'''simple docstring'''


from __future__ import annotations

from collections.abc import Sequence
from typing import Literal





def       lowerCAmelCase					(		UpperCamelCase__				:   str    ,					UpperCamelCase__				:   str       ):


	"""simple docstring"""
	__UpperCAmelCase							=			list(UpperCamelCase__       )
	__UpperCAmelCase							=			list(UpperCamelCase__       )
	__UpperCAmelCase							=			0
	for i in range(len(UpperCamelCase__       )       ):
		if lista[i] != lista[i]:
			count += 1
			__UpperCAmelCase							=			'''_'''
	if count > 1:
		return False
	else:
		return "".join(UpperCamelCase__       )





def       lowerCAmelCase					(		UpperCamelCase__				:   list[str]       ):


	"""simple docstring"""
	__UpperCAmelCase							=			[]
	while True:
		__UpperCAmelCase							=			['''$'''] * len(UpperCamelCase__       )
		__UpperCAmelCase							=			[]
		for i in range(len(UpperCamelCase__       )       ):
			for j in range(i + 1    ,					len(UpperCamelCase__       )       ):
				__UpperCAmelCase							=			compare_string(binary[i]    ,					binary[j]       )
				if k is False:
					__UpperCAmelCase							=			'''*'''
					__UpperCAmelCase							=			'''*'''
					temp.append('''X'''       )
		for i in range(len(UpperCamelCase__       )       ):
			if checka[i] == "$":
				pi.append(binary[i]       )
		if len(UpperCamelCase__       ) == 0:
			return pi
		__UpperCAmelCase							=			list(set(UpperCamelCase__       )       )





def       lowerCAmelCase					(		UpperCamelCase__				:   int    ,					UpperCamelCase__				:   Sequence[float]       ):


	"""simple docstring"""
	__UpperCAmelCase							=			[]
	for minterm in minterms:
		__UpperCAmelCase							=			''''''
		for _ in range(UpperCamelCase__       ):
			__UpperCAmelCase							=			str(minterm % 2       ) + string
			minterm //= 2
		temp.append(UpperCamelCase__       )
	return temp





def       lowerCAmelCase					(		UpperCamelCase__				:   str    ,					UpperCamelCase__				:   str    ,					UpperCamelCase__				:   int       ):


	"""simple docstring"""
	__UpperCAmelCase							=			list(UpperCamelCase__       )
	__UpperCAmelCase							=			list(UpperCamelCase__       )
	__UpperCAmelCase							=			0
	for i in range(len(UpperCamelCase__       )       ):
		if lista[i] != lista[i]:
			count_n += 1
	return count_n == count





def       lowerCAmelCase					(		UpperCamelCase__				:   list[list[int]]    ,					UpperCamelCase__				:   list[str]       ):


	"""simple docstring"""
	__UpperCAmelCase							=			[]
	__UpperCAmelCase							=			[0] * len(UpperCamelCase__       )
	for i in range(len(chart[0]       )       ):
		__UpperCAmelCase							=			0
		__UpperCAmelCase							=			-1
		for j in range(len(UpperCamelCase__       )       ):
			if chart[j][i] == 1:
				count += 1
				__UpperCAmelCase							=			j
		if count == 1:
			__UpperCAmelCase							=			1
	for i in range(len(UpperCamelCase__       )       ):
		if select[i] == 1:
			for j in range(len(chart[0]       )       ):
				if chart[i][j] == 1:
					for k in range(len(UpperCamelCase__       )       ):
						__UpperCAmelCase							=			0
			temp.append(prime_implicants[i]       )
	while True:
		__UpperCAmelCase							=			0
		__UpperCAmelCase							=			-1
		__UpperCAmelCase							=			0
		for i in range(len(UpperCamelCase__       )       ):
			__UpperCAmelCase							=			chart[i].count(1       )
			if count_n > max_n:
				__UpperCAmelCase							=			count_n
				__UpperCAmelCase							=			i

		if max_n == 0:
			return temp

		temp.append(prime_implicants[rem]       )

		for i in range(len(chart[0]       )       ):
			if chart[rem][i] == 1:
				for j in range(len(UpperCamelCase__       )       ):
					__UpperCAmelCase							=			0





def       lowerCAmelCase					(		UpperCamelCase__				:   list[str]    ,					UpperCamelCase__				:   list[str]       ):


