⣠⣤⣤⡤⠤⢤⣤⣀⡀⠀⠐⠒⡄⠀⡠⠒⠀⠀⢀⣀⣤⠤⠤⣤⣤⣤⡄
⠈⠻⣿⡤⠤⡏⠀⠉⠙⠲⣄⠀⢰⢠⠃⢀⡤⠞⠋⠉⠈⢹⠤⢼⣿⠏
⠀⠀⠘⣿⡅⠓⢒⡤⠤⠀⡈⠱⣄⣼⡴⠋⡀⠀⠤⢤⡒⠓⢬⣿⠃
⠀⠀⠀⠹⣿⣯⣐⢷⣀⣀⢤⡥⢾⣿⠷⢥⠤⣀⣀⣞⣢⣽⡿⠃
⠀⠀⠀⠀⠈⢙⣿⠝⠀⢁⠔⡨⡺⡿⡕⢔⠀⡈⠐⠹⣟⠋
⠀⠀⠀⠀⠀⢼⣟⢦⢶⢅⠜⢰⠃⠀⢹⡌⢢⣸⠦⠴⣿
⠀⠀⠀⠀⠀⠘⣿⣇⡬⡌⢀⡟⠀⠀⠀⢷⠀⣧⢧⣵⣿
⠀⠀⠀⠀⠀⠀⠈⢻⠛⠋⠉⠀⠀⠀⠀⠈⠉⠙⢻⡏

                         ⣠⢤⣀
   ⢰⠋⠉⠒⢄  ⣠⠤⠔⢒⠎    ⠈⠳⣤⢤⡀
 ⢀⡏      ⠔⠉            ⢄    ⠘⢦⠈⠑⢤⡀  ⢀⣤⣤⡀
 ⢸⢠⢆                    ⠈⡆    ⢈⠆    ⠙⢔⠋⢀⡼⠃
 ⠸⢨⠊                    ⠈⠃              ⠈⢯⠁
 ⡰⠁                                          ⠈⡆
⣰⠁⢀⣀                                          ⣷
⡇⣂⢸⣿⠂⠠⣀⡠  ⢰⣿⣷  ⣀                      ⡏
⢳⡀               ⠉⠁⠐⠄                  ⢀⡜⠁
 ⠙⢤⡀                                  ⣀⡴⠋
     ⠉⠉⠒⠒⠦⠤⠤⣤⣤⣤⣤⣤⠤⠤⠶⠒⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠉⠑⠲⢄
⠀⠀⠀⠀⠀⢠⣀⡀⠀⠀⣀⣀⡠⠖⠉⠀⠀⠰⡀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠜⠐⣌⠑⡞⠀⠀⠉⠒⠒⠒⠤⣀⢱⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢇⠀⢀⡵⠈⠲⠤⠤⡀⠀⠀⠀⠀⠱⡆⠀⠀⢱
⠀⠀⠀⠀⢠⠬⠦⠀⠀⠀⠀⠀⠀⠈⠓⢄⣀⡀⠀⠱⡀⠀⠈⡆
⢠⡄⠀⠀⢸⡂⠀⢀⡴⢲⣶⡆⠀⠀⡠⣶⣖⣯⣢⡀⢑⡄⠀⡇
⢸⠈⠱⢦⠘⠣⡀⠀⠑⠾⠯⠁⣀⣀⠠⠿⠷⠋⠀⢈⢥⠟⠚⠲⡄
⡇⠀⠀⠈⢇⠀⠙⠶⡀⠀⠒⣀⡱⢎⣀⠂⠀⠀⡤⠊⠸⣄⠀⣀⠞
⠑⡄⠀⠀⢸⡀⠀⠀⠈⠉⣖⡦⣄⣀⣴⡒⠉⠁⠀⠀⠀⠈⠉⠁
⠀⠈⠢⣤⣀⣈⡓⠒⠊⠉⠀⠀⠖⠃⠀⢙
⠀⠀⠀⠀⠀⠀⠇⠀⠀⢀⡀⠀⠀⢀⠆⡸
⠀⠀⠀⠀⠀⠀⠣⡄⠀⢠⡛⡦⠀⢼⡮⢄
⠀⠀⠀⠀⠀⠀⠀⢇⣰⣠⠼⢧⣠⡸⠔⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠉⠑⠲⢄
⠀⠀⠀⠀⠀⢠⣀⡀⠀⠀⣀⣀⡠⠖⠉⠀⠀⠰⡀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠜⠐⣌⠑⡞⠀⠀⠉⠒⠒⠒⠤⣀⢱⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢇⠀⢀⡵⠈⠲⠤⠤⡀⠀⠀⠀⠀⠱⡆⠀⠀⢱
⠀⠀⠀⠀⢠⠬⠦⠀⠀⠀⠀⠀⠀⠈⠓⢄⣀⡀⠀⠱⡀⠀⠈⡆
⢠⡄⠀⠀⢸⡂⠀⢀⡴⢲⣶⡆⠀⠀⡠⣶⣖⣯⣢⡀⢑⡄⠀⡇
⢸⠈⠱⢦⠘⠣⡀⠀⠑⠾⠯⠁⣀⣀⠠⠿⠷⠋⠀⢈⢥⠟⠚⠲⡄
⡇⠀⠀⠈⢇⠀⠙⠶⡀⠀⠒⣀⡱⢎⣀⠂⠀⠀⡤⠊⠸⣄⠀⣀⠞
