Books Emoji Combos

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿
⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿
⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿
⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿
⠙⣿⣧⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠘⢿⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⢀⡀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⠤⠤⠴⠶⠶⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⠏⠀⠀
⠀⠀⠀⠈⣿⣷⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠋⠀⠀⠀
⠀⠀⠀⠀⠘⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⣀⡠⠠⣀⢰⡟⠀⠀⠈⢳⣤⠀⠀⠀⢀⣤⠶⠶⢶⣶⣒⣚⣛⣻⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠉⠀⠀⠀⣰⠏⢾⠃⠀⠀⠀⠀⠙⣧⣀⣰⣿⡏⠉⠉⠉⡉⠉⡏⣿⣼⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠀⠀⠀⢠⣴⠚⠁⣤⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠶⠒⠛⠛⠛⠃⠛⠛⠻⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠚⠛⠋⠉⠉⠉⣉⡇⢲⡖⠚⠉⠀⠀⠀⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣇⣀⣀⣠⣤⣤⣤⠤⠠⠤⣼⡇⠈⠻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣼⠀⠀⠀⠀⠀⢀⣶⡟⢠⣿⠀⠀⠀⠀⠀⢀⢵⠆⠀⠀⠀⠀⠀⠀⠀⢸⢹⠃⠀⣾⡯⣽⡆⠀⠀⠀⡿⢇⠀⠀⠙⣿⣿⣿⣆⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⡏⠀⠀⠀⠀⣀⣾⣟⠀⣼⡇⠀⠀⠀⠀⠀⠘⣬⢴⣶⣶⣶⡶⣦⣶⠀⡟⣼⠀⢰⣟⢀⣿⡇⠀⠀⢸⢿⠸⠀⠀⠀⠈⢻⣿⣿⣧⡀⠀⠀⢰⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⣸⠁⠠⣿⣿⣿⣿⣾⠏⢀⣿⣧⣤⣦⣴⠆⠀⡄⣿⡿⠿⠛⣿⡗⢻⡇⢀⡇⡧⠀⢻⡏⣀⡼⠃⠀⠀⣼⡀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠄⢲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⢠⡀⢀⡏⠀⢸⣛⣻⠿⠋⠁⢀⣸⡿⠉⠀⠌⠈⠀⣼⢸⣿⣇⣶⣿⠿⠳⣼⠁⣼⢱⠃⠀⣠⡿⠋⠁⠀⣄⢀⡏⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀
⠀⠀⠀⠀⠀⣘⠀⠀⠀⠀⢧⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⢀⣆⠀⠁⢸⠁⢰⠀⠀⠀⠀⡀⠀⡿⣿⣧⣤⡄⢸⡄⠀⡟⣼⠿⠿⠿⠿⠿⢾⠏⠀⡟⢨⡖⣿⠋⠉⠉⡅⢸⠈⣿⠃⠂⠀⠀⠀⠀⢀⣷⣆⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀
⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣀⣼⣯⣀⢀⡏⠀⡞⠀⠀⠀⠀⠀⢸⢻⣟⠉⢉⡁⡟⠀⢸⡇⠀⠀⠀⠀⠀⠀⢮⠁⢠⣇⢸⠀⡿⠁⠀⠐⢀⣿⢸⣿⡀⠀⠀⠀⠀⠀⣼⣿⢹⣧⡄⠀⠙⢿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀
⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡴⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠰⣧⣼⠃⡾⣸⠁⢰⠃⠀⠀⠀⠀⠀⣿⣿⣿⣷⣼⢃⠀⠀⣼⠀⠀⠀⠀⠀⠀⣼⠋⡤⢸⡿⢸⡾⠋⢀⡘⡅⢸⣿⣿⣿⣷⠀⠀⠀⠀⠀⢻⣿⣸⣿⣿⣆⠀⠈⢿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀
⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⡿⢾⡿⣹⢇⡏⠀⡾⠀⠀⠀⠀⠀⢰⢿⣿⠀⠈⡛⠈⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠁⡿⢧⠼⠿⠾⠿⠛⠀⠿⠿⢿⡿⠈⠀⠀⠀⠀⠀⠀⠙⠿⣿⣽⢹⢧⡀⠀⠹⣿⣿⣆⠀⠀⠀⠀⠀⠀
⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠄⠀⠀⠀⠀⠀⠀⢠⡏⣸⡓⣈⣡⡟⣸⠁⢠⠃⠀⠈⠁⠀⠀⡼⣿⣿⣷⣼⣧⡆⠀⢸⡇⠀⠀⠀⠀⠀⠰⣦⠀⢰⡿⡿⠀⠀⠀⠀⠀⢰⠀⠀⣸⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⡾⣾⣳⡄⠀⠘⢿⣿⣷⡀⠀⠀⠀⠀
⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣧⡀⠀⠀⠀⢠⣿⢀⣤⡿⢯⣭⢁⡏⠠⡘⠀⠀⠀⠀⠀⢰⣧⣿⠀⢉⠛⢈⠀⠀⡞⢠⠀⠀⠀⠀⠀⠰⠁⠀⣸⣇⡇⠀⠀⠀⠀⠀⡟⠀⠀⣿⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⣿⣧⡙⣦⡀⠀⠻⣿⣿⣄⠀⠀⠀
⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣆⠀⠀⣼⠇⠚⢁⣀⠈⢣⣼⠁⢻⠁⡀⠀⡀⠀⠀⣼⢸⡿⠿⠿⢀⡿⠀⢀⡷⢼⣶⣶⣶⣶⣦⣦⡶⢤⣿⢸⠁⠀⠀⠀⠀⠀⠋⠀⠐⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠹⣿⣿⡉⢷⡀⠀⠙⣿⣿⣦⠀⠀
⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⣰⡟⠀⣀⣿⣞⣃⣾⡇⠐⡏⠀⠙⢺⠁⠀⢀⣇⣼⢿⣶⣾⢸⠁⠀⢸⣹⣿⣿⠋⠀⠀⢩⢻⣿⡀⠏⣼⠀⠀⠀⠀⠀⣰⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣳⣾⡆⠈⢿⣷⣾⡇⢀⠀⠈⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠁⠠⠁⡶⠋⣸⣽⠁⣠⢃⠀⡀⠀⠀⠀⣸⢸⡏⠿⢷⡟⡏⠀⢠⣿⣿⣿⠇⢀⣀⣠⣸⣾⣿⣿⣀⡇⠀⠀⠀⠀⠀⡅⠀⢀⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣨⣿⡿⠃⠀⠀⠻⢿⠃⡏⢷⡀⠀⠻⣿⣷
⣦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠇⠈⠿⢿⡭⢯⢇⡇⠀⡍⠈⠻⠀⡼⠀⠀⡏⣿⣥⣀⣠⢰⠃⠀⢈⡿⣿⠿⠀⠘⠿⡟⢹⣿⡿⠟⢹⠁⠀⠀⠀⣀⢸⠇⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⡉⢩⣰⣷⣄⠀⠀⠀⠀⠸⡟⠀⠳⡄⠀⠘⢿
⠿⢿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⢠⡶⠿⢷⡄⡞⣸⠀⣴⣇⣀⡀⢰⠇⠀⢸⠁⣧⣶⠛⠉⡎⠀⠀⣺⢽⣿⠀⠁⠀⠀⠰⢺⣿⣷⡷⣸⣤⣤⣤⠀⠃⣯⣄⡀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣿⣦⡙⢫⣿⣧⡄⢠⣴⠂⠙⢦⠀⠀⠀⠀⠈
