codeforces#P1712B. Woeful Permutation
Woeful Permutation
Description
You are given a positive integer $n$.
Find any permutation $p$ of length $n$ such that the sum $\operatorname{lcm}(1,p_1) + \operatorname{lcm}(2, p_2) + \ldots + \operatorname{lcm}(n, p_n)$ is as large as possible.
Here $\operatorname{lcm}(x, y)$ denotes the least common multiple (LCM) of integers $x$ and $y$.
A permutation is an array consisting of $n$ distinct integers from $1$ to $n$ in arbitrary order. For example, $[2,3,1,5,4]$ is a permutation, but $[1,2,2]$ is not a permutation ($2$ appears twice in the array) and $[1,3,4]$ is also not a permutation ($n=3$ but there is $4$ in the array).
Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 1\,000$). Description of the test cases follows.
The only line for each test case contains a single integer $n$ ($1 \le n \le 10^5$).
It is guaranteed that the sum of $n$ over all test cases does not exceed $10^5$.
For each test case print $n$ integers $p_1$, $p_2$, $\ldots$, $p_n$ — the permutation with the maximum possible value of $\operatorname{lcm}(1,p_1) + \operatorname{lcm}(2, p_2) + \ldots + \operatorname{lcm}(n, p_n)$.
If there are multiple answers, print any of them.
Input
Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 1\,000$). Description of the test cases follows.
The only line for each test case contains a single integer $n$ ($1 \le n \le 10^5$).
It is guaranteed that the sum of $n$ over all test cases does not exceed $10^5$.
Output
For each test case print $n$ integers $p_1$, $p_2$, $\ldots$, $p_n$ — the permutation with the maximum possible value of $\operatorname{lcm}(1,p_1) + \operatorname{lcm}(2, p_2) + \ldots + \operatorname{lcm}(n, p_n)$.
If there are multiple answers, print any of them.
Samples
<div class="test-example-line test-example-line-even test-example-line-0">2</div><div class="test-example-line test-example-line-odd test-example-line-1">1</div><div class="test-example-line test-example-line-even test-example-line-2">2</div><div class="test-example-line test-example-line-even test-example-line-2"></div>
1
2 1
Note
For $n = 1$, there is only one permutation, so the answer is $[1]$.
For $n = 2$, there are two permutations:
- $[1, 2]$ — the sum is $\operatorname{lcm}(1,1) + \operatorname{lcm}(2, 2) = 1 + 2 = 3$.
- $[2, 1]$ — the sum is $\operatorname{lcm}(1,2) + \operatorname{lcm}(2, 1) = 2 + 2 = 4$.