write a go solution for Description:
You are given a rooted tree. It contains n vertices, which are numbered from 1 to n. The root is the vertex 1.

Each edge has two positive integer values. Thus, two positive integers a_j and b_j are given for each edge.

Output n-1 numbers r_2,r_3,...,r_n, where r_i is defined as follows.

Consider the path from the root (vertex 1) to i (2<=i<=n). Let the sum of the costs of a_j along this path be A_i. Then r_i is equal to the length of the maximum prefix of this path such that the sum of b_j along this prefix does not exceed A_i.

Example for n=9. The blue color shows the costs of a_j, and the red color shows the costs of b_j.

Consider an example. In this case:

- r_2=0, since the path to 2 has an amount of a_j equal to 5, only the prefix of this path of length 0 has a smaller or equal amount of b_j;
- r_3=3, since the path to 3 has an amount of a_j equal to 5+9+5=19, the prefix of length 3 of this path has a sum of b_j equal to 6+10+1=17 ( the number is 17<=19);
- r_4=1, since the path to 4 has an amount of a_j equal to 5+9=14, the prefix of length 1 of this path has an amount of b_j equal to 6 (this is the longest suitable prefix, since the prefix of length 2 already has an amount of b_j equal to 6+10=16, which is more than 14);
- r_5=2, since the path to 5 has an amount of a_j equal to 5+9+2=16, the prefix of length 2 of this path has a sum of b_j equal to 6+10=16 (this is the longest suitable prefix, since the prefix of length 3 already has an amount of b_j equal to 6+10+1=17, what is more than 16);
- r_6=1, since the path up to 6 has an amount of a_j equal to 2, the prefix of length 1 of this path has an amount of b_j equal to 1;
- r_7=1, since the path to 7 has an amount of a_j equal to 5+3=8, the prefix of length 1 of this path has an amount of b_j equal to 6 (this is the longest suitable prefix, since the prefix of length 2 already has an amount of b_j equal to 6+3=9, which is more than 8);
- r_8=2, since the path up to 8 has an amount of a_j equal to 2+4=6, the prefix of length 2 of this path has an amount of b_j equal to 1+3=4;
- r_9=3, since the path to 9 has an amount of a_j equal to 2+4+1=7, the prefix of length 3 of this path has a sum of b_j equal to 1+3+3=7.

Input Format:
The first line contains an integer t (1<=t<=10^4) — the number of test cases in the test.

The descriptions of test cases follow.

Each description begins with a line that contains an integer n (2<=n<=2*10^5) — the number of vertices in the tree.

This is followed by n-1 string, each of which contains three numbers p_j,a_j,b_j (1<=p_j<=n; 1<=a_j,b_j<=10^9) — the ancestor of the vertex j, the first and second values an edge that leads from p_j to j. The value of j runs through all values from 2 to n inclusive. It is guaranteed that each set of input data has a correct hanged tree with a root at the vertex 1.

It is guaranteed that the sum of n over all input test cases does not exceed 2*10^5.

Output Format:
For each test case, output n-1 integer in one line: r_2,r_3,...,r_n.

Note:
The first example is clarified in the statement.

In the second example:

- r_2=0, since the path to 2 has an amount of a_j equal to 1, only the prefix of this path of length 0 has a smaller or equal amount of b_j;
- r_3=0, since the path to 3 has an amount of a_j equal to 1+1=2, the prefix of length 1 of this path has an amount of b_j equal to 100 (100>2);
- r_4=3, since the path to 4 has an amount of a_j equal to 1+1+101=103, the prefix of length 3 of this path has an amount of b_j equal to 102, .. Output only the code with no comments, explanation, or additional text.