Make Them Equal

Description:

Input:

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 $$$10^4$$$.

Output:

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 $$$k$$$.

Sample Input:

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

Sample Output:

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