phytocrip

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡮⠿⣷⠀⠉⠙⠓⠶⣤⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⢻⡇⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠘⣷⠀⠀⡀⠀⠈⠙⣷⣆⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⠷⣶⡀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⢀⡀⠀⠀⢹⡇⠀⠙⢦⣄⣀⠀⠻⣷⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠉⢻⣆⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣾⠃⠀⠀⠸⣷⠀⠀⠀⠉⠉⠁⠀⠘⣷⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⣰⣟⠀⠀⠀⠀⠟⠀⠀⠀⢶⡀⠀⠀⠀⠘⣧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣼⡟⣿⠀⠀⢰⠂⠀⠀⠀⠀⠀⢿⡀⢶⣦⣤⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣷⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠹⣧⠀⢸⡞⢧⣄⣀⠀⠀⢸⡇⠀⠀⠈⠉⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⢳⡀⠉⠉⠀⠀⣼⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠠⣿⣿⣿⣏⣭⣽⣿⣿⣿⣿⣿⣿⣧⣶⣷⣾⣷⣶⣶⣄⡀⠀⠀⠀⠀⠈⢷⡀⠹⢦⡀⠀⢠⡿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠈⠻⣦⡀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠉⠛⢶⡟⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣶⣿⣷⣬⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣧⡀⠉⠉⠉⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣴⠟⠋⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣭⣿⣿⣷⣦⣾⣯⣍⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠟⠛⠛⠿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡙⠿⣿⣿⣿⣿⣿⣿⣿⡏⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠛⠃⣤⡄⢀⣀⠀⠛⠁⢠⡴⣶⠂⠶⠄⢹⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠃⠁⠈⠁⠀⠀⠁⠀⠈⠑⠋⠀⠀⠈⠈⠉⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⠿⠋⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢨⢲⢄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⢋⡯⢫⠵⣦⢰⣦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣸⢃⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣞⣿⣋⣞⣟⡏⡜⣻⠤⠙⣶⢆⠀⠀⠀⢀⡀⣞⠜⡇⢞⡸⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣞⣳⣟⣼⣽⡟⡴⣯⡹⡈⠽⡨⡷⢦⠀⢸⡝⣣⣿⣏⣮⣵⣾⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣳⡾⣴⢷⡸⣘⣖⡇⣱⡻⡝⣱⢚⣇⡾⣘⡷⣿⣧⣻⣷⣯⡞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣫⡿⢽⣯⣟⡶⣱⢺⣂⢻⣿⠙⣵⣟⣤⠷⢬⣳⣼⣾⣽⣛⡮⣿⢿⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢯⡷⣾⣝⡾⣹⣯⢷⡁⢻⡴⢹⡺⣞⠟⣽⡶⣽⣿⠿⣕⢫⡶⡿⣿⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⢷⡻⢮⣿⣗⡾⣿⡌⢹⣯⢸⣿⠧⣍⢷⣾⣾⣧⣿⣾⢯⡽⣽⣶⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⡏⠀⠀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡞⣷⣺⢿⣽⣳⣿⢧⣾⢟⡸⣛⣦⡹⣾⢿⣻⣿⣿⡻⣞⣳⡽⣿⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⠁⠀⠀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⣽⣾⣽⢻⣧⣿⢭⣟⣷⣛⢯⣴⣷⣶⣷⣾⣿⣿⣟⣶⣟⣯⣳⣻⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⠇⠀⠀⠀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢬⡟⡼⣳⢶⡭⣡⡿⢯⣛⣯⣿⡽⣿⣿⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣷⣷⣿⣳⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣻⡯⣶⡜⣭⢫⠝⣝⢳⣜⡍⢿⣥⢿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡤⠤⠤⣤⣾⠟⠁⠀⠀⠀⠀⠀
