Group by Mean

There are multiple batches in a coding school, batch numbers start from 0 and each batch can have multiple students.

You are given an array of arrays ‘Batch’, where each array denotes the ratings of students in that batch.

You have to group the batches such that all the batches with the same mean rating are part of the same group.

Return an array of arrays where each array denotes a group of batches. All the batches should be sorted in each group, and groups should be sorted according to the first batch number in it (Refer to the example below).

For Example :

If Batch = { { 1, 2, 3, 4, 5 }, { 4, 2, 4 }, { 2, 3, 4 }, { 1, 1, 1, 1 }, { 0, 2 } }

Then:
Batch [ 0 ] =  { 1, 2, 3, 4, 5 } has mean equal to ( 1 + 2 + 3 + 4 + 5 ) / 5 = 3
Batch [ 1 ] =  { 4, 2, 4 } has mean equal to 3.33
Batch [ 2 ] =  { 1, 1, 1, 1 } has mean equal to 1
Batch [ 3 ] =  { 2, 3, 4 } has mean equal to 3
Batch [ 4 ] =  { 0, 2 } has mean equal to 1

We will group Batch[0] and Batch[3] together, Batch[2] and Batch[4] together and Batch[1] will be grouped alone.

So we will finally return { { 0, 3 }, { 1 }, { 2, 4 } }.
(Note that we sorted the batch numbers inside each group, and then sorted all the groups by the first batch number inside each of them)

Input Format :

The first line contains a single integer ‘T’ denoting the number of test cases, then each test case follows:

The first line of each test case contains a single integer ‘N’ denoting the number of batches.

The next line contains N integers, where M[i] denotes the number of students in the ith batch.

The next N lines each contains M[i] integers, each denoting the ratings of the batch member.

Output Format :

For each test case, print all the groups, with each group containing batch numbers that are to be grouped together, all the groups are printed in a separate line.

Output for each test case will be printed in a separate line.

Note :

You are not required to print anything; it has already been taken care of. Just implement the function.

Constraints :

1 <= T <= 10      
1 <= N <= 200
1 <= M <= 100
0 <= Batch[i][j] <= 10^6

Time limit: 1 sec