⠀⠀⠀⠈⠉⠙⠛⠻⠿⢿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣄⣠⣿⢁⡟⠀⢀⡼⣿⢁⡇⠀⢻⡋⠉⡙⡟⠀⠀⠀⣴⡤⣽⣿⠀⠀⠀⠀⡿⣼⣷⡄⠀⠀⠖⠒⣼⡟⣼⡇⣿⣷⣟⣿⠇⠠⣿⠿⠃⣿⢁⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⡇⣯⡿⣎⠉⢽⣿⣟⢋⡴⠃⠈⠣⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⡿⢿⣿⣿⣿⣿⠃⣼⣥⣤⡌⢴⠇⣸⠂⠂⡿⠛⠛⢿⠀⣀⢀⢀⢀⡾⠋⡿⠊⠀⠀⢸⣷⣿⡻⣿⣧⣤⣀⣹⡟⢀⣿⣿⠛⠛⠛⠿⠃⢸⠿⠗⢰⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠋⣸⢸⣿⢳⡏⣷⣌⠱⣶⣿⣥⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣴⡿⢀⠁⠀⠀⣾⡏⠀⡯⠀⢰⠿⢿⣿⡟⢠⡇⠸⣨⣙⣇⣸⠃⠀⠀⠀⣿⣿⣿⣿⣆⠙⢿⡟⠀⠀⢸⡿⣽⠀⠀⠀⠀⡆⡞⠀⠀⣼⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠘⣿⣸⠁⣿⢻⢿⠋⠹⣿⣀⡞⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⠟⠛⠛⣹⡿⠁⢸⣸⠀⣴⠾⠛⣹⠁⣸⡆⢠⡏⣡⠈⣻⠀⠀⠀⣼⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⣼⣷⡇⠀⠀⠀⠘⢰⠇⠀⠀⣿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢠⡇⡿⠀⡟⠈⣽⠘⡷⣈⠉⠀⠀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠇⠀⠀⣴⣮⡿⣦⠀⣿⢃⠘⠫⢿⢛⡇⠀⣷⠀⣸⣛⣛⣰⡇⠀⠀⢰⣿⡿⢿⠿⠿⠿⠿⠧⣴⣤⣤⣿⣻⠃⠀⠀⠀⠀⠘⠀⠀⢰⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢸⢳⣿⢶⡇⢠⡏⠀⡇⢹⣧⡀⠚⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢰⠷⢿⣟⡁⢠⠇⠀⠃⢈⡟⣻⡓⣿⠀⢰⡿⢀⡟⠁⠉⠉⢹⠂⠀⡟⣿⢱⡟⢠⡀⠀⠀⡀⣟⠀⢸⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⡿⣸⡿⢸⣴⢸⡇⢸⡇⢸⠈⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⡀⢀⠹⣇⡼⢀⠀⠀⣸⢿⣶⢾⡇⠀⣿⣧⢸⣟⣓⠒⡖⡼⠀⢸⣧⡿⣼⠇⣾⣭⠿⠛⢡⡿⠀⣼⣷⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡇⡿⠇⣿⡇⢸⠀⢸⠇⡾⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢀⣿⣿⣿⢣⠏⠁⠏⠀⣆⡿⣿⡷⣾⠁⠰⣿⠀⣯⣭⣍⣹⢳⠃⠀⣾⣸⣧⣿⢀⣯⣽⣶⡄⡼⠁⢀⣿⣿⠃⠀⠀⠀⠀⠘⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢸⢳⡇⢰⡟⠁⣾⠀⣸⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⣼⣽⣿⠇⡎⠀⡀⣸⢹⢻⣿⣿⣶⡏⠀⣼⡏⢸⣣⣾⣀⡿⡼⠀⢸⡟⣿⢹⡇⢸⠷⣶⡀⠁⡇⠀⢸⢻⡿⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⣿⢸⠁⣸⠁⠷⡟⠀⣿⠀⡇⢠⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢰⣿⣿⡟⢰⠃⢀⣇⠇⣸⡞⠋⠛⢻⠁⠀⣿⡷⣿⣧⣈⣉⢀⡇⠀⣾⢃⣿⡞⠁⣿⢦⣉⣀⠀⠀⠀⡾⣼⡇⠀⠀⠀⠀⠀⡀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣶⣇⡟⠀⡿⠀⢠⡇⠀⡏⠀⠀⢸⣿⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢀⣾⣿⣿⠁⢿⠀⣼⡘⠀⠱⠿⢿⣿⠉⠀⢸⣿⢳⠏⣸⢏⣿⣼⠁⢰⡿⢸⣏⡟⠒⠳⠾⠿⣿⣀⡀⢀⣇⣿⠀⠀⠀⠀⠀⢠⡄⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⣰⣧⣄⢸⡇⠀⡇⡞⠀⠀⣿⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢸⣿⣿⠇⣼⡊⢰⠯⠃⣖⣶⣿⣯⠁⠀⠀⣿⡽⣼⡆⠀⠈⢇⡇⠀⣼⡇⣼⣾⠀⠀⠀⠀⠀⠀⢠⡧⢸⢸⡏⠀⠀⠀⠀⠀⣾⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢿⣾⣄⢸⢧⡇⠀⠀⡇⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢰⣿⣿⡟⣸⠁⠀⡾⠉⣸⠻⣵⣿⣹⠁⠀⣼⡿⢧⣿⣀⡀⠀⢸⠀⢠⣿⢀⣟⡿⢦⣠⡀⠀⠀⠀⣾⡆⡟⢸⠇⠀⠀⠀⠀⠀⡇⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣟⠚⣿⠉⠈⣼⡃⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢾⣿⣿⠃⣹⠃⢾⣷⢠⣯⣿⣇⡀⢠⡇⢰⣾⠃⣸⡻⠿⠏⠏⣯⠀⣸⡇⢸⣿⡇⠈⠉⠁⠀⠀⢰⣷⢣⣧⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢻⠀⣿⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⡀⣴⣿⣿⡇⣀⡇⢀⣾⡇⣾⣼⣷⠛⠁⠘⠀⣿⡿⠀⣿⣿⣷⡦⢰⠃⠀⣿⠁⣿⣿⣁⣶⡆⠀⠀⠀⣸⠹⣸⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣮⡀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣰⣿⣿⡿⣸⣿⠀⣼⣿⢰⣧⠗⠶⠦⡟⠀⢸⣿⠇⣸⣿⣥⣤⡄⡞⠀⢸⡟⢠⡿⣧⡀⠀⠀⠀⠀⢀⡇⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢇⠀⢓⠀⠈⢡⠳⠃⣴⣿⠇⣼⣽⢒⡒⢾⠃⠀⣿⡿⠠⣿⣿⣛⠿⠃⠃⠀⣾⠇⣸⠇⠀⠀⠀⠀⠀⠀⣸⠁⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠈⢠⡼⠀⢀⡞⡇⣸⣿⠇⢠⣯⣷⣦⣁⡞⠀⢸⣿⠇⢸⣿⣴⣯⡿⠀⠀⢰⣿⠀⣿⣄⡀⠀⠀⠀⠀⢀⡏⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⠀⣸⠇⠀⢸⡾⢠⣿⡏⠀⣾⣿⡀⠒⣨⠳⢀⣏⣿⠀⣿⣷⣬⣍⠁⠀⠀⣼⡇⢀⡟⠈⠉⣿⡶⢶⠦⠼⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⢡⣿⣿⡄⢠⣿⠁⣞⣿⠁⢰⠃⣉⣭⡿⠿⡅⣸⣽⡇⣰⡟⣟⣛⣦⠀⠀⢀⣿⠀⢸⠇⠀⢰⣋⡉⣻⠀⠀⠀⢰⠃⣆⣀⣀⠀⠠⠤⣤⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⢀⣿⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣦⣿⣿⣽⡇⣞⡏⣸⣿⡏⠀⣾⡞⢫⣄⣰⣮⢀⣿⣿⢀⣿⠿⣿⣿⡏⠀⠀⣸⡇⠀⣾⠀⠀⢸⡉⠙⡏⠀⠀⡀⣼⢠⣁⡉⠉⠉⢛⣛⣿⣯⣀⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠀⠛⢁⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣻⠛⣿⣿⠻⢰⣿⢠⣿⣿⠁⢰⣻⡿⢿⣭⣡⠇⣸⢹⡏⢸⣟⡛⠛⠿⠀⠀⢀⣿⠁⢠⡏⠀⠀⣯⣉⣛⣃⡀⠀⠁⡇⣼⣭⣍⣙⣛⡛⠷⣿⣯⣿⡿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⡀⠀⠀⠀⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣥⣯⣿⡏⢠⠇⠃⣾⢻⡇⠀⣟⣿⡆⢀⣼⠉⢀⡇⣾⠁⣹⣿⣿⣷⡄⠀⠀⣸⡟⠀⣸⠇⠀⢠⣧⣭⣽⡛⠋⠀⠰⠓⣇⣀⣐⠛⠯⣉⣹⣷⡿⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣻⡇⢠⣶⢤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⣿⢿⡿⣿⣿⢱⣟⠀⣸⣏⣿⠀⠀⡞⠉⠉⠻⣇⣀⣼⢰⡏⣸⣿⡦⢤⣤⠐⠀⠀⣿⠁⠀⣿⠀⠀⣼⣧⣤⣿⣥⠀⠀⡴⢹⣅⣈⠭⢿⣟⠛⣿⣿⡏⢰⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣰⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣾⠏⠸⣵⡟⠁⣸⡼⢠⡿⣸⠇⠀⣸⠁⠀⠀⠀⠀⠈⡿⣾⠁⣿⢧⣿⣽⠟⠀⠀⢸⣿⠀⢰⡇⠀⠀⣷⣤⣼⠏⠉⠀⢀