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 sz(x) (int)x.size() 
#define pb push_back 
#define mp make_pair 
#define fi(a, b) for(int i=a; i<=b; i++) 
#define fj(a, b) for(int j=a; j<=b; j++) 
#define fo(a, b) for(int o=a; o<=b; o++) 
#define fdi(a, b) for(int i=a; i>=b; i--) 
#define fdj(a, b) for(int j=a; j>=b; j--) 
#define fdo(a, b) for(int o=a; o>=b; o--) 

#ifdef LOCAL
#define err(...) fprintf(stderr, __VA_ARGS__)
#else
#define err(...) while(false) {}
#endif

typedef long long ll; 
typedef pair<int, int> pii; 
typedef pair<ll, ll> pll; 
typedef vector<int> vi; 
typedef vector<ll> vll;
typedef vector<pii> vpii; 
typedef vector<pll> vpll; 
typedef long double ld;
typedef unsigned long long ull;

/////////////////////////////////

int const MAX = 1e5 + 41;

int n;
int a[MAX];
int b[MAX];
int c[MAX];

vi per;

bool cmp(int i, int j) {
	return c[i] > c[j];
}

int par[MAX];
ll ans[MAX];
ll add[MAX];
vi ver[MAX];

int find(int x) {
	if (par[x] == x) return x;
	return par[x] = find(par[x]);
}

void solve() {
	fi(1, n - 1) {
		per.pb(i);
	}
	sort(per.begin(), per.end(), cmp);

	fi(1, n) {
		par[i] = i;
		ver[i].pb(i);
	}

	for (int id : per) {
		int x = find(a[id]);
		int y = find(b[id]);
		if (sz(ver[x]) < sz(ver[y])) {
			swap(x, y);
		}
		for (int z : ver[y]) {
			ans[z] += add[y];
			ans[z] += (ll) (sz(ver[x]) - sz(ver[y])) * c[id];
			ans[z] -= add[x];
		}
		add[y] = 0;
		add[x] += (ll) sz(ver[y]) * c[id];
		ver[x].insert(ver[x].end(), ver[y].begin(), ver[y].end());
		par[y] = x;
	}
	fi(1, n) {
		ans[i] += add[find(i)];
		printf("%lld\n", ans[i]);
	}
}

int main() {
#ifdef LOCAL
	freopen("input.txt", "r", stdin);
	freopen("output.txt", "w", stdout);
#endif

  scanf("%d", &n);
  fi(1, n - 1) {
  	scanf("%d %d %d", &a[i], &b[i], &c[i]);
  }
	solve();		

	
#ifdef LOCAL
	err("ELAPSED TIME: %.3Lf\n", (ld) clock() / CLOCKS_PER_SEC);
#endif	
	
	return 0;
}