题目描述
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
输入格式
见题面
输出格式
见题面