human
PYTHON3 solution for "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...":



Write me a Python program to find the minimal possible number of inversions in the deque after the whole array is processed?
assistant
#Here is Python program to find the minimal possible number of inversions in the deque after the whole array is processed.
 'Sorted List\n==============\n\n:doc:`Sorted Containers<index>` is an Apache2 licensed Python sorted\ncollections library, written in pure-Python, and fast as C-extensions. The\n:doc:`introduction<introduction>` is the best way to get started.\n\nSorted list implementations:\n\n.. currentmodule:: sortedcontainers\n\n* :class:`SortedList`\n* :class:`SortedKeyList`\n\n'
from __future__ import print_function
u='lists'
t='len_lists'
s='maxes'
r='len_maxes'
q='index'
p='len_index'
o='offset'
n='load'
m='len'
l='use ``sl.add(value)`` instead'
k=all
j=sum
i=sorted
h=property
c='list index out of range'
b=isinstance
a=ImportError
S=type
R=IndexError
Q=NotImplementedError
P=slice
O='{0!r} not in list'
N=list
L='{0!r} is not in list'
K=False
J=reversed
I=True
H=iter
E=ValueError
D=print
C=range
B=None
A=len
import sys,traceback as T
from bisect import bisect_left,bisect_right,insort as d
from itertools import chain as M,repeat as e,starmap as U
from math import log
from operator import add,eq,ne,gt,ge,lt,le,iadd as F
from textwrap import dedent as f
try:from collections.abc import Sequence,MutableSequence as V
except a:from collections import Sequence,MutableSequence as V
from functools import wraps
from sys import hexversion as g
if g<50331648:
    from itertools import imap as map,izip as zip
    try:from thread import get_ident
    except a:from dummy_thread import get_ident
else:
    from functools import reduce as G
    try:from _thread import get_ident
    except a:from _dummy_thread import get_ident
def W(fillvalue='...'):
    'Decorator to make a repr function return fillvalue for a recursive call.'
    def A(user_function):
        C=user_function;A=set()
        @wraps(C)
        def B(self):
            B=id(self),get_ident()
            if B in A:return fillvalue
            A.add(B)
            try:D=C(self)
            finally:A.discard(B)
            return D
        return B
    return A
class X(V):
    'Sorted list is a sorted mutable sequence.\n\n    Sorted list values are maintained in sorted...