# Shifting Sort Solution Codeforces

The new generation external memory contains an array of integers .

This type of memory does not support changing the value of an arbitrary element. Instead, it allows you to cut out any segment of the given array, cyclically shift (rotate) it by any offset and insert it back into the same place.

## Shifting Sort Solution Codeforces

Technically, each cyclic shift consists of two consecutive actions:

1. You may select arbitrary indices  and  () as the boundaries of the segment.
2. Then you replace the segment  with it’s cyclic shift to the left by an arbitrary offset . The concept of a cyclic shift can be also explained by following relations: the sequence  is a cyclic shift of the sequence  to the left by the offset  and the sequence  is a cyclic shift of the sequence  to the left by the offset .

For example, if , then choosing  and  yields a segment . This segment is then shifted by the offset  to the left, and you get a segment  which then takes the place of of the original elements of the segment. In the end you get .

Sort the given array  using no more than  cyclic shifts of any of its segments. Note that you don’t need to minimize the number of cyclic shifts. Any method that requires  or less cyclic shifts will be accepted.

Input

### Shifting Sort Solution Codeforces

The first line contains an integer  () — the number of test cases.

The next  lines contain the descriptions of the test cases.

The first line of each test case description contains an integer  () — the length of the array. The second line consists of space-separated elements of the array  (). Elements of array  may repeat and don’t have to be unique.

## Shifting Sort Solution Codeforces

Output

Print  answers to all input test cases.

The first line of the answer of each test case should contain an integer  () — the number of actions to sort the array. The next  lines should contain descriptions of the actions formatted as “  ” (without quotes) where  and  () are the boundaries of the segment being shifted, while  () is the offset value. Please remember that only the cyclic shifts to the left are considered so the chosen segment will be shifted by the offset  to the to the left.

Note that you are not required to find the minimum number of cyclic shifts needed for sorting. Any sorting method where the number of shifts does not exceed  will be accepted.

If the given array  is already sorted, one of the possible answers is  and an empty sequence of cyclic shifts.

If there are several possible answers, you may print any of them.

Example
input

Copy

## Shifting Sort Solution Codeforces

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

output

Copy
1
1 2 1
1
1 3 2
3
2 4 1
2 3 1
1 3 2
4
2 4 2
1 5 3
1 2 1
1 3 1

Note

Explanation of the fourth data set in the example:

1. The segment  is selected and is shifted to the left by
2. The segment  is then selected and is shifted to the left by
3. After that the segment  is selected and is shifted to the left by
4. And in the end the segment  is selected and is shifted to the left by