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 <algorithm>  
#include <iostream>  
#include <sstream>  
#include <string>  
#include <cstring>
#include <vector>  
#include <queue>  
#include <set>  
#include <map>  
#include <cstdio>  
#include <cstdlib>  
#include <cctype>  
#include <cmath>  
#include <list>  
#include <cassert>
#include <ctime>
#include <climits>
using namespace std;  

#define PB push_back  
#define MP make_pair  
#define SZ(v) ((int)(v).size())  
#define FOR(i,a,b) for(int i=(a);i<(b);++i)  
#define REP(i,n) FOR(i,0,n)  
#define FORE(i,a,b) for(int i=(a);i<=(b);++i)  
#define REPE(i,n) FORE(i,0,n)  
#define FORSZ(i,a,v) FOR(i,a,SZ(v))  
#define REPSZ(i,v) REP(i,SZ(v))  
typedef long long ll;
typedef unsigned long long ull;
ll gcd(ll a,ll b) { return b==0?a:gcd(b,a%b); }

const int MAXN = 100000;
const int MAXM = MAXN - 1;
typedef struct E { int a, b, c; } E;
bool operator<(const E &p, const E &q) { return p.c > q.c; }

int n, m;
E e[MAXM];

int par[MAXN], sz[MAXN]; ll val[MAXN];

int find(int a) { if (par[a] == a) return a; int b = par[a]; par[a] = find(b); if (par[a] != b) val[a] += val[b]; return par[a]; }

void run() {
	scanf("%d", &n); m = n - 1; REP(i, m) { scanf("%d%d%d", &e[i].a, &e[i].b, &e[i].c); --e[i].a, --e[i].b; }

	sort(e, e + m);
	REP(i, n) par[i] = i, sz[i] = 1, val[i] = 0;
	REP(i, m) {
		int a = find(e[i].a), b = find(e[i].b); assert(a != b);
		if (sz[a] < sz[b]) swap(a, b);
		val[a] += (ll)e[i].c*sz[b];
		val[b] += (ll)e[i].c*sz[a];
		val[b] -= val[a]; par[b] = a; sz[a] += sz[b];
		//printf("state:"); REP(j, n) printf(" %d=(%d,%d,%lld)", j + 1, par[j] + 1, par[j] == j ? sz[j] : -1, val[j]); puts("");
	}
	REP(i, n) {
		int rt = find(i);
		ll curval = i == rt ? val[i] : val[i] + val[rt];
		printf("%lld\n", curval);
	}
}

int main() {
	run();
	return 0;
}