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡞⣇⠷⣬⣼⣧⣟⣾⣾⣻⢿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣿⣿⣿⣿⣿⣿⣽⢿⣿⣿⡟⣿⣴⣻⠟⠁⠀⠀⠀⠀⠀⠀⠀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣶⣾⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣷⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣟⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⢿⣿⣿⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⡀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣟⣾⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣻⡿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣠⣶⣤⣶⣿⣿⣿⣿⣿⣿⣿⣦⡀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣯⠤⠬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢐⣿⢷⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡄⠀⠉⠙⠛⣻⠿⠛⠉⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⠇⠀⣠⢔⣽⣵⣶⣶⣤⣤⣸⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⡿⠿⣿⣶⣾⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡲⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠀⠀⠈⠻⢿⣿⣿⣿⣿⡿⠟⣡⠎⢀⣿⣿⣿⣿⣿⣿⣯⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠀⠀⠀⠀⠀⠀⢉⣉⣀⣀⡼⠁⠀⠠⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⡇⠉⠛⠻⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠂⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣷⣦⡀⠀⢻⣿⣿⣿⣿⣿⣿⣻⣟⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠈⠻⣿⣿⣿⣿⣿⣟⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⢀⣿⣿⣿⣿⣿⣿⣯⣻⣿⣿⣿⣧⠀⠀⠀⠉⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠙⠻⣿⡟⣳⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⣀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠂⠀⠀⢀⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀
⠀⠀⠀⠀⠀⠀⠈⠙⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠘⠉⠁⠀⠀⠀⣴⠖⠀⣠⡟⠀⠀⡸⠉⣹⠟⠀⡸⠋⣹⠟⠀⢀⡴⠚⢉⣵⠀⠀⣰⠆⡠⢶⡇⠀⠀⣿⠋⠉⠉
⠀⢀⣴⣿⠿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡠⣺⠃⢀⣴⡟⠀⢀⠜⢀⣾⠃⢀⠜⠀⣼⠃⢀⣼⠋⢀⡴⣿⠁⢀⣴⣯⠎⢡⡟⠀⣠⣾⠃⠀⡠⠂
⢀⣸⣿⢾⣹⢿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣳⣤⣄⣤⣤⣒⣊⣀⣙⣒⣋⣈⣓⣚⣁⣀⣈⣛⣒⣁⣀⣈⣛⣒⣁⣙⣒⣉⣀⣛⣒⣉⣚⣁⣀⣘⣓⣊⣁⣙⣒⣋⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢀⣀⣀⣠⣤⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⠛⠋⠉⠉⠛⣧⠀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣀⣤⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀
⠀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀
⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀
⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀
⠀⠙⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀
