Array

Chiaki has an array of integers $a_1,a_2,\dots,a_n$. Chiaki can replace an element $a_x$ with another integer $y$. Let the resulting array be $b_1,b_2,\dots,b_n$. Chiaki would like to know the minimum value of $|a_x-y| + \sum_{k=1}^{n} k \cdot c_k$, where $c_k$ is the number of distinct integers in $b_1,b_2,\dots,b_k$.

There are multiple test cases. The first line of the input contains an integer $T$, indicating the number of test cases. For each test case:

The first line contains an integer $n$ ($1 \le n \le 10^6$), the length of the array.

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^9$).

It is guaranteed that the sum of $n$ over all test cases will not exceed $10^6$.

For each test case, output an integer denoting the answer.