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# Construct the Lexicographically Largest Valid Sequence

Last Updated: 12 Mar, 2021
Difficulty: Moderate

## PROBLEM STATEMENT

#### You are given a positive integer N. Your task is to create the lexicographically largest sequence of length 2*N - 1 containing integers between 1 to N such that:

``````1. 1 occurs in the sequence exactly once.
2. Each integer between 2 to N(inclusive) occurs in the sequence exactly twice.
3. For each integer i between 2 to N, the distance between the two occurrences of i should be exactly i.
``````

#### Note:

``````1. A sequence A is lexicographically larger than a sequence B (of the same length), if in the first position where A and B differ, sequence A has a number greater than the corresponding number in B.
2. It is guaranteed that under the given constraints, there is always a solution.
``````
##### Input Format:
``````The first line contains an integer, ‘T’ which denotes the number of test cases or queries to be run. Then, the T test cases follow.

The first and the only line of each test case contains one integer N, as described in the problem statement.
``````
##### Output Format:
``````For each test case, print in a new line, 2*'N' - 1 space-separated integer representing the lexicographically largest sequence for the given input.
``````
##### Note:
``````You do not need to print anything. It has already been taken care of. Just implement the given function.
``````
##### Constraints:
``````1 <= T <= 100
1 <= N <= 20

Time Limit: 1 second
``````