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1 초 128 MB 19 10 10 52.632%

## 문제

Farmer John is decorating his Spring Equinox Tree (like a Christmas tree but popular about three months later). It can be modeled as a rooted mathematical tree with N (1 <= N <= 100,000) elements, labeled 1...N, with element 1 as the root of the tree. Each tree element e > 1 has a parent, P_e (1 <= P_e <= N). Element 1 has no parent (denoted '-1' in the input), of course, because it is the root of the tree.

Each element i has a corresponding subtree (potentially of size 1) rooted there. FJ would like to make sure that the subtree corresponding to element i has a total of at least C_i (0 <= C_i <= 10,000,000) ornaments scattered among its members. He would also like to minimize the total amount of time it takes him to place all the ornaments (it takes time K*T_i to place K ornaments at element i (1 <= T_i <= 100)).

Help FJ determine the minimum amount of time it takes to place ornaments that satisfy the constraints.  Note that this answer might not fit into a 32-bit integer, but it will fit into a signed 64-bit integer.

For example, consider the tree below where nodes located higher on the display are parents of connected lower nodes (1 is the root):

               1
|
2
|
5
/ \
4   3

Suppose that FJ has the following subtree constraints:

                  Minimum ornaments the subtree requires
|     Time to install an ornament
Subtree      |       |
root   |   C_i  |  T_i
--------+--------+-------
1    |    9   |   3
2    |    2   |   2
3    |    3   |   2
4    |    1   |   4
5    |    3   |   3

Then FJ can place all the ornaments as shown below, for a total cost of 20:

            1 [0/9(0)]     legend: element# [ornaments here/
|                      total ornaments in subtree(node install time)]
2 [3/9(6)]
|
5 [0/6(0)]
/ \
[1/1(4)] 4   3 [5/5(10)]

## 입력

• Line 1: A single integer: N
• Lines 2..N+1: Line i+1 contains three space-separated integers: P_i, C_i, and T_i

## 출력

• Line 1: A single integer: The minimum time to place all the ornaments

## 예제 입력 1

5
-1 9 3
1 2 2
5 3 2
5 1 4
2 3 3


## 예제 출력 1

20