D. Make Them Equal SOLUTION Codeforces Round #673 (Div. 2)

Make Them Equal SOLUTION

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:

choose three integers i, j and x (1≤i,j≤n; 0≤x≤109);

assign ai:=ai−x⋅i, aj:=aj+x⋅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?

 

Input

The first line contains one integer t (1≤t≤104) — the number of test cases. Then t test cases follow.

 

The first line of each test case contains one integer n (1≤n≤104) — the number of elements in the array. The second line contains n integers a1,a2,…,an (1≤ai≤105) — the elements of the array.

 

It is guaranteed that the sum of n over all test cases does not exceed 104.

 

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≤k≤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≤i,j≤n; 0≤x≤109) 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.

 

Example

inputCopy

3

4

2 16 4 18

6

1 2 3 4 5 6

5

11 19 1 1 3

outputCopy

2

4 1 2

2 3 3

-1

4

1 2 4

2 4 5

2 3 3

4 5 1

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