⡇⣽⠦⠼⠿⠷⢾⣭⣿⣿⡅⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠘⢉⡆⠘⠏⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⠛⠀⢠⠏⠆⢠⢯⠇⣾⢃⡿⠀⢠⡯⠀⠀⠀⠀⠀⢰⢳⡏⢰⣿⡝⠿⣿⠆⠀⠀⣿⣿⠀⣸⠓⢶⣤⣥⣤⣀⣀⠀⠀⠸⠀⠋⠛⢒⣲⣤⣤⣤⣿⣯⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⣸⠁⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⡇⠠⣀⡟⠀⢀⡄⡾⣸⡏⣸⠇⠀⣞⠀⠀⠀⠀⠀⢠⠞⣾⠃⠜⢺⣿⣋⡷⠀⠀⢰⣿⡇⠀⡿⢠⣿⠟⠉⠉⢿⣿⣿⣿⣿⢠⠉⠛⠛⠯⠭⢭⣬⣿⣿⣧⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢠⣿⡦⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡟⠁⢀⣷⠃⠀⡞⢸⣷⡿⢀⡿⠀⢰⠟⢷⣶⠀⠀⠀⡿⢳⡟⠀⠀⠀⠙⠛⠃⠀⠀⣼⠟⠀⢸⣇⣿⣿⠀⢤⣄⠀⣿⣿⣿⡇⠘⠛⠓⠶⣶⡒⠒⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠈⠋⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣼⠁⠀⢾⠏⢀⣤⢣⣞⣿⠃⣼⠃⢀⣿⠃⠀⠀⢀⠀⢸⡧⣼⠃⣰⣗⣶⣶⣦⣤⣄⠀⠻⡇⠀⣼⣿⢏⣉⠐⢿⡯⠀⣿⣿⣿⢃⣤⢤⡄⠀⢦⣭⣿⣷⡝⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⢿⠟⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢰⠇⠀⣰⡿⠀⡞⠰⠋⢁⡟⢰⡟⠀⣼⠷⠯⠿⣰⠋⠀⣿⢣⡟⢀⣿⣿⠆⠀⠈⠉⠁⠀⠆⠀⢠⣿⣿⣿⡙⠀⠀⠀⢰⣿⣿⡿⠘⠳⠤⣼⠿⣋⣙⣶⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠿⣿⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠀⢠⣿⢁⡘⣅⡼⢠⡾⠀⣿⠃⢰⣿⡾⠹⠇⠁⠀⢸⡟⢸⠇⣸⣍⠛⢿⡷⠦⠀⠀⠀⠀⠀⢸⣿⣏⠉⠉⠀⠀⢀⣾⣿⣽⡇⠀⠀⠀⠀⠀⠈⠉⠁⠉⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠀⢰⡞⣿⡞⠀⠙⠧⣿⠃⣼⡏⠀⠀⣤⡿⠓⠒⠂⠃⣰⢃⡿⠀⣿⣯⣿⡮⡇⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠷⠶⣴⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣶⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⡾⣿⡿⢁⠀⠀⣰⠏⣸⣿⠁⠀⢀⣈⣛⣦⡀⠀⢸⡟⣸⠇⢰⡿⣮⡙⣻⡟⠀⠀⠀⠀⠀⢀⣿⣿⣿⡟⠀⠀⠰⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⡟⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠻⢶⣿⠀⠀⠀⢠⡿⢠⣿⡏⠀⠀⠻⣦⡈⠉⠉⠀⣾⢃⡿⠀⣿⠷⣿⣟⡿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⢃⣤⣀⠀⢾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠀⢸⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠠⠄⠀⣾⢃⣿⣿⠁⠀⠀⣠⣇⣽⡦⠀⠘⡟⣸⡇⢸⣿⣿⣶⣬⣅⠀⠀⠀⠀⠀⣠⣿⣿⣟⠁⠀⠀⠘⣧⠘⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣙⢶⡀⢾⠀⢸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⠀⣸⠏⣼⣿⡇⠀⠀⣩⣭⣅⡀⠀⠀⠀⠀⣿⢰⣾⡎⣿⣹⣷⡁⠀⠀⠀⣠⠞⢩⡿⠀⠉⠉⠛⠲⠦⣽