⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡆⠀⠀⢀⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢠⡺⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢋⡿⠉⢉⡿⢥⡀⡠⣴⠆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢀⡞⠁⢀⡞⠁⢠⠿⡊⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠤⣀⠀⠀⠀⡜⢀⣠⡞⠀⢀⡞⠀⢠⠏⠀⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⠎⣠⠖⠦⣄⡉⢢⡜⠀⢸⡿⠇⢠⠟⠀⣠⠏⠀⡰⠁⠀⠀⠀
⠀⠀⠀⠀⠀⢰⠃⡴⠃⡸⠢⢄⣉⡟⠀⢠⠏⠀⢠⠏⠀⣿⣿⠀⡰⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠱⢜⣁⠜⠁⠀⢀⠎⠀⣠⠏⣠⣿⣿⠀⣰⠃⠀⡰⠁⠀⢀⡴⢒⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣰⠏⠀⣿⣿⠃⡼⠁⠀⡼⠳⢄⣠⠎⢀⠎⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣰⠃⠀⣰⠃⢀⡼⠁⠀⡾⡉⠓⠤⣀⣠⠋⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣴⠃⠀⣰⠃⢀⡾⠁⢀⡜⠀⠈⠑⠤⣀⣀⡴⠁⠀
⣰⠺⢍⡑⠤⣀⠀⣠⢫⢧⣴⠃⠀⡼⠁⢀⡞⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢯⡳⢦⣈⠑⠦⣉⣡⠋⣰⢳⣄⡼⠁⢠⠟⢀⣠⠪⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠒⠬⣓⠦⣄⣀⡼⢡⠎⠀⠉⠐⠻⣚⠫⣌⠙⠶⣍⢢⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠑⠢⠥⠔⠃⠀⠀⠀⠀⠀⠀⠑⡆⣱⠀⣼⢰⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡴⠁⡼⣡⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡜⢁⡼⡱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢄⣞⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡆⠀⠀⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢠⡺⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢋⡿⠉⢉⡿⢥⡀⡠⣴⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢀⡞⠁⢀⡞⠁⢠⠿⡊⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠤⣀⠀⠀⠀⡜⢀⣠⡞⠀⢀⡞⠀⢠⠏⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠎⣠⠖⠦⣄⡉⢢⡜⠀⢸⡿⠇⢠⠟⠀⣠⠏⠀⡰⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠃⡴⠃⡸⠢⢄⣉⡟⠀⢠⠏⠀⢠⠏⠀⣿⣿⠀⡰⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠱⢜⣁⠜⠁⠀⢀⠎⠀⣠⠏⣠⣿⣿⠀⣰⠃⠀⡰⠁⠀⢀⡴⢒⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣰⠏⠀⣿⣿⠃⡼⠁⠀⡼⠳⢄⣠⠎⢀⠎⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣰⠃⠀⣰⠃⢀⡼⠁⠀⡾⡉⠓⠤⣀⣠⠋⡠⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣴⠃⠀⣰⠃⢀⡾⠁⢀⡜⠀⠈⠑⠤⣀⣀⡴⠁⠀ ⣰⠺⢍⡑⠤⣀⠀⣠⢫⢧⣴⠃⠀⡼⠁⢀⡞⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢯⡳⢦⣈⠑⠦⣉⣡⠋⣰⢳⣄⡼⠁⢠⠟⢀⣠⠪⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠒⠬⣓⠦⣄⣀⡼⢡⠎⠀⠉⠐⠻⣚⠫⣌⠙⠶⣍⢢⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⠢⠥⠔⠃⠀⠀⠀⠀⠀⠀⠑⡆⣱⠀⣼⢰⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡴⠁⡼⣡⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡜⢁⡼⡱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢄⣞⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