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 N = 100005;
int n, fa[2 * N], size[2 * N], val[2 * N];
ll tag[2 * N];
struct edge
{
	int a, b, c;
} e[N];
vector<int> g[2 * N];
bool operator<(const edge &x, const edge &y) { return x.c > y.c; }

int find(int x) { return fa[x] == x ? x : fa[x] = find(fa[x]); }

void dfs(int u)
{
	if (u <= n) size[u] = 1;
	for (int v : g[u]) dfs(v), size[u] += size[v];
	for (int v : g[u]) tag[v] += 1ll * (size[u] - size[v]) * val[u];
}
void get(int u)
{
	for (int v : g[u]) tag[v] += tag[u], get(v);
}

int main()
{
	scanf("%d", &n);
	for (int i = 1; i < n; i++) scanf("%d%d%d", &e[i].a, &e[i].b, &e[i].c);
	sort(e + 1, e + n);
	for (int i = 1; i <= n; i++) fa[i] = i;
	for (int i = 1; i < n; i++)
	{
		int s = find(e[i].a), t = find(e[i].b);
		fa[n + i] = n + i, val[n + i] = e[i].c;
		fa[s] = fa[t] = n + i;
		g[n + i].push_back(s), g[n + i].push_back(t);
	}
	dfs(2 * n - 1);
	get(2 * n - 1);
	for (int i = 1; i <= n; i++) printf("%lld\n", tag[i]);
}
