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;

using ll = long long;
using ld = long double;
using D = double;
using uint = unsigned int;
template<typename T>
using pair2 = pair<T, T>;

#ifdef WIN32
#define LLD "%I64d"
#else
#define LLD "%lld"
#endif

#define pb push_back
#define mp make_pair
#define all(x) (x).begin(),(x).end()
#define fi first
#define se second

const int maxn = 200005;

vector<pair<int, pair2<int>>> edges;
int n;
int p[maxn], s[maxn];
ll add[maxn];
int sz[maxn];

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

void unite(int a, int b)
{
    a = find(a);
    b = find(b);
    if (s[a] > s[b]) swap(a, b);
    p[a] = b;
    add[a] -= add[b];
    if (s[a] == s[b]) s[b]++;
    sz[b] += sz[a];
}

ll calc(int x)
{
    return p[x] == x ? add[x] : add[x] + calc(p[x]);
}

int main()
{
    scanf("%d", &n);
    for (int i = 0; i < n - 1; i++)
    {
        int a, b, c;
        scanf("%d%d%d", &a, &b, &c);
        a--, b--;
        edges.pb({c, {a, b}});
    }
    for (int i = 0; i < n; i++)
    {
        p[i] = i;
        s[i] = 0;
        sz[i] = 1;
    }
    sort(all(edges));
    reverse(all(edges));
    for (auto t : edges)
    {
        int a = find(t.se.fi);
        int b = find(t.se.se);
//         cout << "merge " << a << ' ' << b << endl;
        add[a] += (ll)t.fi * sz[b];
        add[b] += (ll)t.fi * sz[a];
        unite(a, b);
    }
    for (int i = 0; i < n; i++) printf("%lld\n", calc(i));
    return 0;
}