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 ll long long
#define INF 1000000005
#define MOD 1000000007
#define EPS 1e-10
#define rep(i,n) for(int i=0;i<(int)(n);++i)
#define rrep(i,n) for(int i=(int)(n)-1;i>=0;--i)
#define srep(i,s,t) for(int i=(int)(s);i<(int)(t);++i)
#define each(a,b) for(auto (a): (b))
#define all(v) (v).begin(),(v).end()
#define len(v) (int)(v).size()
#define zip(v) sort(all(v)),v.erase(unique(all(v)),v.end())
#define cmx(x,y) x=max(x,y)
#define cmn(x,y) x=min(x,y)
#define fi first
#define se second
#define pb push_back
#define show(x) cout<<#x<<" = "<<(x)<<endl
#define spair(p) cout<<#p<<": "<<p.fi<<" "<<p.se<<endl
#define svec(v) cout<<#v<<":";rep(kbrni,v.size())cout<<" "<<v[kbrni];cout<<endl
#define sset(s) cout<<#s<<":";each(kbrni,s)cout<<" "<<kbrni;cout<<endl
#define smap(m) cout<<#m<<":";each(kbrni,m)cout<<" {"<<kbrni.first<<":"<<kbrni.second<<"}";cout<<endl

using namespace std;

typedef pair<int,int> P;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<double> vd;
typedef vector<P> vp;
typedef vector<string> vs;

const int MAX_N = 200005;

struct edge
{
    int from,to;
    ll cost;
    bool operator< (const edge& another) const {
        return cost > another.cost;
    }
};

struct eda
{
    int to;
    ll cost;
};

vector<eda> G[MAX_N];
int id;
int nw[MAX_N];

class UF {
private:
    int sz; vector<int> par,nrank,size;
public:
    UF(){}
    UF(int node_size){ sz = node_size; par.resize(sz),nrank.resize(sz),size.resize(sz);
        rep(i,sz){ par[i] = i; nrank[i] = 0; size[i] = 1;} }
    int find(int x){ if(par[x] == x){ return x; }else{ return par[x] = find(par[x]); } }
    void unite(int x,int y,ll cost){
        x = find(x),y = find(y);
        if(x == y) return;
        if(nrank[x] < nrank[y]) swap(x,y);
        ++id;
        G[id].pb((eda){nw[x],cost*size[y]}),G[id].pb((eda){nw[y],cost*size[x]});
        nw[x] = id;
        par[y] = x; size[x] += size[y];
        if(nrank[x] == nrank[y]) nrank[x]++;
    }
    int query(int x){ x = find(x); return size[x]; }
    bool same(int x,int y){ return find(x) == find(y); }
};

ll sm[MAX_N];

void dfs(int u,ll dist){
    sm[u] = dist;
    rep(i,len(G[u])){
        dfs(G[u][i].to,dist+G[u][i].cost);
    }
}

int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);
    int n;
    cin >> n;
    vector<edge> vec(n-1);
    rep(i,n-1){
        int a,b,c;
        cin >> a >> b >> c;
        vec[i] = (edge){a-1,b-1,c};
    }
    sort(all(vec));
    rep(i,n){
        nw[i] = i;
    }
    id = n-1;
    UF uf(n);
    rep(i,n-1){
        uf.unite(vec[i].from,vec[i].to,vec[i].cost);
    }
    dfs(id,0);
    rep(i,n){
        cout << sm[i] << "\n";
    }
    return 0;
}
