i]<<endl;
	}
}