B. Make Them Equaltime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given an array a consisting of n positive integers, numbered from 1 to n. You can perform the following operation no more than 3n times:  choose three integers i, j and x (1 \le i, j \le n; 0 \le x \le 10^9);  assign a_i := a_i - x \cdot i, a_j := a_j + x \cdot i. After each operation, all elements of the array should be non-negative.Can you find a sequence of no more than 3n operations after which all elements of the array are equal?InputThe first line contains one integer t (1 \le t \le 10^4) — the number of test cases. Then t test cases follow.The first line of each test case contains one integer n (1 \le n \le 10^4) — the number of elements in the array. The second line contains n integers a_1, a_2, \dots, a_n (1 \le a_i \le 10^5) — the elements of the array.It is guaranteed that the sum of n over all test cases does not exceed 10^4.OutputFor each test case print the answer to it as follows:  if there is no suitable sequence of operations, print -1;  otherwise, print one integer k (0 \le k \le 3n) — the number of operations in the sequence. Then print k lines, the m-th of which should contain three integers i, j and x (1 \le i, j \le n; 0 \le x \le 10^9) for the m-th operation. If there are multiple suitable sequences of operations, print any of them. Note that you don't have to minimize k.ExampleInput
3
4
2 16 4 18
6
1 2 3 4 5 6
5
11 19 1 1 3
Output
2
4 1 2
2 3 3
-1
4
1 2 4
2 4 5
2 3 3
4 5 1

3
4
2 16 4 18
6
1 2 3 4 5 6
5
11 19 1 1 3

2 4 1 2 2 3 3 -1 4 1 2 4 2 4 5 2 3 3 4 5 1 
['constructive algorithms', 'greedy', 'math', '*2000']