CF1416B Make Them Equal

You 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: 1. choose three integers $ i $ , $ j $ and $ x $ ( $ 1 \le i, j \le n $ ; $ 0 \le x \le 10^9 $ ); 2. 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?

The 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 $ .

For 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 $ .