⠀⠀⠀⠀⠉⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣤⣤⣄⣀⣀⣤⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠈⠉⠉⠙⠛⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣅⣀⢈⣩⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⠴⣒⣤⣀⡲⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣿⣯⡿⠟⠋⠈⠻⡛⠋⠹⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⠊⢔⢉⢙⣹⡿⠳⣙⡊⣓⣉⣒⡤⡀⠀⠀⠀⠀⠀⣰⡟⣡⠟⠁⠀⠀⠀⠀⠀⠈⠑⠢⡍⡧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⡇⠀⠻⣿⠟⠁⠀⠀⠀⠉⠉⠻⣟⠋⠙⠓⢤⣠⡴⣶⡿⣛⣉⣁⠒⠢⣄⣀⠀⣀⣤⡶⢺⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠱⡀⢾⠁⠀⠀⠀⣀⡠⠤⠶⠒⣺⠿⣟⢠⣯⣃⣳⡾⠲⠷⣮⣥⣴⣮⣤⣤⣬⣿⣟⣻⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠢⣷⣦⣤⣾⣿⣷⣶⡂⢉⡤⢊⣥⣿⡿⠿⠿⢿⣦⣤⣀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⡤⢤⣄⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠋⡴⣻⣿⠏⠀⠀⠀⠘⢿⢯⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⢽⣿⣦⡄⠀⠀
⠀⠀⠀⠀⠈⠄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣡⢁⡏⠀⠀⠀⠀⠀⠈⠫⣳⠄⢹⡆⠀⠀⠀⠀⣠⣴⣿⣿⣿⠞⠁⠈⢿⢿⡷⠀⠀
⠀⠀⣰⣾⣏⠩⡉⢴⣄⠀⠀⠀⠀⢠⢂⡴⢛⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣾⣿⡀⠀⢠⣾⣿⣿⡿⠟⠁⠀⠀⠀⣸⣾⠃⠀⢀
⠀⣰⡇⠈⠙⠤⣽⣧⣿⣷⣤⣀⣴⣡⡤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠛⠋⠁⠀⠀⠀⣀⣴⣾⡿⠁⠀⠀⠘
⢰⣟⣹⡄⠀⠀⠀⠉⠛⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⡖⠁⢸⣿⠃⠀⠀⠀⠀
⢹⡇⠂⢡⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⠀⠠⣬⣧⣀⡜⠁⠀⠀⠀⠀⠀
⠀⠱⡄⠀⠣⠀⣠⣤⣤⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢶⠃⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠢⢀⣙⠿⣿⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡾⡄⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠑⠊⠁⢀⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢷⣿⣿⡶⠤⢕⡄⠀⠀⠀
⠀⠀⠀⣠⠔⠂⢶⣶⣿⠟⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀
⠀⣠⡎⠀⣀⣠⡾⠟⠃⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀
⠀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⣴⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣶⡷⠋⣸⣾⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡛⠛⠛⠛⠛⠛⠋⠀⠀⠛⠛⠛⠛⠛⠛⣻⣿⡿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⠶⠟⠋⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⠃⠀⠀⠀⠀⣰⣤⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⣀⣴⣴⣆⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⣾⣟⣥⣶⡿⠟⠛⢷⣿⣷⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠻⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣠⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠐⠐⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⠤⢄⠀⢐⠀⠀⠀⡆⢀⡤⠤⡀⠀⡂⠀⠀⢰⠀⣰⣶⢢⠀⠠⡀⢢⡧⠀⣴⠒⢆⠀⡆⠀⠀⠀⠀⡇⠀⣤⣤⡀⠀⠀⢰⠀⣠⠤⢄⠀⠀⠀⠀⡆⢀⠖⠒⡄⠀⠀
⠀⠀⠻⣄⡼⠀⠐⠀⠀⠀⡇⠈⢯⠴⠃⠀⠃⠀⠀⢸⠀⠙⡿⠛⠀⢿⡷⣿⡇⠀⢱⢰⠃⠀⡇⠀⠀⠀⠀⡇⠘⢿⣿⠃⠀⠀⢸⠀⠱⡄⠝⠀⢠⠀⠀⡇⠈⢲⡐⠁⠀⠀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⢸⠆⠀⠀⡇⠀⠀⢸⠀⠀⣷⠀⠀⣾⠟⠋⠅⠀⠐⢸⠀⠀⡇⠀⠀⠀⠀⡇⠀⢸⠇⠀⠀⠀⢸⠀⠀⡇⠀⠀⠐⠀⠀⡇⠀⠸⠃⠀⠀⠀
⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⡇⠀⠘⠂⠀⠀⠁⠀⠀⢸⠀⠀⠉⠀⠀⡿⡀⠀⠀⠀⠀⠈⠀⠀⡇⠀⠀⠀⠀⡇⠀⠘⠃⠀⠀⠀⢸⠀⠀⠒⠀⠀⡆⠀⠀⡇⠀⠈⠁⠀⢰⠀
⢸⢠⣶⣢⣤⡄⠀⠀⠀⠀⡇⢐⣷⢷⠿⠁⡅⠀⠀⣸⢪⣾⣷⣵⣬⡷⠌⠀⠃⢴⣦⣠⣤⣄⡇⠀⠀⠀⠀⡗⣷⢵⣞⣶⣳⠀⢸⠀⠀⣤⡄⠀⡇⠀⣰⡗⣻⣶⣞⣶⣳⠀
⢸⠀⠀⠀⠘⠁⠐⠀⠀⠀⡇⠈⠀⠁⠀⠀⠀⠀⠀⢸⠁⠉⠈⠈⠁⡿⠀⢸⠃⠃⠀⠀⠈⠁⡇⠀⠀⠀⠀⡇⠁⠁⠈⠀⠁⡄⢸⠀⠀⠁⠀⠀⡇⠀⢿⡇⠉⠈⠈⠀⢹⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡔⠀⠀⢸⠀⠀⠀⠀⠀⣧⠀⠐⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡆⠀⠀⢸⠀⠀⠀⠀⠀⣧⠃⠠⢀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠀
⠈⢓⡀⠀⠀⡔⠃⠀⠀⠀⠙⣢⠀⠀⢠⠞⠃⠀⠀⠀⢹⠄⠀⠀⣾⡯⠀⠀⢈⣵⠀⠀⠰⡿⠇⠀⠀⠀⠀⠑⣆⠀⠀⢠⠚⠀⠈⠲⡄⠀⠀⡔⠃⠀⠀⠈⡃⠀⠀⢰⡉⠀
⠀⠊⠀⠀⠀⠉⡆⠀⠀⠀⡖⠁⠀⠀⠈⢱⠀⠀⠀⢸⠁⠀⠀⠀⠈⣷⢂⢡⡋⠁⠀⠀⠀⠈⡃⠀⠀⠀⠀⡖⠁⠀⠀⠈⢱⠀⢰⠊⠀⠀⠀⠉⡆⠀⠀⡏⠀⠀⠀⠀⢹⠀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡇⠀⠀⠀⠀⠘⠀⠀⠀⢸⠀⠀⠀⠀⠀⡿⠂⠬⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⢸⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠰⡀⠀⠀⢸⠀⠀⣀⠀⠀⡇⠀⠀⠀⠀⢀⡀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠈⡇⠀⣀⡀⠀⢸⠳
⠀⠀⢾⣛⣛⣒⠃⠀⠀⠀⡇⠰⣏⣙⣓⣺⡁⠀⠀⢸⠀⠻⠬⠭⠭⡇⠀⠀⠀⠀⠯⠭⠭⠍⡇⠀⠀⠀⠀⡇⠰⣏⣛⣓⡲⠀⢸⠀⢾⣉⣛⣒⡇⠀⠀⡇⠘⠧⢭⡭⢹⠀
⠀⠀⠀⢠⡤⠀⠐⠀⠀⠀⡇⠀⠀⠀⠀⠘⠃⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⣀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⢽⡇⢸⠀
⠀⠀⠀⢐⡯⠀⢰⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⡄⠀⡇⠀⠀⠀⠀⡇⠀⠈⣯⡄⠀⠁⢸⠀⠀⠀⠀⠀⠁⠀⠀⡇⠀⠀⣹⡇⠸⠀
⠀⠀⠀⣘⣟⠀⢸⣖⠍⣎⡆⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⢠⣤⠀⡔⠀⠀⠐⠀⠀⢹⡆⠀⡇⠀⠀⠀⠀⡇⠀⠀⢽⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠰⢽⡇⠀⠀
⠀⠀⠀⠱⠷⠀⢸⣮⠈⠢⡇⠀⠀⠀⠀⠀⠄⠀⠀⢰⠀⠀⢸⣗⠀⠘⠀⠀⢸⠀⠀⢸⡆⠀⡇⠀⠀⠀⠀⡇⠀⠰⢿⡄⠀⠀⢸⠀⠀⣄⣶⠀⠀⠀⠀⠁⠀⠀⠛⠇⠀⡄
⠀⠀⠀⢠⣖⠀⢸⣜⢤⣵⡇⠀⢀⣀⠀⠀⡄⠀⠀⢸⠀⠀⢾⡶⠆⣴⠀⠀⢸⠀⠈⣷⡆⠀⡇⠀⠀⠀⠀⠃⠀⠀⣿⡃⠀⡀⠰⠀⠀⠱⣶⠀⠀⠀⠀⠄⠀⠘⣭⡆⠀⡀
⠀⠀⠀⢰⣗⠀⢸⣟⢾⢿⡇⠀⣹⣿⠀⠀⡇⠀⠰⣾⠀⠀⣰⡿⠀⢸⠀⠀⢸⠀⠀⢁⡁⠀⡇⠀⠀⠀⠀⡆⠀⠀⠮⠇⠀⡇⠐⠀⠀⠸⣟⠀⢀⠀⠀⠇⠀⠈⠒⠃⠀⡁
⠀⠀⠀⢛⣓⠀⢸⠿⣇⣿⡇⠀⠈⣭⠀⠀⡇⠀⠀⢹⠀⠀⠮⡯⠀⢸⠀⠀⢸⠀⠠⣺⡅⠀⡇⠀⠀⠀⠀⠃⠀⠀⠲⢦⠀⡇⠀⠀⠀⠨⣗⠀⢸⠀⠀⠀⠀⠀⣽⡃⠀⡇
⠀⠀⠀⣰⡿⠀⢸⠀⠉⠻⡇⠀⠘⠙⠃⠀⣧⠀⣠⣿⠀⠀⢰⠦⠀⢸⠀⠀⢸⠀⠀⢸⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⡇⠐⠀⠀⠮⠷⠀⢘⠀⠀⠀⠀⠀⣿⡆⠀⡇
⠀⠀⠀⣔⠿⠀⢸⠀⠀⠀⢳⠀⠢⢻⠁⠀⣿⠀⢸⢾⠀⠀⢨⣯⠀⢸⡄⠀⣸⠀⠀⠼⢇⠀⡇⠀⠀⠀⠀⢰⠀⠈⢻⡟⠀⡇⠠⠀⠀⠘⠛⠀⢸⠀⠀⠀⠀⠀⣿⡂⠀⡇
⠀⠀⠀⠸⠛⠀⢸⠀⠀⠐⣬⠀⠀⣿⠀⠀⣿⣁⢿⣿⠀⠀⢼⡓⠀⢸⡇⠀⣸⠀⠐⡼⡇⠀⡇⠀⠀⠀⠀⢸⠀⠀⢘⣓⠀⡇⠀⠄⠀⢸⣟⠀⢨⠀⠀⠁⠀⠀⣛⡂⠀⡇
⠀⠀⠀⢸⣗⠀⢸⠀⠀⠀⢸⠀⠘⠳⠀⠀⡏⠈⠙⣿⠀⠀⠓⠧⠀⢸⡣⠈⢻⠀⠀⠋⠃⠀⠇⠀⠀⠀⠀⠈⠀⠀⠰⠶⠀⡇⠀⡇⠀⣐⡶⠀⢸⠀⠀⢀⠀⠐⣿⡇⠀⡇
⠀⠠⠤⠤⠤⠤⠼⠀⠀⠀⠸⠤⠤⠄⠤⠀⠇⠀⢠⣶⣧⣤⣤⣄⣄⣸⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠇⠀⢧⢤⠬⠥⠤⠼⠀⠀⠸⠠⠤⠤⠤⠤⠇
⠀⠀⡖⡂⣀⡀⣠⣄⣀⣠⢀⣀⢰⣊⢁⡆⣀⡀⢃⣁⠉⠉⠁⠚⠇⠸⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠘⠓⠛⠛⠃⠛⠋⠘⠛⠘⠊⠚⠛⠘⠃⠛⢛⣟⡇⠀⠀⠀⠀⢰⣧⡸⡆⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⢧⠀⠀⠀⠀⢰⡟⠓⢲⡄⡧⠀⠀⢸⡖⢷⡄⣰⠗⠛⠚⡟⠛⠋⣴⠟⢛⢦⡀⣠⡞⠛⠷⠀⣿⠛⢲⡄⣾⠀⣾⠚⢲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣿⣼⣧⠀⠀⠀⢸⡗⠒⠚⣁⣷⠒⠒⢺⡇⠀⣹⠃⠀⠀⠘⡇⠀⣰⡇⠄⡀⢸⡇⣿⠀⠀⠀⠀⡷⠶⣞⢅⣿⡄⡷⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠞⠀⠀⠸⠆⠀⠀⠨⠇⠀⠀⠈⠧⠀⠀⠸⠇⠀⠽⠀⠀⠀⠈⠗⠈⠀⠙⠶⠶⠎⠀⠘⠳⠴⠞⠀⠿⠀⠹⠮⠿⠇⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⡀⠀⠀⡤⠀⣠⣤⣤⣀⠀⣤⡀⠀⢀⣤⢀⣤⣤⣤⣄⣤⡀⠀⣀⣤⣔⣤⡤⣄⡀⣤⠀⠀⠀⠀⢀⣆⣤⣦⣤⣤⣧⡤⡤⠀⠀⢠⣦⣤⣤⢤⡄⢠⣤⣤⣤⠀⠀⠀⠀
⠀⢸⠹⣦⡀⣿⢰⠏⠀⠀⢹⡄⣿⠳⣤⡞⣿⠈⣿⣤⣄⠀⣿⠹⣦⢻⣟⣿⠁⠀⡈⢀⣷⢀⠀⠀⠀⣿⠹⡇⠀⢀⣿⡚⢗⣷⠀⠀⢸⡇⣿⣠⣰⠟⢸⣧⣤⡄⠀⠀⠀⠀
⠀⢹⠀⠈⢷⣟⠸⢧⣀⣀⡾⠁⣿⠀⠉⠀⣿⢨⣇⣀⣀⡀⣽⠀⠘⢿⡿⢹⣯⣯⣧⣿⣿⣀⣢⣀⣾⠏⠉⢻⡄⠸⣿⠀⠐⢿⣄⣀⡾⠃⣿⢁⣹⣤⢼⣇⣀⣀⠀⠀⠀⠀
⠀⠈⠀⠀⠀⠁⠀⠀⠉⠁⠀⠀⠁⡆⠀⠀⡉⡊⠉⠉⠁⠀⠈⠀⠀⢀⠀⠀⠈⠻⣙⡳⣕⢻⣉⠄⠁⠀⠀⠀⠁⠀⠡⠀⡀⠀⠈⠉⠀⢀⡨⣯⠀⠉⠀⣠⠟⡯⣖⣦⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠖⠸⢿⠿⣿⡷⢷⡶⠷⠷⠖⠄⠿⠿⣾⢾⣿⣿⣿⣿⣿⢿⡦⣿⠲⢿⠾⠶⢷⠿⠿⠿⠶⠄⠀⡞⠿⠃⠀⠀⠀⢧⣇⣞⠘⡤⠧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡿⠂⠣⡿⠿⠿⠛⠺⠷⠛⠟⠟⠟⠟⠟⠿⠿⠿⠙⠿⠟⠿⠿⠟⠟⠯⠯⠄⠀⠀⠀⠀⠀⠀⠀⣿⡟⣶⣿⣿⣦⣤⣤⡈⢿⣥⠇⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⡛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⡔⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⡿⢿⣿⣿⣿⣷⣄⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⢀⣤⣀⢦⣤⡀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⣶⣦⣾⣦⣶⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠃⠻⠿⠃⠺⣿⠟⠸⠿⠿⠿⠿⠿⠿⠯⠄⠀⠛⠘⢻⣿⢿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡿⠟⢷⣿⠿⠉⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠐⠐⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⡟⣭⠋⠙⠙⠊⠓⢩⡳⣏⠷⡋⠓⠙⠉⠛⠑⣏⡿⣱⢏⠉⠉⠘⠉⠈⢹⢞⣝⡎⠉⠁⠋⠉⠁⡯⡽⣹⡝⢧⡏⠙⠛⠊⠙⠋⣻⠼⠉⠋⠙⠓⠛⢙⡯⣝⡎⠁⠙⠈⠁⠙⣎⢯⣝