	"""simple docstring"""
	__UpperCAmelCase							=			[[0 for x in range(len(UpperCamelCase__       )       )] for x in range(len(UpperCamelCase__       )       )]
	for i in range(len(UpperCamelCase__       )       ):
		__UpperCAmelCase							=			prime_implicants[i].count('''_'''       )
		for j in range(len(UpperCamelCase__       )       ):
			if is_for_table(prime_implicants[i]    ,					binary[j]    ,					UpperCamelCase__       ):
				__UpperCAmelCase							=			1

	return chart





def       lowerCAmelCase					(		):


	"""simple docstring"""
	__UpperCAmelCase							=			int(input('''Enter the no. of variables\n'''       )       )
	__UpperCAmelCase							=			[
	    float(UpperCamelCase__       )
	    for x in input(
	        '''Enter the decimal representation of Minterms \'Spaces Separated\'\n'''       ).split()
	]
	__UpperCAmelCase							=			decimal_to_binary(UpperCamelCase__    ,					UpperCamelCase__       )

	__UpperCAmelCase							=			check(UpperCamelCase__       )
	print('''Prime Implicants are:'''       )
	print(UpperCamelCase__       )
	__UpperCAmelCase							=			prime_implicant_chart(UpperCamelCase__    ,					UpperCamelCase__       )

	__UpperCAmelCase							=			selection(UpperCamelCase__    ,					UpperCamelCase__       )
	print('''Essential Prime Implicants are:'''       )
	print(UpperCamelCase__       )


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					main()

'''simple docstring'''


def       lowerCAmelCase					(		UpperCamelCase__				:   Tuple       ):


	"""simple docstring"""
	# if the collection is empty, returns empty
	if collection == []:
		return []

	# get some information about the collection
	__UpperCAmelCase							=			len(UpperCamelCase__       )
	__UpperCAmelCase							=			max(UpperCamelCase__       )
	__UpperCAmelCase							=			min(UpperCamelCase__       )

	# create the counting array
	__UpperCAmelCase							=			coll_max + 1 - coll_min
	__UpperCAmelCase							=			[0] * counting_arr_length

	# count how much a number appears in the collection
	for number in collection:
		counting_arr[number - coll_min] += 1

	# sum each position with it's predecessors. now, counting_arr[i] tells
	# us how many elements <= i has in the collection
	for i in range(1    ,					UpperCamelCase__       ):
		__UpperCAmelCase							=			counting_arr[i] + counting_arr[i - 1]

	# create the output collection
	__UpperCAmelCase							=			[0] * coll_len

	# place the elements in the output, respecting the original order (stable
	# sort) from end to begin, updating counting_arr
	for i in reversed(range(0    ,					UpperCamelCase__       )       ):
		__UpperCAmelCase							=			collection[i]
		counting_arr[collection[i] - coll_min] -= 1

	return ordered





def       lowerCAmelCase					(		UpperCamelCase__				:   Any       ):


	"""simple docstring"""
	return "".join([chr(UpperCamelCase__       ) for i in counting_sort([ord(UpperCamelCase__       ) for c in string]       )]       )


if __name__ == "__main__":
					# Test string sort
					assert counting_sort_string("thisisthestring") == "eghhiiinrsssttt"

					__lowerCAmelCase	:       str						       =	input("Enter numbers separated by a comma:\n").strip()
					__lowerCAmelCase	:       List[Any]						       =	[int(item) for item in user_input.split(",")]
					print(counting_sort(unsorted))
