





from __future__ import annotations

from collections.abc import Sequence
from typing import Literal

def   a_   (			lowerCAmelCase_				:      str,     lowerCAmelCase_				:      str     ):
   __lowerCAmelCase							     =     list(lowerCAmelCase_     )
   __lowerCAmelCase							     =     list(lowerCAmelCase_     )
   __lowerCAmelCase							     =     0
   for i in range(len(lowerCAmelCase_     )     ):
      if lista[i] != lista[i]:
         count += 1
         __lowerCAmelCase							     =     '_'
   if count > 1:
      return False
   else:
      return "".join(lowerCAmelCase_     )

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

def   a_   (			lowerCAmelCase_				:      int,     lowerCAmelCase_				:      Sequence[float]     ):
   __lowerCAmelCase							     =     []
   for minterm in minterms:
      __lowerCAmelCase							     =     ''
      for _ in range(lowerCAmelCase_     ):
         __lowerCAmelCase							     =     str(minterm % 2     ) + string
         minterm //= 2
      temp.append(lowerCAmelCase_     )
   return temp

def   a_   (			lowerCAmelCase_				:      str,     lowerCAmelCase_				:      str,     lowerCAmelCase_				:      int     ):
   __lowerCAmelCase							     =     list(lowerCAmelCase_     )
   __lowerCAmelCase							     =     list(lowerCAmelCase_     )
   __lowerCAmelCase							     =     0
   for i in range(len(lowerCAmelCase_     )     ):
      if lista[i] != lista[i]:
         count_n += 1
   return count_n == count

def   a_   (			lowerCAmelCase_				:      list[list[int]],     lowerCAmelCase_				:      list[str]     ):
   __lowerCAmelCase							     =     []
   __lowerCAmelCase							     =     [0] * len(lowerCAmelCase_     )
   for i in range(len(chart[0]     )     ):
      __lowerCAmelCase							     =     0
      __lowerCAmelCase							     =     -1
      for j in range(len(lowerCAmelCase_     )     ):
         if chart[j][i] == 1:
            count += 1
            __lowerCAmelCase							     =     j
      if count == 1:
         __lowerCAmelCase							     =     1
   for i in range(len(lowerCAmelCase_     )     ):
      if select[i] == 1:
         for j in range(len(chart[0]     )     ):
            if chart[i][j] == 1:
               for k in range(len(lowerCAmelCase_     )     ):
                  __lowerCAmelCase							     =     0
         temp.append(prime_implicants[i]     )
   while True:
      __lowerCAmelCase							     =     0
      __lowerCAmelCase							     =     -1
      __lowerCAmelCase							     =     0
      for i in range(len(lowerCAmelCase_     )     ):
         __lowerCAmelCase							     =     chart[i].count(1     )
         if count_n > max_n:
            __lowerCAmelCase							     =     count_n
            __lowerCAmelCase							     =     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(lowerCAmelCase_     )     ):
               __lowerCAmelCase							     =     0

def   a_   (			lowerCAmelCase_				:      list[str],     lowerCAmelCase_				:      list[str]     ):
   __lowerCAmelCase							     =     [[0 for x in range(len(lowerCAmelCase_     )     )] for x in range(len(lowerCAmelCase_     )     )]
   for i in range(len(lowerCAmelCase_     )     ):
      __lowerCAmelCase							     =     prime_implicants[i].count('_'     )
      for j in range(len(lowerCAmelCase_     )     ):
         if is_for_table(prime_implicants[i],     binary[j],     lowerCAmelCase_     ):
            __lowerCAmelCase							     =     1

   return chart

def   a_   (			):
   __lowerCAmelCase							     =     int(input('Enter the no. of variables\n'     )     )
   __lowerCAmelCase							     =     [
       float(lowerCAmelCase_     )
       for x in input(
           'Enter the decimal representation of Minterms \'Spaces Separated\'\n'     ).split()
   ]
   __lowerCAmelCase							     =     decimal_to_binary(lowerCAmelCase_,     lowerCAmelCase_     )

   __lowerCAmelCase							     =     check(lowerCAmelCase_     )
   print('Prime Implicants are:'     )
   print(lowerCAmelCase_     )
   __lowerCAmelCase							     =     prime_implicant_chart(lowerCAmelCase_,     lowerCAmelCase_     )

   __lowerCAmelCase							     =     selection(lowerCAmelCase_,     lowerCAmelCase_     )
   print('Essential Prime Implicants are:'     )
   print(lowerCAmelCase_     )


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     main()








from collections.abc import Sequence

def   a_   (			lowerCAmelCase_				:      Sequence[float],     lowerCAmelCase_				:      bool = False     ):
   if not arr:
      return 0

   __lowerCAmelCase							     =     0 if allow_empty_subarrays else float('-inf'     )
   __lowerCAmelCase							     =     0.0
   for num in arr:
      __lowerCAmelCase							     =     max(0 if allow_empty_subarrays else num,     curr_sum + num     )
      __lowerCAmelCase							     =     max(lowerCAmelCase_,     lowerCAmelCase_     )

   return max_sum


if __name__ == "__main__":
     from doctest import testmod

     testmod()

     _snake_case  :   Optional[Any]						   =  [-2, 1, -3, 4, -1, 2, 1, -5, 4]
     print(F"""{max_subarray_sum(nums) = }""")