⣝⢮⠀⢀⡤⣄⠀⢰⡻⣜⢯⡇⠀⣠⣤⡀⠀⣞⢾⣱⣻⠀⣤⣶⢦⠀⢘⡾⣲⡇⠀⣴⠶⡄⠀⡷⣝⣣⢯⣳⡇⠀⣠⣤⡀⠀⣗⣻⠀⢠⡤⣄⠀⠸⣞⡵⡆⢀⣴⠶⡄⠀⢾⡱⣎
⣞⣭⠀⠘⣷⠝⠀⢰⢫⡞⢧⡇⠈⢫⡽⠃⠀⣛⣮⢳⣻⠀⠈⣯⠋⠀⢸⣿⣳⡇⠀⠙⣽⠁⠀⡿⣜⢧⣫⠶⡇⠈⢻⡿⠃⠀⢮⣽⠀⠑⣷⠝⠀⢸⣥⣛⡇⠀⢱⡛⠁⠀⣯⢳⡭
⠾⣜⠀⠀⣯⠀⠀⢸⢣⡟⣫⡇⠀⢸⡃⠀⠀⣯⡵⣻⢼⠀⠀⣿⠀⠀⢸⣟⡭⠇⠀⠀⣽⠀⠀⡟⣭⡞⣥⡻⡇⠀⢸⡇⠀⠀⣏⢾⠀⠀⡿⠀⠀⢘⠶⣭⡇⠀⢸⡇⠀⠀⣮⢳⣝
⠿⣼⠀⠀⠓⠀⠀⢨⠷⣹⢣⡇⠀⠘⠃⠀⠀⢧⡳⢏⣿⠀⠀⠉⠀⠀⢸⡮⣝⡃⠀⠀⠁⠀⠀⡽⣲⡝⡶⣹⡇⠀⠘⠃⠀⠀⣎⢿⠀⠀⠛⠀⠀⢨⢟⡲⡇⠀⠈⠁⠀⠀⣟⡲⣭
⠿⣼⢀⣴⢢⣠⣄⢨⢟⡵⣫⡇⢐⢵⠱⠞⠂⡯⣵⠟⣾⢨⣶⣳⣳⢫⢘⣶⣙⡆⠰⡢⣠⢠⣄⡷⣣⠟⣵⢣⡗⣷⡓⠎⣷⠱⣎⢿⠀⠀⣄⣄⠀⢘⣮⣳⡇⣸⡖⢞⣶⡱⣞⡱⣮
⣻⢼⠀⠀⠀⠀⠁⢘⣮⢳⢧⡇⠀⠀⠀⠀⠀⡽⣲⢟⣻⠀⠀⠀⠀⠀⢸⡳⢾⡃⠀⠀⠀⠀⠀⡳⢧⡻⣜⣫⡇⠀⠀⠀⠀⠀⣎⢿⠀⠀⠀⠀⠀⢘⢶⣻⡇⠀⠀⠀⠀⠀⣞⣵⢣
⡳⢞⠀⠀⠀⠀⠀⢘⢶⣋⡞⡇⠀⠀⠀⠀⠀⡿⣱⢮⢿⠀⠀⠀⠀⠀⢸⣹⢳⡅⠀⠀⠀⠀⠀⣟⡳⡽⣜⣣⡇⠀⠀⠀⠀⠀⣏⢾⠀⠀⠀⠀⠀⢘⡮⡵⡇⠀⠀⠀⠀⠀⡷⣮⢯
⢯⢽⠀⠀⠀⠀⠀⢨⠷⣙⡞⡇⠀⠀⠀⠀⠀⡟⣥⠿⣾⠀⠀⠀⠀⠀⢸⡳⢯⢆⠀⠀⠀⠀⠀⣧⣟⡵⣛⠶⡇⠀⠀⠀⠀⠀⣎⢿⠀⠀⠀⠀⠀⢘⡶⣹⡇⠀⠀⠀⠀⠀⣿⢮⣗
⣏⠾⣴⠀⠀⠀⣴⠞⣯⢳⣝⣣⡆⠀⠀⢠⣞⡻⣵⢻⡜⣯⠀⠀⠀⢾⡿⣹⠯⣞⡵⠀⠀⠐⣿⣳⢎⢷⣹⢫⡵⡆⠀⠀⢠⡶⣎⡟⣴⠀⠀⠀⡴⣯⢜⡳⢎⡇⠀⠀⠰⡿⣱⢯⡾
⣭⢳⠉⠀⠀⠀⠈⢹⢎⡷⣺⡆⠀⠀⠀⠀⢩⢳⢮⠷⣾⠀⠀⠀⠀⠀⢿⣱⡟⡇⠀⠀⠀⠀⠀⣳⢎⣧⢗⢯⡆⠁⠀⠀⠀⠁⣟⣼⠁⠀⠀⠀⠈⣮⢻⣹⡇⠀⠀⠀⠀⠸⣱⠯⣝
⢾⡭⠀⠀⠀⠀⠀⢘⣮⠳⣧⡇⠀⠀⠀⠀⠀⡟⢮⣳⢿⠀⠀⠀⠀⠀⢸⣳⡽⡇⠀⠀⠀⠀⠀⢯⣝⣚⢮⡳⡇⠀⠀⠀⠀⠀⡞⣼⠀⠀⠀⠀⠀⢨⡷⣽⡇⠀⠀⠀⠀⠀⣯⢻⣜
⡷⣹⠀⠀⠀⠀⠀⠸⣜⠯⣖⡇⠀⠀⠀⠀⠀⣯⢳⣭⣻⠀⢀⣀⣀⠀⢹⣣⠷⡃⠀⢀⣀⡀⠀⣯⢞⣱⢫⡵⡃⠀⠀⠀⠀⠀⡽⣹⠀⠀⠀⠀⠀⢸⡳⢧⡇⠀⣀⣀⡀⠐⣯⢛⡼
⣳⢧⠀⠺⢉⣉⡡⠺⣭⢻⡜⡇⠐⠍⡉⡉⠝⣮⢗⡮⣽⠀⠙⠦⠤⠜⢱⡭⢯⡅⠈⠫⠤⠤⠏⣷⢎⣷⢻⡜⡇⠐⠏⣉⣉⠰⡝⣽⠀⠪⠙⢉⠩⠲⣝⣳⡇⠘⠲⢤⡴⠋⣞⣭⢾
⡽⣎⠀⠀⢂⡄⠀⢘⢧⡻⣜⡇⠀⠀⠀⠀⠀⣯⡾⢼⣹⠀⠀⠀⠀⠀⢸⡵⣋⠆⠀⠀⠀⠀⠀⡯⣞⢧⣻⢭⡇⠀⠀⣀⠀⠀⣝⢾⠀⠀⠀⠀⠀⢘⢧⡳⡇⠀⠀⢽⠇⠀⣟⢦⢿
⡿⡼⠀⠀⢐⣇⠀⢸⢧⡻⣼⡁⠀⠀⠀⠀⠀⢶⣹⢳⣻⠀⠀⠀⠀⠀⢰⡳⣏⠇⠀⠀⢰⠆⠀⣽⡺⣍⡞⢧⡃⠀⠀⣾⡄⠀⣏⢿⠀⠀⠀⠀⠀⢨⠷⣹⠇⠀⠀⢭⠅⠀⣯⠞⣧
⣳⣝⠀⠀⡈⠗⠀⢸⣷⣟⣧⡇⠀⠀⠀⠀⠀⣯⢳⢯⡳⠀⠀⠠⠦⠀⢸⣱⢏⡆⠀⠀⠉⠅⠀⣷⢳⡹⣜⢧⡃⠀⠀⡯⠀⠀⢮⣻⠀⠀⠀⠀⠀⢨⡻⡵⡃⠀⠐⠬⠅⠀⣳⢯⣳
⡷⣹⠀⠀⠰⠚⠀⢸⢿⣲⣽⠇⠀⠀⠀⠀⠀⣷⣛⡷⣹⠀⠀⠨⠃⠀⠸⣎⢯⠆⠀⢀⢹⡄⠀⡿⣧⣛⢮⡳⡅⠀⠘⠽⠄⠀⢯⠶⠀⠀⣔⣓⠀⢰⣫⢵⡃⠀⠀⠋⠃⠀⢯⡳⣭
⣝⣧⠀⠀⠠⣴⠀⢸⡿⣵⣫⡇⠀⡠⣀⠀⠀⣟⠾⣱⣣⠀⠀⠮⡇⠂⢸⣭⢯⡆⠀⠀⣭⡅⠀⣟⡶⡝⡯⣵⠇⠀⠀⣭⡇⠀⣏⡟⠀⠀⠨⠬⠀⢸⢲⣏⠆⠀⢈⣭⡆⠀⡿⡽⣖
⡟⡶⠀⠀⠨⠥⠀⢸⣿⡶⣿⡅⠀⡈⢬⠀⠀⣾⠻⡵⣿⠀⠀⣐⡂⠀⢸⣎⠿⡄⠀⠀⢠⡄⠀⣿⢼⡹⣵⢫⠆⠀⠐⠊⠆⠀⡗⣞⠀⠀⠈⠍⠀⢨⡗⣮⠇⠀⠈⠐⠁⠀⡷⡽⣞
⡏⣷⠀⠀⢱⡾⠀⢸⣿⣹⣾⡇⠀⠀⣿⠀⠀⡏⣿⢱⢏⠀⠀⠇⡆⠀⢸⡎⣏⡹⠀⠰⣸⠆⠀⡿⣶⡹⡶⣏⡇⠀⠀⢰⣶⠀⡿⣸⠀⠀⠀⣉⠀⢸⢷⢹⡆⠀⠀⣸⡇⠀⣏⣱⢿
⣽⢲⠀⠀⠰⠍⠀⢸⣣⡽⣟⡇⠀⠘⠘⠂⠀⣿⣜⣻⣾⠀⠀⠠⡤⠀⢸⡺⣥⢻⠀⠀⢥⡅⠀⣿⣱⢳⡝⢧⡃⠀⠀⠓⠃⠀⣟⢧⠀⠀⣄⣕⠀⢸⢏⡷⡆⠀⠀⣲⡂⠀⡞⣭⡳
⣏⡳⠀⠀⡈⠏⠀⢸⡶⣹⡼⡇⠀⢤⣲⠀⠀⣿⡲⢽⣭⠀⠀⢨⡇⠀⢸⡷⣵⣻⠀⠀⢖⣂⠀⣷⡹⢮⣝⡳⡅⠀⠀⢛⡆⠀⡟⣮⠀⠀⠸⠱⠀⢸⢮⣳⡅⠀⠀⣮⠂⠀⣿⢣⢟
⢷⣹⠀⠀⠸⠛⠀⢸⡵⣳⡝⡎⠀⠀⣓⠀⠀⣿⣏⣷⡿⠀⠀⣸⡆⠀⢸⣿⣱⢻⠀⠐⠜⠎⠀⢷⣹⠳⣎⢷⡁⠀⠀⢸⣖⠀⡿⣜⠀⠀⢐⠷⠀⢸⡻⣶⡃⠀⠀⣺⠆⠀⣯⣛⣮
⡯⢵⠀⠀⢐⠖⠀⢸⡝⣧⡝⡗⠀⠐⠲⠀⠀⡿⣜⢏⣾⠀⠀⠪⠆⠀⢸⡷⣏⣿⠀⠀⠛⠃⠀⢳⡎⡿⣜⢮⡃⠀⠀⢰⠃⠀⣟⣮⠀⠀⢐⠾⠀⢸⣳⢳⡅⠀⠀⣽⡀⠀⣧⢳⡼
⣯⢳⣀⣀⣈⣀⣀⣸⢽⡲⡽⣱⣀⣀⣀⣀⣀⢿⣙⢾⡝⣆⣀⣀⣀⣀⣸⣟⡼⢾⡀⣀⣀⣀⣀⠸⣵⣛⡬⢷⣁⣀⣀⣀⣀⣀⢯⡳⣄⣀⣈⣈⣀⣸⢧⡟⣆⢀⣀⣀⣀⡀⣷⢫⢞
⣮⠳⣝⣾⡳⣝⡶⣹⣎⢷⣙⡳⣎⣽⣺⣍⣯⢮⣝⡽⣹⡻⣽⢻⠽⣟⡿⡼⢧⡟⣼⠳⣎⠶⣭⢻⡜⣵⢫⡳⣭⠖⣧⠳⡞⣼⢣⠿⡽⣝⢮⣷⣛⢮⣳⢽⡞⢯⡞⣖⢧⡽⣲⢏⡞
⣧⢻⡜⣷⢻⣟⡳⣟⢯⣛⢿⡹⣟⢾⡻⣼⢳⣛⣟⡾⣗⡻⣬⢳⡻⣼⣟⣽⡟⣾⡵⣻⣜⡻⡜⣧⠻⣜⣏⡳⣝⢾⡱⢯⡝⣎⢯⣝⡳⣎⡟⡼⣜⣛⣮⢳⣭⢳⡞⣭⠞⣵⢣⣏⢞
⣧⢳⡻⣼⣷⢮⢳⡝⣎⢧⣟⡾⢾⣣⣿⡜⣧⢽⡶⢿⣜⣳⢯⣗⠿⣶⡟⣮⣽⣞⣷⢷⢮⣵⣟⠾⣿⡜⣶⡟⣾⡧⣿⡳⣾⣛⣾⡶⣹⢎⡳⡽⣭⢳⣺⡝⡾⣡⢟⡼⣹⢎⠷⣎⢯
⣧⢛⣶⣟⣾⣏⣧⠻⣜⡏⣷⣟⣻⠳⣷⠽⣾⢻⣏⣳⣻⢯⡳⣎⠿⣷⡹⢶⣟⡼⣎⣻⡷⣿⢎⡟⣦⣛⣷⡽⣾⢽⣿⢗⡿⣞⡞⣷⡹⣎⠿⡱⣧⣛⣧⣛⡵⢫⣎⠷⣭⢞⡹⣎⠷
⣧⣛⢾⣺⣱⢻⡖⣟⡲⢽⢧⡝⣮⣛⣯⢟⡼⣻⢧⡳⡽⢮⡳⣭⣛⣷⢏⣟⡟⣷⡽⣞⡳⡽⡾⡽⣞⡵⢯⣞⡽⢿⢿⣯⠿⡼⣹⢶⡳⣭⢫⢗⣫⢗⡶⣹⣚⠷⣎⣛⢦⣏⡳⣭⣛
⡗⣮⣓⡧⣞⣣⡟⡶⣙⣧⣏⡾⣱⢧⡞⣝⠶⣽⢮⣵⣯⢷⡝⣶⡹⣎⣟⣮⣽⣲⣽⣶⣙⡷⣙⢷⡹⣼⣳⣞⣭⢷⣯⣷⣯⣗⡯⢯⡵⣫⡟⣯⣷⢾⡗⣧⣹⣽⣬⡻⣜⢶⣹⠲⣭
⡝⣶⣹⠿⣞⡲⣿⣵⡟⢾⣜⢻⣧⣿⠿⣮⡿⢿⣚⣯⣎⣷⡹⣿⢻⣞⣯⣿⣿⢵⣚⣼⢣⣿⡝⣮⢳⡳⣿⡽⣟⢮⣓⣿⡾⣏⣿⣳⢽⣹⡟⣿⣞⣧⡿⣽⣷⣎⡷⡹⡞⣮⣳⣛⠶
⡻⣔⣻⢽⡹⢿⡿⣭⣟⣧⣺⡽⣧⣿⢫⡽⣹⣿⡜⣿⣜⣶⡹⢯⡻⣜⣿⣷⣻⣿⣧⣿⢿⣿⣵⣳⣟⣽⣟⠿⣽⣮⠿⣿⣱⢯⣿⣵⣋⣾⡟⣿⢽⣹⣶⣹⣷⢎⣳⣝⡳⣝⠧⣝⡞
⣻⢼⡹⢮⣝⡳⣛⡴⣫⡜⣧⣛⠶⣭⡟⣼⣳⡝⣾⡻⣭⢟⡽⣭⢳⢧⡳⢧⣳⢫⡽⣽⡳⣟⡾⣝⢧⣛⢮⡻⣼⢯⡹⢧⣟⢾⡱⣎⢿⣡⡟⣭⣟⢮⡳⡝⣮⢟⡿⣺⢵⣫⡝⡶⣹
⡗⣮⠝⣧⠞⣵⢫⡵⢣⣟⡴⣫⠟⣾⢿⡞⣷⢿⡿⣷⣾⢿⣶⡟⣷⢾⡝⣿⢾⣷⣿⣾⣿⣿⣿⢿⣾⣯⣷⣻⢿⡾⣿⢿⡿⣷⢿⣾⣟⣱⡾⢿⣯⢳⡽⣜⣷⣯⣟⡳⣯⢧⡽⣱⢧
