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 xx first
#define yy second
#define mp make_pair
#define pb push_back
#define mset(x, y) memset(x, y, sizeof x)
#define mcpy(x, y) memcpy(x, y, sizeof x)
using namespace std;

typedef long long LL;
typedef pair <int, int> pii;

inline int Read()
{
	int x = 0, f = 1, c = getchar();
	for (; !isdigit(c); c = getchar())
		if (c == '-')
			f = -1;
	for (;  isdigit(c); c = getchar())
		x = x * 10 + c - '0';
	return x * f;
}

const int MAXN = 100005;

struct Edge
{
	int u, v, w;
	bool operator < (const Edge &b) const
	{
		return w > b.w;
	}
} e[MAXN];

LL ans[MAXN], tag[MAXN];
vector <int> g[MAXN];
int n, f[MAXN];

inline int Find(int x)
{
	while (x ^ f[x])
		x = f[x] = f[f[x]];
	return x;
}

inline void Merge(int x, int y, int w)
{
	x = Find(x), y = Find(y);
	if (g[x].size() < g[y].size())
		swap(x, y);
	for (auto i : g[y])
		ans[i] += tag[y] - tag[x], ans[i] += 1LL * (g[x].size() - g[y].size()) * w;
	tag[x] += 1LL * g[y].size() * w;
	for (auto i : g[y])
		g[x].pb(i);
	f[y] = x;
}

int main()
{
#ifdef wxh010910
	freopen("data.in", "r", stdin);
#endif
	n = Read();
	for (int i = 1; i <= n; i ++)
		f[i] = i, g[i].pb(i);
	for (int i = 1; i < n; i ++)
		e[i].u = Read(), e[i].v = Read(), e[i].w = Read();
	sort(e + 1, e + n);
	for (int i = 1; i < n; i ++)
		Merge(e[i].u, e[i].v, e[i].w);
	for (int i = 1; i <= n; i ++)
		printf("%lld\n", ans[i] + tag[Find(i)]);
	return 0;
}
