⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡙⣦⡆⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⣀⣴⠶⠟⠂⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢸⡝⡄⠀⠀⠘⢿⣷⣤⡀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⣠⣶⣿⣿⡅⠀⠀⣀⣀⣠⣾⠟⠁⠀⢀⡤⠚⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣻⣿⣷⣦⡠⠘⣿⢿⣧⠰⠀⠄⠉⠂⠈⠀⠈⠀⡂⣰⣿⣿⣿⠋⢠⣾⣿⢟⣹⡿⢏⡀⠀⣴⠏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⢿⣟⣿⣿⡌⢿⣿⣿⣆⢀⠀⠀⠀⠀⠂⠀⢠⠇⡟⡼⢸⠟⣡⢻⣏⣽⣿⠟⠛⠉⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠳⡀⠉⠻⣿⠷⣤⣜⢿⣿⠧⢃⠀⠀⠀⠂⢠⢏⣜⡿⢁⣾⣣⣿⣿⣿⠟⠁⠀⡀⣤⡿⠁⠀⠀⠀⠀⣀⠀⠀⠀
⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠘⣄⣠⣼⣾⣿⣿⣿⣿⣷⡺⣶⡀⢰⣰⣿⢾⣿⣶⢟⣿⣾⣿⣿⣋⣤⣶⣯⡶⠟⠁⠀⠀⢀⡴⠋⣿⡄⠀⠀
⡄⠀⠀⠀⡞⡇⠀⠀⠀⠀⠀⠀⠀⠈⠺⣵⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠿⣿⡿⠋⠀⠀⠀⣀⠔⣋⠀⢀⡏⣷⠀⠀
⡘⣆⠀⠀⡃⢹⠀⢀⠀⠀⠀⠀⠀⠀⠈⠉⢩⣿⣿⣿⡍⠹⣿⣿⣿⣿⡿⠛⠉⢫⡿⠟⠁⣿⣻⣮⣽⠟⠁⠀⠀⠀⠀⠀⢰⡿⢀⣨⣇⠝⠃⠀
⠈⠻⣶⡄⠓⣘⣧⢜⢆⠀⣀⢴⢷⠦⠀⠀⠀⠻⣿⣯⣿⣿⣿⣿⡿⢯⡸⢷⠶⢏⣀⣠⢾⠿⠴⠦⠀⠘⣆⠀⠀⠀⠀⢀⢾⠇⣸⣃⠊⠀⠀⡰
⠀⠀⠀⠉⠓⢲⣼⣯⣔⣋⣰⠋⠀⠀⠀⠀⠀⠀⠙⣿⣾⣟⢻⢻⣷⡾⣷⠚⠉⢉⡯⢷⡃⠀⠀⠀⠀⡀⠸⡄⠀⠀⠴⣣⣯⣴⡟⢃⡤⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠉⠓⢶⡿⠏⠉⣍⣉⢩⡴⠶⠲⠚⢱⢹⣿⣎⢺⡿⢸⡿⣴⡴⡃⡄⢸⣷⣴⣠⣠⣠⠽⣖⣒⢶⠲⢻⣯⣿⡿⠋⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠆⠨⢦⡈⠀⣸⠂⣨⣮⡟⣿⣾⣤⣼⣷⡿⣱⣿⡅⣄⡉⠻⣿⣿⣿⣿⣿⣷⣮⢤⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠘⠘⡺⢿⣶⣪⠵⣺⠵⣻⠃⢸⢯⠉⠉⣹⠣⣿⢷⣿⡞⠣⢴⣿⣿⣿⣿⣿⣿⠞⢛⡿⢶⣤⠀⠀⠀⠀⠀⠀⠀
⢀⡀⠀⠀⠀⠈⢉⡦⢤⣰⣶⣚⠻⡟⣦⣐⢷⣮⣵⢾⣵⡶⢋⣼⠧⢴⡏⣦⡸⣼⣛⢻⣷⣦⣿⢿⠋⣹⢟⠻⢻⣿⣧⡷⠻⣶⠆⠀⠀⠀⠀⠀
⠩⠻⢷⣠⢲⠾⣿⠶⢤⣅⣉⣫⣽⣶⣥⣈⡟⠓⠏⠍⢓⣤⣾⡇⣠⡼⣿⣿⣿⡿⢛⠉⡉⠛⢉⢫⣊⡧⠶⠟⢛⠛⠉⠁⣛⠷⢤⣒⡦⠀⠀⠀