⣻⢼⡹⢎⡽⣎⠷⣙⡷⣎⠷⣭⣛⢾⡿⣫⠷⣿⡿⣿⢳⡻⣟⠾⣟⡞⣿⢞⣟⡿⣿⢿⡻⡽⣟⢿⣻⢗⣟⢧⡻⣼⣫⡟⡵⣫⢿⣭⠞⣭⣟⣿⣿⣿⣶⣭⣶⡻⢾⣵⢯⣳⢭⡳⣏
⣧⢻⡜⢯⡜⣮⢻⣝⡲⣭⢻⡱⣎⢿⡹⣟⠿⣻⡿⣝⣣⢟⡼⣹⢶⡹⢖⣫⠾⣱⢯⡷⡽⣝⡮⢷⢯⣞⡼⢣⣏⡷⣝⡼⢳⣽⣺⠵⣫⠷⣹⣿⣿⢿⣿⣿⣿⣿⣗⢮⣻⢮⣓⡯⣛
⣞⣳⢚⣧⠻⣜⡳⢮⡻⣜⡧⣟⡼⣲⣝⢮⣛⣵⡳⣮⣽⣎⣳⣓⣮⣽⣏⣾⣻⠵⣟⢾⣽⣯⣿⣯⣿⣶⣽⢗⡾⣜⢮⡵⣻⢶⡹⣏⡵⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⢋⡾⣕⢯
⡧⣝⣞⣲⢻⣜⡹⢇⡷⣓⢾⡱⣞⡻⢿⣏⢿⢿⡛⡿⣿⢿⣹⢿⡿⣿⣽⢯⡿⣿⡝⣮⡿⣝⡿⣿⢽⣯⣟⢿⣾⣜⢯⣓⣯⢾⡱⣏⡾⣗⢯⣛⡿⣿⢿⢿⣿⢿⣛⢧⣳⢫⣞⣚⢮
⣟⡞⣼⢲⢏⡶⣹⣋⡶⣹⢎⣗⡣⢟⢧⡺⣭⠞⣭⢳⡝⡶⣹⢎⣷⢽⡎⣿⡺⣵⢻⡵⢏⣞⣞⢧⡻⡾⣭⡳⣞⡜⣧⢿⡱⣏⢷⣹⣳⣏⡳⢎⡷⡽⣋⢷⣙⣮⢏⡾⣸⡳⢧⢯⣳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢀⣀⣀⣠⣤⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⠛⠋⠉⠉⠛⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣀⡤⣤⢤⡤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣀⣤⣶⠿⠛⠋⠁⠁⠀⠀⠀⠉⠛⣯⣳⡀⠀⠀⠀⠀⠀⠀⢠⡿⠃
⠀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣿⠀⠀⠀⠀⠀⣠⡿⠃⠀
⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⢹⡆⠀⠀⢸⣿⠀⠀⠀⠀⢠⡿⠁⠀⠀
⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠀⠀⢀⣮⠏⠀⠀⠀⠀⠘⣷⡀⠀⠀
⠀⠙⠿⣶⣤⣀⠀⠀⠀⠀⠈⠻⢦⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀
⠀⠀⠀⠀⠉⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣤⣤⣄⣀⣀⣤⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠈⠉⠉⠙⠛⠉⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠎⠉⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⡄⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠀⠀⠀⠀⡰⢳⡀⠈⠉⠀⠀⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠈⠫⡅⠀⠀⢈⠽⠋⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⣇⠤⠤⣺⠀⠰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠈⠀⣠⢄⠈⠁⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⠒⠉⠀⠀⠁⠢⠀⠜⠀⠀⠀⡖⠐⠂⠠⠄⣀⠀⠀⠀⠀⠀⠀⡠⠊⠀⡠⠊⡇⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⢤⢀⣀⠀⠁⠐⠂⠠⠎⠀⡠⠊⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠈⢆⠀⠉⠑⠒⠠⠤⡠⠞⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠘⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠤⣀⠀⠁⠂⠄⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠔⠂⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠂⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⡀⠀⠉⠂⡄
⠀⠀⠀⠀⠀⠀⢀⠀⢀⠈⠢⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⢄⠀⠀⠀⠀⠀⡔⠁⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠒⠉⠁⣀⠤⠄⠒⠁
⠀⠀⠀⠀⠀⠀⢸⠀⢸⠳⢄⠀⠑⠄⠤⠐⠈⠁⢀⠀⢀⠎⠀⠀⠀⢀⠎⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⢀⡀⠤⠐⠂⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠑⢄⣀⡠⠤⠒⢩⠃⠀⡌⠀⠀⠀⡠⠃⢀⣞⣀⠤⠤⠔⠒⠒⠉⠲⡀⠀⠀⠀⢠⠇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡀⠜⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⡜⠀⠀⠀⠔⠀⠀⠀⢀⣀⡀⠤⠄⠐⠒⠢⡀⠈⢆⠀⠀⢸⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠠⠒⠉⢀⡠⠔⠉⠀⠀⠀⠀⠀⠀⠀⣎⠀⠸⡁⠀⠀⠀⠈⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠱⡄⠘⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡎⠀⠀⠐⠪⠥⣀⣐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠈⠇⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠀⠒⠢⠤⢀⣀⠀⠉⢱⠀⠀⠀⢀⠤⠤⠀⣀⣘⣄⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠁⠀⠀⠘⡄⠀⡆⠀⡠⠃⢀⡀⢀⣀⡀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢡⡐⠁⢠⠎⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣅⣀⢈⣩⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣀⠴⣒⣤⣀⡲⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣿⣯⡿⠟⠋⠈⠻⡛⠋⠹⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⠊⢔⢉⢙⣹⡿⠳⣙⡊⣓⣉⣒⡤⡀⠀⠀⠀⠀⠀⣰⡟⣡⠟⠁⠀⠀⠀⠀⠀⠈⠑⠢⡍⡧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠐⡇⠀⠻⣿⠟⠁⠀⠀⠀⠉⠉⠻⣟⠋⠙⠓⢤⣠⡴⣶⡿⣛⣉⣁⠒⠢⣄⣀⠀⣀⣤⡶⢺⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠱⡀⢾⠁⠀⠀⠀⣀⡠⠤⠶⠒⣺⠿⣟⢠⣯⣃⣳⡾⠲⠷⣮⣥⣴⣮⣤⣤⣬⣿⣟⣻⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠢⣷⣦⣤⣾⣿⣷⣶⡂⢉⡤⢊⣥⣿⡿⠿⠿⢿⣦⣤⣀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⡤⢤⣄⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠋⡴⣻⣿⠏⠀⠀⠀⠘⢿⢯⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⢽⣿⣦⡄⠀⠀
⠀⠀⠀⠀⠈⠄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣡⢁⡏⠀⠀⠀⠀⠀⠈⠫⣳⠄⢹⡆⠀⠀⠀⠀⣠⣴⣿⣿⣿⠞⠁⠈⢿⢿⡷⠀⠀
⠀⠀⣰⣾⣏⠩⡉⢴⣄⠀⠀⠀⠀⢠⢂⡴⢛⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣾⣿⡀⠀⢠⣾⣿⣿⡿⠟⠁⠀⠀⠀⣸⣾⠃⠀⢀
⠀⣰⡇⠈⠙⠤⣽⣧⣿⣷⣤⣀⣴⣡⡤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠛⠋⠁⠀⠀⠀⣀⣴⣾⡿⠁⠀⠀⠘
⢰⣟⣹⡄⠀⠀⠀⠉⠛⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⡖⠁⢸⣿⠃⠀⠀⠀⠀
⢹⡇⠂⢡⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⠀⠠⣬⣧⣀⡜⠁⠀⠀⠀⠀⠀
⠀⠱⡄⠀⠣⠀⣠⣤⣤⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢶⠃⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠢⢀⣙⠿⣿⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡾⡄⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠑⠊⠁⢀⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢷⣿⣿⡶⠤⢕⡄⠀⠀⠀
⠀⠀⠀⣠⠔⠂⢶⣶⣿⠟⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀
⠀⣠⡎⠀⣀⣠⡾⠟⠃⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀
⠀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠶⣶⣿⣿⣿⣿⣿⣿⣿⠃⠀⠈⣿⣿⣿⣿⣿⣿⣷⣶⡶⠂
⠀⠀⠀⠀⠈⠻⣿⣷⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⡆⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⣀⠀⠀⠸⣿⣯⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣁⣴⣾⣿⣷⣦⣄⢻⣿⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠟⠋⠀⠉⠻⢿⣿⣿⣧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠁⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣤⣤⣤⣤
⠀⢀⣀⣀⣀⣀⣞⣿⣴⣵⣿⣶⣿⣿⣶⣿⣗⣷⣷⣿⣷⣱⣀⣠⣂⣰⣲⣴⣟⣶⣿⣳⣾⣾⣶⣤⣔⣻⣽⣷⣆⣀⣶⣿⣴⣧⣿⣿⣿⣿⣷⣿⣗⣳⣷⣾⣿⣹⣀⣀⣀⣀⣀⡀⠀
⠀⠀⠀⠀⠀⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢴⣿⣿⣿⢿⣿⣿⣿⠿⣿⣿⢿⣷⣗⡿⡇⡟⡭⠉⢘⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣽⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢸⢿⡻⣿⣿⡿⣿⣿⡾⣻⣏⠹⢿⣾⣵⣧⢷⣇⠀⠸⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢈⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⣤⣾⣇⣿⣿⣿⣽⣻⣿⢻⣸⣼⣼⢸⡿⣿⣼⣿⣆⡈⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍⣙⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣙⣽⣺⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⡀⠀
