⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢯⡝⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⣼⢻⡘⣿⡄.̵̼͚̤͇͎̮̦̠͙̎͗́̅̉͒͋̈́̋̆̉̇̏͋́̀͂͘͝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀.̴̡̨̨̝̻̲̤̩͓͚̲̻̻̥̳̪͕͖͉͔͓̭̯̩̦͓̗͔̥̩͕̠̤͚̫̝̬̎͌̾̔̃̈́́̾́́͛̿̿̚͝͝ͅ⠀⠀⠀⠀⠀⠀⠀⢰⡿⢰⣇⣈⡇⠸⣿⡶⠶⠾⠛⠛⠶⠶⣤⣤⣀⠀⠀⠀⠀⢀⣤⠾⢛⠉⣿⡇.̴̧̡̧̨̧̨̹̥̣̲̫͙͚̱̼̥̲͙͚͕̤̻̤̣̭͙̬̦͍͖͍̱͙̱͇̞͚̝̭͓̦̳̫̯̺̻̳͓͛̆́̆̿̚͜ͅ⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣤⡴⢋⡴⠚⢹⢠⣿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠞⢧⣄⣾⣸⡏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀.̸̧͔͕͍̘̲̗͔͕͙̭̹̦̞̳͖̯̗͙͇̭̫̩͇̜͈͇̼̘͖͉͔̣̼͈̝̻̞̪̂̔̀̂̍͆̋͊̍̌͒̍̈́̍̂̔̀̑̇̈̇̽̀̽͋͂͑̋̈͋̀̏̋̎̿̄̈́͜͝͝͝͝͝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠘⣿⣍⣿⡟⢿⣆⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⡀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⣿⡀⠀⠀⣠⣾⣿⣭⣿⣯⣽⡿⠆⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀.̸̡̛͍̼͌̎̓̋͑̆̑̀͋̄́̏̍̓̆͌͗̔̔̓̉͛͆͐̋́̃̈͆̕̚͘̕͝͝⠀⠀⠀⠀⠀⢩⣭⣄⣀⠿⠇⠀⠈⠉⠉⠁⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀.̵͉̮̺͙̹͙͇͔̟̖̞̭͈̰͙̭̼͚͔͙͓͔̖͂̋͠
⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣄⠀⠘⣿⡉⣹⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣿⠁⠀⠀.̸̢̯͍̹̩͇̟̫̤͚̜̲͔͎͉͎̰̱̭̠̭̗̖̙̺̟̓̅́̋̓̈̈́̉̊̃̿͋̈͂͌͘͘ͅ⠀⠀⠀⠀⠀⠀⠀⠻⣷⣬⣓⣀⣸⣿⠁⣠⠀⢦⢹⣦⠀⠀⠀⠀.̸̢̡̛̛̣̬͔̰̺͚̤̟̬̪̺͕̖͕̗̺̬̗͖͚̯̩͍̱̜͈̘̭̠͎̥̩̖̰̮̖̘͓͇̭̟̞̺̪̬̏̆̔̋̔̽̆̆̈́̌̊͒̂̈́͋̓̽͒͐͗͛͒͊̓͆̅͂̏̊̿̀̈́̀͜͠͝͠⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡉⠛⠉⠙⢿⠶⢶⡶⠿⠋⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢶⣦⣤⠾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀.̸̨̢̡̤̻̟͔̰̩̜̱͎̘̩̳̺̲̱̳̦͙̦͍͙̺͈̰̫͖̺̺̫͈̩̖͖̹͍͕͎̺͔̩̲̭̊͑̽͌̐̆ͅ⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀
⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀.̴̨͉͎̩̝͕͕͉͍̘̱̞̦̳͍̤͎̗̬̼͕̍̂̓̄̌͗͑͆̒͑͌͌͊̃̐̐̔̊̈́̑́͆͑͗͛͗͂̀͊͘͘̕̚͜͜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢻⠟⠀⠀.̴̰͕͉̲̯̭̹̏̈̀̇̅͑̏̐̂͂͛͐̇̚̚͜͜͜͠ͅ⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠟⢻⠾⣁⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠉⠀⠀⠀⠉⢻⡆⠀⠀⠀⢰⠶⣆⠀⠀⠀⠀⠀⢻⣷⣶⢿⣦⡀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⣿⠀⡿⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇
⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢀⣴⠞⠋⠀⠀⠀⠀⠀⣠⡾⠛⠀⠀⠀⣀⣴⡏⢸⣧⡀⠀⠀.̴̢̧̛̹̯͖̙͈̼̲̰̠͇͎̗͖͖̩̘͕̙͙̞̝͇͚͎̱͙̲͓̥̣̺̝͈̓͆̄̎̈́̎̒͋̓̾̈̾̀̈͒͗́͛͗͊̉̔͊̊̃̃͗͆͂̾̀̄͆̕͝͝͝⠀⠀⢸⣿⠀⢰⣿⠁
⢸⣿⠀⠀⠀.̶̢̼͎̞̜̫͊̌̀͒̎͐̅̍̇͐͊̆̎̏̈̿͂́͘̚̕͠͝͠⠀⠀⠀⠀⢀⣿⣧⣴⠞⠋⠁⠀⠀⠀⠀⠀⣠⡞⠋⠀.̴̨̹̜̘̱̹̫͓̝̫̫̹͔̱̪̺͇̇̾̈́͗͂̃͆̀͂͆͐̎́͂̋͂͂̑͑͌͌͐̎̋̆̓̄̊̄̏͗͐̿̅̓̒͗̉̒̾̏̕̕̚̕͜͠͠͠⠀⠀⠀⢸⡟⠁⠀⠀⠘⢿⣆⠀⠀⠀⢸⣿⠀⣾⠇⠀
⠀⣿⠀⠀⠀⠀⠀⢀⣴⣾⠟⠋⠀⠀⠀⠀⠀.̷̧̫͕͕͖̺̖̠̦̝̩̥͇̰̼̠̟̺͙̬̣̱͒͊̏͌͐̆͐́͋̈́̈́͊̂̓̽̐̔͂̋̓͝⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⢸⡏⠀⠀⠀⢸⣿⣸⡟⠀⠀
⠀⣿⡆⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⢀⣿⠇⠀⠀⠀⢸⣿⣿⠃⠀⠀
⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠸⣿⡀⠀⠀⠀⣼⣿⡟⠀⠀⠀
⠀⣿⣿⣷⣄⠀⠀⠀⠀⠀.̴̛̻̥̞̟̰͉̖̀̆̋͆̓̃̑̌͂̀͒̒͆̓͐̈́̒̈́̃͝͝⠀⠀⢀⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢿⣧⠀⠀⠀⣿⣿⡇⠀⠀⠀
⠀⠻⠀⠙⠛⠓⠲⠶⠶⠶⠖⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠗⠀⠀⠀⠸⠿⠀⠀⠘⠛⠛⠁⠀⠀⠀