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;
typedef long long ll;
const int maxn=100010;
const int inf=0x3f3f3f3f;
typedef pair<int,int> pr;
inline ll read()
{
	ll x=0,f=1;char c=getchar();
	while(!isdigit(c)){if(c=='-')f=-1;c=getchar();}
	while(isdigit(c)){x=x*10+c-'0';c=getchar();}
	return x*f;
}
template<typename T>inline void Min(T &x,ll y){if(x>y)x=y;}
struct edge{
	int from,to;
	ll w;
	bool operator < (const edge &rhs) const {
		return w>rhs.w;
	}
}e[maxn<<1];
int n,fa[maxn];
ll tag[maxn],ans[maxn];
vector<int> g[maxn];
inline int find(int x){return x==fa[x]?x:fa[x]=find(fa[x]);}
inline void merge(int x,int y,ll w)
{
	int fx=find(x),fy=find(y);
	if(g[fx].size()<g[fy].size()) swap(fx,fy);
	for(int i=0;i<g[fy].size();i++) ans[g[fy][i]]+=1LL*tag[fy]-tag[fx]+(g[fx].size()-g[fy].size())*w;
	tag[fx]+=1LL*(ll)g[fy].size()*w;for(int i=0;i<g[fy].size();i++) g[fx].push_back(g[fy][i]);
	fa[fy]=fx;find(x),find(y);
}
int main()
{
	n=read();
	for(int i=1;i<=n;i++) g[i].push_back(i),fa[i]=i;
	for(int i=1;i<n;i++) e[i].from=read(),e[i].to=read(),e[i].w=read();
	sort(e+1,e+n);
	for(int i=1;i<n;i++) merge(e[i].from,e[i].to,e[i].w);
	for(int i=1;i<=n;i++) printf("%lld\n",ans[i]+tag[find(i)]);
	return 0;
}