[Solution] Permutation And Median CodeChef Solution

[Solution] Permutation And Median CodeChef Solution

Given a sequence A$A$ of N$N$ elements, Chef defines a function F(i)$F(i)$ (1≤i≤N)$(1\le i\le N)$ as the median of the first i$i$ elements of the sequence.

Chef wants to get a permutation P$P$ of length N$N$ such that Pi=F(i)$P_i=F(i)$ ∀$\mathrm{\forall }$ 1≤i≤N$1\le i\le N$. Can you help Chef in achieving this?

Note that:

• The median of a sequence is the middle element in the sorted order of the sequence. If N$N$ is even, choose the element at N2$\frac{N}{2}$ position in the sorted order. If N$N$ is odd, choose the middle element.
• A permutation of length N$N$ is an array of N$N$ integers P=[P1,P2,…,PN]$P=[P_1,P_2,\dots ,P_N]$ such that every integer from 1$1$ to N$N$ (inclusive) appears in it exactly once. For example, [2,5,4,1,3]$[2,5,4,1,3]$ is a permutation of

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•  length 5$5$ while [2,5,2,1,3]$[2,5,2,1,3]$ is not.

Input Format

• First line will contain T$T$, number of test cases. Then the test cases follows.
• Each test case consists of a single line of input, an integer N$N$, the length of the required

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•  permutation.

Output Format

For each test case, output in a new line, N$N$ space-separated integers, denoting a permutation satisfying the condition.

Constraints

• 1≤T≤700$1\le T\le 700$
• 1≤N≤105$1\le N\le {10}^5$
• Sum of N$N$ over all test cases does not exceed 2⋅105