CF1339B Sorted Adjacent Differences

You have array of $ n $ numbers $ a_{1}, a_{2}, \ldots, a_{n} $ . Rearrange these numbers to satisfy $ |a_{1} - a_{2}| \le |a_{2} - a_{3}| \le \ldots \le |a_{n-1} - a_{n}| $ , where $ |x| $ denotes absolute value of $ x $ . It's always possible to find such rearrangement. Note that all numbers in $ a $ are not necessarily different. In other words, some numbers of $ a $ may be same. You have to answer independent $ t $ test cases.

The first line contains a single integer $ t $ ( $ 1 \le t \le 10^{4} $ ) — the number of test cases. The first line of each test case contains single integer $ n $ ( $ 3 \le n \le 10^{5} $ ) — the length of array $ a $ . It is guaranteed that the sum of values of $ n $ over all test cases in the input does not exceed $ 10^{5} $ . The second line of each test case contains $ n $ integers $ a_{1}, a_{2}, \ldots, a_{n} $ ( $ -10^{9} \le a_{i} \le 10^{9} $ ).

For each test case, print the rearranged version of array $ a $ which satisfies given condition. If there are multiple valid rearrangements, print any of them.

In the first test case, after given rearrangement, $ |a_{1} - a_{2}| = 0 \le |a_{2} - a_{3}| = 1 \le |a_{3} - a_{4}| = 2 \le |a_{4} - a_{5}| = 2 \le |a_{5} - a_{6}| = 10 $ . There are other possible answers like "5 4 5 6 -2 8". In the second test case, after given rearrangement, $ |a_{1} - a_{2}| = 1 \le |a_{2} - a_{3}| = 2 \le |a_{3} - a_{4}| = 4 $ . There are other possible answers like "2 4 8 1".