human
In fact, the problems E1 and E2 do not have much in common. You should probably think of them as two separate problems.

You are given an integer array a[1 … n] = [a_1, a_2, …, a_n].

Let us consider an empty [deque](https://tinyurl.com/pfeucbux) (double-ended queue). A deque is a data structure that supports adding elements to both the beginning and the end. So, if there are elements [3, 4, 4] currently in the deque, adding an element 1 to the beginning will produce the sequence [\color{red}{1}, 3, 4, 4], and adding the same element to the end will produce [3, 4, 4, \color{red}{1}].

The elements of the array are sequentially added to the initially empty deque, starting with a_1 and finishing with a_n. Before adding each element to the deque, you may choose whether to add it to the beginning or to the end.

For example, if we consider an array a = [3, 7, 5, 5], one of the possible sequences of actions looks like this:    1. |  add 3 to the beginning of the deque: |  deque has a sequence [\color{red}{3}] in it.
  
---|---|---  
  2. |  add 7 to the end of the deque: |  deque has a sequence [3, \color{red}{7}] in it.
  
  3. |  add 5 to the end of the deque: |  deque has a sequence [3, 7, \color{red}{5}] in it.
  
  4. |  add 5 to the beginning of the deque: |  deque has a sequence [\color{red}{5}, 3, 7, 5] in it.
  
  
Find the minimal possible number of inversions in the deque after the whole array is processed. 

An inversion in sequence d is a pair of indices (i, j) such that i < j and d_i > d_j. For example, the array d = [5, 3, 7, 5] has exactly two inversions — (1, 2) and (3, 4), since d_1 = 5 > 3 = d_2 and d_3 = 7 > 5 = d_4.

Input

The first line contains an integer t (1 ≤ t ≤ 1000) — the number of test cases.

The next 2t lines contain descriptions of the test cases. 

The first line of each test case description contains an integer n (1 ≤ n ≤ 2 ⋅ 10^5) — array size. The second line of the description contains n space-separated integers a_i (-10^9 ≤ a_i ≤ 10^9) — elements of the array.

It is...
Solve the task in PYTHON3.

Write me a Python code to find the minimal possible number of inversions in the deque after the whole array is processed?
assistant
#Here is Python code to find the minimal possible number of inversions in the deque after the whole array is processed.

class BIT:
    def __init__(self, n):
        self.n = n
        self.bit = [0]*(self.n+1) # 1-indexed

    def init(self, init_val):
        for i, v in enumerate(init_val):
            self.add(i, v)

    def add(self, i, x):
        # i: 0-indexed
        i += 1 # to 1-indexed
        while i <= self.n:
            self.bit[i] += x
            i += (i & -i)

    def sum(self, i, j):
        # return sum of [i, j)
        # i, j: 0-indexed
        return self._sum(j) - self._sum(i)

    def _sum(self, i):
        # return sum of [0, i)
        # i: 0-indexed
        res = 0
        while i > 0:
            res += self.bit[i]
            i -= i & (-i)
        return res

    def lower_bound(self, x):
        s = 0
        pos = 0
        depth = self.n.bit_length()
        v = 1 << depth
        for i in range(depth, -1, -1):
            k = pos + v
            if k <= self.n and s + self.bit[k] < x:
                    s += self.bit[k]
                    pos += v
            v >>= 1
        return pos

    def __str__(self): # for debug
        arr = [self.sum(i,i+1) for i in range(self.n)]
        return str(arr)

import sys
import io, os
input = sys.stdin.buffer.readline
#input = io.BytesIO(os.read(0,os.fstat(0).st_size)).readline

t = int(input())
from collections import deque
for _ in range(t):
    n= int(input())
    A = list(map(int, input().split()))
    X = set(A)
    X = list(X)
    X.sort()
    toid = {}
    for i, x in enumerate(X):
        toid[x] = i
    A = [toid[a] for a in A]
    bit = BIT(n+2)
    q = deque([])
    ans = 0
    for p in A:
        m = bit.sum(0, p)
        M = bit.sum(p+1, bit.n)
        if m < M:
            ans += m
        else:
            ans += M
        bit.add(p, 1)
    print(ans)