#### Binary Insertion Sort

A
```"""
This is a pure Python implementation of the binary insertion sort algorithm

For doctests run following command:
python -m doctest -v binary_insertion_sort.py
or
python3 -m doctest -v binary_insertion_sort.py

For manual testing run:
python binary_insertion_sort.py
"""

def binary_insertion_sort(collection: list) -> list:
"""
Sorts a list using the binary insertion sort algorithm.

:param collection: A mutable ordered collection with comparable items.
:return: The same collection ordered in ascending order.

Examples:
>>> binary_insertion_sort([0, 4, 1234, 4, 1])
[0, 1, 4, 4, 1234]
>>> binary_insertion_sort([]) == sorted([])
True
>>> binary_insertion_sort([-1, -2, -3]) == sorted([-1, -2, -3])
True
>>> lst = ['d', 'a', 'b', 'e', 'c']
>>> binary_insertion_sort(lst) == sorted(lst)
True
>>> import random
>>> collection = random.sample(range(-50, 50), 100)
>>> binary_insertion_sort(collection) == sorted(collection)
True
>>> import string
>>> collection = random.choices(string.ascii_letters + string.digits, k=100)
>>> binary_insertion_sort(collection) == sorted(collection)
True
"""

n = len(collection)
for i in range(1, n):
value_to_insert = collection[i]
low = 0
high = i - 1

while low <= high:
mid = (low + high) // 2
if value_to_insert < collection[mid]:
high = mid - 1
else:
low = mid + 1
for j in range(i, low, -1):
collection[j] = collection[j - 1]
collection[low] = value_to_insert
return collection

if __name__ == "__main":
user_input = input("Enter numbers separated by a comma:\n").strip()
try:
unsorted = [int(item) for item in user_input.split(",")]
except ValueError:
print("Invalid input. Please enter valid integers separated by commas.")
raise
print(f"{binary_insertion_sort(unsorted) = }")
```