

from __future__ import annotations

from collections.abc import Sequence
from typing import Literal
def 							__SCREAMING_SNAKE_CASE     (   a__    :   str			,a__    :   str       )					->				str | Literal[False]:
	__A :			Tuple		    =			list(a__       )
	__A :			Optional[int]		    =			list(a__       )
	__A :			int		    =			0
	for i in range(len(a__       )       ):
		if lista[i] != lista[i]:
			count += 1
			__A :			int		    =			"""_"""
	if count > 1:
		return False
	else:
		return "".join(a__       )
def 							__SCREAMING_SNAKE_CASE     (   a__    :   list[str]       )					->				list[str]:
	__A :			Optional[Any]		    =			[]
	while True:
		__A :			Tuple		    =			["""$"""] * len(a__       )
		__A :			Union[str, Any]		    =			[]
		for i in range(len(a__       )       ):
			for j in range(i + 1			,len(a__       )       ):
				__A :			int		    =			compare_string(binary[i]			,binary[j]       )
				if k is False:
					__A :			List[str]		    =			"""*"""
					__A :			Any		    =			"""*"""
					temp.append("""X"""       )
		for i in range(len(a__       )       ):
			if checka[i] == "$":
				pi.append(binary[i]       )
		if len(a__       ) == 0:
			return pi
		__A :			Optional[Any]		    =			list(set(a__       )       )
def 							__SCREAMING_SNAKE_CASE     (   a__    :   int			,a__    :   Sequence[float]       )					->				list[str]:
	__A :			List[str]		    =			[]
	for minterm in minterms:
		__A :			List[Any]		    =			""""""
		for _ in range(a__       ):
			__A :			Union[str, Any]		    =			str(minterm % 2       ) + string
			minterm //= 2
		temp.append(a__       )
	return temp
def 							__SCREAMING_SNAKE_CASE     (   a__    :   str			,a__    :   str			,a__    :   int       )					->				bool:
	__A :			Optional[Any]		    =			list(a__       )
	__A :			Tuple		    =			list(a__       )
	__A :			Any		    =			0
	for i in range(len(a__       )       ):
		if lista[i] != lista[i]:
			count_n += 1
	return count_n == count
def 							__SCREAMING_SNAKE_CASE     (   a__    :   list[list[int]]			,a__    :   list[str]       )					->				list[str]:
	__A :			Optional[int]		    =			[]
	__A :			Tuple		    =			[0] * len(a__       )
	for i in range(len(chart[0]       )       ):
		__A :			str		    =			0
		__A :			Any		    =			-1
		for j in range(len(a__       )       ):
			if chart[j][i] == 1:
				count += 1
				__A :			Optional[Any]		    =			j
		if count == 1:
			__A :			int		    =			1
	for i in range(len(a__       )       ):
		if select[i] == 1:
			for j in range(len(chart[0]       )       ):
				if chart[i][j] == 1:
					for k in range(len(a__       )       ):
						__A :			List[str]		    =			0
			temp.append(prime_implicants[i]       )
	while True:
		__A :			Optional[Any]		    =			0
		__A :			Any		    =			-1
		__A :			int		    =			0
		for i in range(len(a__       )       ):
			__A :			List[Any]		    =			chart[i].count(1       )
			if count_n > max_n:
				__A :			Dict		    =			count_n
				__A :			Tuple		    =			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(a__       )       ):
					__A :			Union[str, Any]		    =			0
def 							__SCREAMING_SNAKE_CASE     (   a__    :   list[str]			,a__    :   list[str]       )					->				list[list[int]]:
	__A :			Any		    =			[[0 for x in range(len(a__       )       )] for x in range(len(a__       )       )]
	for i in range(len(a__       )       ):
		__A :			List[Any]		    =			prime_implicants[i].count("""_"""       )
		for j in range(len(a__       )       ):
			if is_for_table(prime_implicants[i]			,binary[j]			,a__       ):
				__A :			Union[str, Any]		    =			1

	return chart
def 							__SCREAMING_SNAKE_CASE     (   )					->				None:
	__A :			Any		    =			int(input("""Enter the no. of variables\n"""       )       )
	__A :			List[str]		    =			[
	    float(a__       )
	    for x in input(
	        """Enter the decimal representation of Minterms 'Spaces Separated'\n"""       ).split()
	]
	__A :			Dict		    =			decimal_to_binary(a__			,a__       )

	__A :			Union[str, Any]		    =			check(a__       )
	print("""Prime Implicants are:"""       )
	print(a__       )
	__A :			Optional[Any]		    =			prime_implicant_chart(a__			,a__       )

	__A :			Any		    =			selection(a__			,a__       )
	print("""Essential Prime Implicants are:"""       )
	print(a__       )


if __name__ == "__main__":
			import doctest

			doctest.testmod()
			main()












"""simple docstring"""



from collections import defaultdict
from math import gcd







def 						__lowercase	(  snake_case_    :    int = 1500000		)  ->int:



    '''simple docstring'''







    __A       :		defaultdict							=	defaultdict(snake_case_		)
    __A       :		Any							=	2
    while 2 * euclid_m * (euclid_m + 1) <= limit:
        for euclid_n in range((euclid_m % 2) + 1							,snake_case_							,2		):
            if gcd(snake_case_							,snake_case_		) > 1:
                continue
            __A       :		List[Any]							=	2 * euclid_m * (euclid_m + euclid_n)
            for perimeter in range(snake_case_							,limit + 1							,snake_case_		):
                frequencies[perimeter] += 1
        euclid_m += 1
    return sum(1 for frequency in frequencies.values() if frequency == 1		)


if __name__ == "__main__":
       print(f'''{solution() = }''')




