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>

using namespace std;

#define pb push_back
#define fi first
#define se second

const int N = 1e5 + 1;

typedef pair<int,int> ii;
int n;
int child[N] , vis[N] , d[N] ;
long long ans[N] , tcdall[N] , tcd[N];
vector<ii> adj[N];
vector<int> all , vi[N];

void dfs(int u,int pa){
	child[u] = 1;
	for(int i = 0 ; i < adj[u].size() ; ++ i){
		int v = adj[u][i].fi;
		if(!vis[v] && v != pa){
			dfs(v , u);
			child[u] += child[v];
		}
	}
}
int findcen(int u , int pa , int sz){
	for(int i = 0 ; i < adj[u].size() ; ++ i){
		int v = adj[u][i].fi;
		if(!vis[v] && child[v] > sz/2 && v != pa)
			return findcen(v , u , sz);
	}
	return u;
}
void dfs1(int u,int pa ,int pos){
	for(int i = 0 ; i < adj[u].size() ; ++i){
		int v = adj[u][i].fi , w = adj[u][i].se;
		if(!vis[v] && v != pa){
			d[v] = min(d[u] , w);
			vi[pos].pb(d[v]); all.pb(d[v]);
			dfs1(v,u,pos);
		}
	}
}
void dfs2(int u , int pa , int pos){
	int pos1 = upper_bound(all.begin(),all.end(),d[u]) - all.begin();
	int pos2 = upper_bound(vi[pos].begin(),vi[pos].end(),d[u]) - vi[pos].begin();
	ans[u] += d[u] * ( all.size() - pos1 + pos2 - vi[pos].size() + 1) + tcdall[pos1-1] - tcd[pos2-1];
	for(int i = 0 ; i < adj[u].size() ; ++i){
		int v = adj[u][i].fi ;
		if(!vis[v] && v != pa)
			dfs2(v,u,pos);
				
	}
}
void centroid(int root){
	dfs(root,root);
	if(child[root] == 1) return;
	int cen = findcen(root,root,child[root]);
	
	vis[cen] = true;
	memset(d,0x3f,sizeof d);
	all.clear();
	
	for(int i = 0 ; i < adj[cen].size() ; ++i){
		int v = adj[cen][i].fi , w = adj[cen][i].se;
		if(!vis[v]){
			vi[i].clear();
			d[v] = w; vi[i].pb(w); all.pb(w);
			dfs1(v,v,i);
		}
	}
	
	sort(all.begin() , all.end());
	for(int i = 0 ; i < all.size() ; ++ i){
		if( i == 0) tcdall[i] = all[i];
		else tcdall[i] = tcdall[i-1] + all[i];
	}
	for(int i = 0 ; i < adj[cen].size() ; ++i){
		int v = adj[cen][i].fi ;
		if(!vis[v]){
			sort(vi[i].begin() , vi[i].end());
			for(int j = 0 ; j < vi[i].size() ; ++ j){
				if( j == 0) tcd[j] = vi[i][j];
				else tcd[j] = tcd[j-1] + vi[i][j];
			}
			dfs2(v,v,i);		
		}
	}
	ans[cen] += tcdall[all.size()-1];
	for(int i = 0 ; i < adj[cen].size() ; ++i){
		int v = adj[cen][i].fi ;
		if(!vis[v]) centroid(v);
	}
}
signed main(){
	scanf("%d",&n);
	for(int i = 1 ; i < n ; ++ i ){
		int u , v , w;
		scanf("%d%d%d",&u,&v,&w);
		adj[u].pb(ii(v,w));
		adj[v].pb(ii(u,w));
	}
	centroid(1);
	for(int i = 1 ; i<= n ;++ i)
		printf("%lld\n",ans[i]);
}