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;
typedef pair<int, int> PII;

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

#define N 100010
int n;
int px[N], py[N], pz[N];
int a[N];
int f[N], st[N], ed[N], ne[N];
int b[N]; // index
int ib[N];
ll S[N];
ll ad[N];

int cmp(int x, int y) {
	return pz[x] < pz[y];
}

int fa(int x) {
	if (f[x] == x) return x;
	return f[x] = fa(f[x]);
}

int main() {
	cin >> n;
	for (int i = 0; i < n-1; i ++) {
		cin >> px[i] >> py[i] >> pz[i];
		px[i] --;
		py[i] --;
		a[i] = i;
	}
	sort(a, a+n-1, cmp);
	for (int i = 0; i < n; i ++) {
		f[i] = i;
		st[i] = ed[i] = i;
	}
	for (int i = n-2; i >= 0; i --) {
		int x = px[a[i]], y = py[a[i]];
		x = fa(x); y = fa(y);
		if (x > y) swap(x, y);
		f[y] = x;
		ne[ed[x]] = st[y];
		ed[x] = ed[y];
	}
	for (int i = 0, j = 0; i < n; i ++) {
		b[j] = i;
		ib[i] = j;
		j = ne[j];
	}
	for (int i = 0; i < n; i ++) {
		f[i] = i;
		st[i] = ed[i] = i;
	}
	for (int i = n-2; i >= 0; i --) {
		int x = px[a[i]], y = py[a[i]], z = pz[a[i]];
		x = fa(x); y = fa(y);
		if (x > y) swap(x, y);
		int sx = b[ed[x]] - b[st[x]] + 1;
		int sy = b[ed[y]] - b[st[y]] + 1;
		//printf ("P %d %d\n", sx, sy);
		ad[b[st[x]]] += (ll)sy*z;
		ad[b[ed[x]]+1] -= (ll)sy*z;
		ad[b[st[y]]] += (ll)sx*z;
		ad[b[ed[y]]+1] -= (ll)sx*z;
		f[y] = x;
		ne[ed[x]] = st[y];
		ed[x] = ed[y];
	}
	ll cc = 0;
	for (int i = 0; i < n; i ++) {
		cc += ad[i];
		S[ib[i]] = cc;
	}
	for (int i = 0; i < n; i ++) cout << S[i] << endl;
	return 0;
}