


import os
import string
import sys


UpperCAmelCase__   	=							1 << 8

UpperCAmelCase__   	=							{
    '''tab''': ord('''\t'''),
    '''newline''': ord('''\r'''),
    '''esc''': 27,
    '''up''': 65 + ARROW_KEY_FLAG,
    '''down''': 66 + ARROW_KEY_FLAG,
    '''right''': 67 + ARROW_KEY_FLAG,
    '''left''': 68 + ARROW_KEY_FLAG,
    '''mod_int''': 91,
    '''undefined''': sys.maxsize,
    '''interrupt''': 3,
    '''insert''': 50,
    '''delete''': 51,
    '''pg_up''': 53,
    '''pg_down''': 54,
}

UpperCAmelCase__   	=							KEYMAP['''up''']
UpperCAmelCase__   	=							KEYMAP['''left''']

if sys.platform == "win32":
  UpperCAmelCase__   	=							[]
  UpperCAmelCase__   	=							{
      b'''\xe0H''': KEYMAP['''up'''] - ARROW_KEY_FLAG,
      b'''\x00H''': KEYMAP['''up'''] - ARROW_KEY_FLAG,
      b'''\xe0P''': KEYMAP['''down'''] - ARROW_KEY_FLAG,
      b'''\x00P''': KEYMAP['''down'''] - ARROW_KEY_FLAG,
      b'''\xe0M''': KEYMAP['''right'''] - ARROW_KEY_FLAG,
      b'''\x00M''': KEYMAP['''right'''] - ARROW_KEY_FLAG,
      b'''\xe0K''': KEYMAP['''left'''] - ARROW_KEY_FLAG,
      b'''\x00K''': KEYMAP['''left'''] - ARROW_KEY_FLAG,
  }

for i in range(10):
  UpperCAmelCase__   	=							ord(str(i))
def 				UpperCAmelCase_					(							)     ->			Dict:







 """simple docstring"""


 if os.name == "nt":
  import msvcrt

  _lowercase							      ="mbcs"
  # Flush the keyboard buffer
  while msvcrt.kbhit():
   msvcrt.getch()
  if len(__a						) == 0:
   # Read the keystroke
   _lowercase							      =msvcrt.getch()

   # If it is a prefix char, get second part
   if ch in (b"\x00", b"\xe0"):
    _lowercase							      =ch + msvcrt.getch()
    # Translate actual Win chars to bullet char types
    try:
     _lowercase							      =chr(WIN_KEYMAP[cha]						)
     WIN_CH_BUFFER.append(chr(KEYMAP['''mod_int''']						)						)
     WIN_CH_BUFFER.append(__a						)
     if ord(__a						) in (
         KEYMAP["insert"] - 1 << 9,
         KEYMAP["delete"] - 1 << 9,
         KEYMAP["pg_up"] - 1 << 9,
         KEYMAP["pg_down"] - 1 << 9,
     ):
      WIN_CH_BUFFER.append(chr(126						)						)
     _lowercase							      =chr(KEYMAP['''esc''']						)
    except KeyError:
     _lowercase							      =cha[1]
   else:
    _lowercase							      =ch.decode(__a						)
  else:
   _lowercase							      =WIN_CH_BUFFER.pop(0						)
 elif os.name == "posix":
  import termios
  import tty

  _lowercase							      =sys.stdin.fileno()
  _lowercase							      =termios.tcgetattr(__a						)
  try:
   tty.setraw(__a						)
   _lowercase							      =sys.stdin.read(1						)
  finally:
   termios.tcsetattr(__a     ,						termios.TCSADRAIN     ,						__a						)
 return ch



def 				UpperCAmelCase_					(							)     ->			List[Any]:







 """simple docstring"""


 _lowercase							      =get_raw_chars()
 if ord(__a						) in [KEYMAP["interrupt"], KEYMAP["newline"]]:
  return char

 elif ord(__a						) == KEYMAP["esc"]:
  _lowercase							      =get_raw_chars()
  if ord(__a						) == KEYMAP["mod_int"]:
   _lowercase							      =get_raw_chars()
   if ord(__a						) >= KEYMAP["arrow_begin"] - ARROW_KEY_FLAG and ord(__a						) <= KEYMAP["arrow_end"] - ARROW_KEY_FLAG:
    return chr(ord(__a						) + ARROW_KEY_FLAG						)
   else:
    return KEYMAP["undefined"]
  else:
   return get_raw_chars()

 else:
  if char in string.printable:
   return char
  else:
   return KEYMAP["undefined"]








from math import ceil, sqrt





def      lowerCAmelCase_ (       __a = 1000000		)     ->		int:







  """simple docstring"""





  lowerCamelCase__:      Optional[int]			  =0

  for outer_width in range(3	,    (limit // 4) + 2		):
    if outer_width**2 > limit:
      lowerCamelCase__:      Dict			  =max(ceil(sqrt(outer_width**2 - limit		)		)	,    1		)
    else:
      lowerCamelCase__:      str			  =1
    if (outer_width - hole_width_lower_bound) % 2:
      hole_width_lower_bound += 1

    answer += (outer_width - hole_width_lower_bound - 2) // 2 + 1

  return answer


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