⣄⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠯⠈⠉⠁⠃⢸⢀⣿⡇⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⡿⢠⣿⣿⠀⠀⣸⠋⠀⠈⣷⠀⠀⠀⢸⡇⠀⠀⠈⠉⠙⠛⠃⠀⠀⢰⡏⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣦⢜⣆⣠⣿⡿⢹⠃⠀⢸⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣾⠃⢸⣿⠇⠀⠀⣿⣞⢁⣰⠏⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⢸⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣸⡏⠀⢠⡿⠀⠀⣠⠷⠯⢯⣅⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⠀⠀⡾⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⡿⠀⠀⣼⠃⠀⠀⢿⣀⠀⠀⠀⠀⠀⠀⣿⣥⣀⣤⣤⣤⡀⠀⠀⠀⠀⣸⠀⠈⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇⠀⢰⠃⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⠃⠀⢠⡟⠀⠀⣰⠶⣭⣝⡓⠀⠀⠀⢰⡿⢷⣿⠿⠿⢿⣿⣤⣄⣀⠀⡏⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠀⠀⣾⠁⠀⢀⡏⠀⡏⢰⡇⠀⠀⠀⣿⣧⣿⣇⠀⣀⣴⣿⣷⠀⡿⢸⣷⡀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⡅⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣸⠉⣻⠶⣮⠀⠀⠀⢸⣿⣼⣿⠟⠃⠛⠋⡻⣿⢠⠇⣯⢷⣱⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠯⣤⣋⣸⠇⠀⠀⠀⣿⣿⢿⣿⢶⣿⣷⠎⣿⡟⣸⢸⣿⣇⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⡏⠀⢠⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣤⠾⠋⠀⠀⠀⣸⡟⢯⠈⠸⣷⣍⣡⣾⡟⢳⡇⣾⣍⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⡿⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⠀⠀⠠⢾⣟⡁⠀⠀⠀⠀⢀⣿⢿⡟⣀⣇⣿⡉⣹⡏⠀⣸⢡⡇⠘⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢰⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠉⠛⠀⠀⠀⣸⣿⣿⣇⣿⣽⣆⢷⠋⠀⡢⡏⣼⠁⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣼⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡿⠀⣸⢛⣶⣤⣄⣀⠀⠀⠀⢀⣿⠇⠉⠙⠻⣿⣷⣾⠦⣀⣿⢡⡇⠀⠴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⡟⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣸⠇⢀⣏⠉⠋⣿⡟⣯⠉⣿⠀⣸⣿⠀⣐⣦⣤⣈⠙⠛⠿⠛⠛⣸⠁⢰⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠇⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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