⠑⡄⠀⠀⢸⡀⠀⠀⠈⠉⣖⡦⣄⣀⣴⡒⠉⠁⠀⠀⠀⠈⠉⠁
⠀⠈⠢⣤⣀⣈⡓⠒⠊⠉⠀⠀⠖⠃⠀⢙
⠀⠀⠀⠀⠀⠀⠇⠀⠀⢀⡀⠀⠀⢀⠆⡸
⠀⠀⠀⠀⠀⠀⠣⡄⠀⢠⡛⡦⠀⢼⡮⢄
⠀⠀⠀⠀⠀⠀⠀⢇⣰⣠⠼⢧⣠⡸⠔⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣆⢀⡀⣰⣿⣦
⠀⢰⠉⠉⠒⠲⢄⠀⢿⣿⣿⠿⠿⣿⣿⡿⠀⡠⠖⠒⠉⢱
⠀⢸⠀⣿⣷⣦⠀⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠁⣴⣾⣿⠀⡇
⠀⢸⠀⢿⡿⠋⢀⠤⠄⠀⠀⠀⠀⠀⠀⠠⠤⡀⠙⣿⡿⠀⡇
⠀⠸⡇⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⢸⣇
⢠⠏⠀⠀⠀⠐⢤⣠⣤⡀⠀⠀⠀⠀⢀⣤⣄⡤⠂⠀⠀⠀⢹⡄
⠈⣧⠀⠤⣀⠀⢿⣿⣿⡇⠀⠀⠀⠀⢿⣿⣿⡇⣀⠤⠀⢀⡟
⠀⠈⢳⠩⠭⠀⠀⠉⠉⠀⠀⠺⠗⠀⠀⠉⠉⠀⠭⠍⣠⠎
⠀⠀⠀⠘⠷⣄⣀⡀⠀⠀⠑⠊⠑⠊⠀⠀⢀⣀⡤⠞⠁⢾⣧⣼⡷
⠀⠀⠀⠀⠀⡔⠉⠙⠛⠛⠻⠿⠿⠟⠛⠛⠉⠉⢢⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠈⠒⠒⡏⠀⠁⠈⠁⠈⠀⠹⡒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⡰⡁⡁⡁⡁⡁⡁⡁⡁⣣
⠀⠀⠀⠀⠀⠀⠀⠧⡤⠤⢤⣤⣤⡤⠤⢤⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⡸⠁⠈⢇⣀⠎

⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠒⠚⠛⠓⢲⣶⡤
⠀⠀⠀⠀⢀⡴⠚⠁⠁⠁⠁⣁⠵⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀★
⠀⠀⢀⣴⠁⠁⠁⠁⠁⢁⡞⠁
⠀⢠⡞⠁⠁⠁⠁⠁⢁⠏⠀⠀
⢀⡾⠁⠁⠁⠁⠁⢁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢠⡿
⣼⠁⠁⠁⠁⠁⠁⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣶⡄⣰⣿
⣿⠁⠁⠁⠁⠁⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠏
⣿⠁⠁⠁⠁⠁⠁⢻⡄⠀⠀⠀⣴⠿⢿⣆⠀⢀⣴⣿⣿⣿⣿⠃
⢻⠁⠁⠁⠁⠁⠁⠉⣷⡀⠀⠀⣿⠀⠾⠏⣴⣿⣿⣿⣿⣿⡟
⠈⢧⠁⠁⠁⠁⠁⠁⠉⠷⣄⠀⠹⡄⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠘⢆⠁⠁⠁⠁⠁⠁⠁⠉⠳⣄⠹⣦⡀⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠈⢳⡁⠁⠁⠁⠁⠁⠁⠁⠉⠙⠶⡿⣿⣿⣿⣿⣿⣿⠷
⠀⠀⠀⠀⠉⠳⣅⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⠁⣁⡥⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠳⢧⣥⣥⣥⡥⠥⠵⠛⠋⠁⠀⠀