⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⡾⠛⠛⠛⠛⠻⠶⣦⣀⠀⠀⠀⢀⣤⠾⠛⠉⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣼⣇⠀⠀⠀⠀⠀⠲⠶⢿⣷⣶⣶⣯⣥⡤⠤⠀⢀⣤⢴⠛⠙⠓⠒⡦⣄⠀⠀
⠀⢀⣠⣴⠟⠉⠉⠉⠛⠛⠳⣤⠶⠶⠾⠋⠙⠉⠉⠛⠋⠛⠶⠦⠟⠁⢀⣀⣀⠀ ⠙⢲⡀
⢠⡟⠁⠀⠀⣀⡤⠤⣄⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣅⠈⢳⠀⠀⠀⢠⠇
⠘⣷⠀⠀⢰⡏⣠⠞⠉⠀⠀⢀⣶⣆⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠘⢧⡾⠀⠀⠀⣸⠀
⠀⣧⠀⠀⠈⢻⠋⠀⠀⠀⢀⢀⠛⠃⠀⢀⣘⣽⠀⡀⠀⠉⢩⢠⣠⠀⠀⠀⠈⠁⠀⢀⡞⠋⠀
⠀⠈⢿⣄⡀⠀⠀⠀⠀⠀⠸⢿⠻⠁⠀⠈⣉⣈⣉⣀⣀⠀⠙⠛⠛⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀
⠀⠀⠀⢹⡏⣴⠀⠀⠀⢀⢀⣤⠖⠚⠋⠉⠉⢹⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⣇⠀⠀⠀
⠀⠀⠀⠸⣇⢹⡀⠀⢀⡿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠙⠛⣿⣿⣷⡄⠀⠀⠀⣯⠀⠀⠀
⠀⠀⠀⠀⡟⢸⡄⢀⣞⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠻⠿⢿⠀⠀⢠⡟⠀⠀⠀
⠀⠀⠀⠀⠻⣦⠀⢸⡏⠁⠀⣾⣿⠆⠀⠀⠀⣀⠀⠀⠀⠀⢺⣿⠇⠀⠐⢾⠇⢀⣼⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢿⡆⠘⣯⣁⡀⠈⠉⠀⠀⠀⠘⠯⠃⠀⠀⠀⠀⠁⠀⠐⣦⢟⣴⠚⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢈⡽⣿⠉⠉⠛⢶⣄⣀⡤⠶⠶⠦⣄⠀⠀⠀⠀⢀⣠⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣈⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⢷⣶⣶⡿⠛⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢿⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠋⠀⠉⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣰⣟⣎⣧⡀⠀⠀⠀⠀⠀⠸⣯⠤⠀⠀⠀⠀⠀⠀⠀⠀⣱⠇⠀⣀⣀⣀⠀⠀⠀⠀
⠀⠀⠀⣼⡋⠈⢻⣮⡳⣄⠀⠀⣠⠤⠖⠻⡶⠀⠀⠀⠀⠀⣠⡤⠞⠉⣧⠖⡫⠂⠙⢻⡄⠀⠀
⠀⠀⠀⡿⡇⠀⠈⡇⡙⠺⣅⣸⢷⠟⠓⢦⡙⠓⠓⠒⠋⠉⠉⠀⠀⠀⠹⡆⠀⠀⠀⠸⡇⠀⠀
⠀⠀⠀⢷⢧⠀⢀⣇⡇⠀⠀⢹⣼⡀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⢦⣤⠖⠚⠁⠀⠀
⠀⠀⠀⠈⢯⡀⣼⡿⠀⠀⠀⠀⢧⢷⡀⠀⠀⢹⡀⠀⠀⠀⠀⠀⢀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠉⠛⠛⠒⠒⠒⠚⢷⣿⣦⣀⣸⠇⠀⢀⣀⣤⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠒⠒⠋⠁⠀⠀⠀