⠀⠀⠀⠀⠀⠈⠛⢻⣻⠟⠋⢻⠛⠛⣿⣏⠟⠛⠛⣟⡟⠋⠠⠻⣿⣾⣿⣿⣿⢿⣿⣿⠿⣿⣿⣿⣝⣿⠫⠾⠯⠈⠛⢻⣛⠟⠋⢻⡛⠛⢿⣏⠟⠛⠛⢿⡟⠟⠀⠀⠀⣤⣠⣀⣠
⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡔⣒⣽⣿⣿⣿⣿⣿⣟⢽⣾⣿⣬⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠙⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⢿⣯⣴⣽⣿⣽⣿⠿⠋⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⡏⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡮⡻⣆⠀⠀⠀⠀⠀⠀⠀⣠⣾⣭⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣝⡽⣦⠀⠀⠀⠀⢀⣴⣿⢿⡿⠋⠀⠀⠰⠶⣶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠈⢻⣞⢞⢷⡀⠀⣠⣾⣿⣷⠟⠁⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣻⢿⣦⣄⠀⠀⠹⣯⣫⣷⣴⣿⣯⡾⠋⠀⣀⣤⠴⠚⠉⢱⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣯⡛⢿⣦⣀⠙⡟⠁⠀⠈⢻⡥⠖⠋⠁⣀⣤⡶⠞⠛⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠑⠒⠒⠒⠲⠭⠿⠷⠽⠿⣷⣧⡀⠀⢀⣼⣡⣴⣾⡻⠭⠵⠒⠒⠋⠉⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠶⠶⠶⣶⣶⣤⣤⣤⠎⠁⠀⠙⣿⠋⠀⠈⠱⣌⣀⣤⣤⡴⠶⠾⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣄⠀⠀⢀⢿⡀⠀⠀⣰⣋⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶
⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣼⣥⣴⣽⣾⣿⣿⣿⣿⣾⢿⣿⣿⢮⣽⣾⣿⣦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣹⣿⣿⣿⣿⣿⣿⣿⣧⣿⠸⣟⢯⡉⣟⣿⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⣿⣿⡿⣿⣿⡿⣿⣿⢰⢹⣿⣻⣿⣇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣿⣿⢸⣟⣿⣿⣿⣹⣜⣼⡾⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣭⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣽⣿⣿⢽⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⣽⣿⢿⣿⣿⣻⣿⣿⢟⣷⣿⣿⣮⡟⠙⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣲⣊⣭⡾⡿⣿⣿⣿⣿⣿⣺⣿⣿⣖⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡻⣻⣿⣺⢷⣿⣾⡿⠟⠋⠈⠉⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣷⡅⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡠⡀⣾⣂⣰⣷⣠⣵⣀⠀⢠⣤⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡭⣿⢿⢽⣿⣿⣻⢿⣿⣿⣿⣿⣿⣿⢿⡟⣯⠿⠏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣾⣮⢇⣿⣿⡿⣿⢟⣿⣿⡅⣿⡞⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣹⣿⣿⡿⣻⣿⣿⢻⣾⣧⡟⣼⣹⡇⢸⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠛⠛⠛⠚⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠯⣧⣷⣿⣷⣻⣽⢯⣿⣿⣿⣿⣿⢿⣿⣿⣾⢷⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠁⠈⠉⠉⠉⢉⣭⣭⣍⡉⠉⠁⠈⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣟⢯⣿⠽⢹⠀⠉⠉⠉⠉⠉⠉⣹⣳⣉⢀⢉⣉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡉⠉⠁⠀
⠀⠀⠀⠀⠀⣠⡶⣿⣿⣿⣿⢧⠀⢀⣈⠤⢟⣿⣽⣿⣷⣿⣿⣿⣿⣾⠟⣟⣿⡏⠀⠈⢉⣠⣶⣶⣦⣀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠛⠛⠛
⠀⠀⠀⠀⠀⢾⣿⣿⠿⣿⣽⣯⡈⣳⡷⣶⣟⣏⣿⣿⣿⣿⣷⣞⠿⡿⣿⣻⠿⣿⣴⣿⣿⣿⣿⣿⣿⣽⣶⡄⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⣧⡄⠉⣿⡷⡻⠓⠛⠻⠿⠏⠁⢀⡀⣀⣀⣀⣀⣽⣝⣿⣮⣽⣿⣯⣟⣿⣿⣧⠀⠉⠉⢿⣿⣿⡟⠛⠀⣀⡀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢈⣿⣿⣿⣿⣻⣿⠟⠁⠀⣀⣿⣧⣠⣀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⡮⠟⣿⣿⡿⣿⣿⣷⠿⣏⣽⣶⣴⣶⣄⠀⣤⣴⣾⣿⣿⣿⣿⣿⡾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠚⠛⠛⠛⠁⢀⠀⣀⣤⣿⣿⣾⣿⣿⡷⣼⣿⣿⣯⣿⣿⣿⣶⣿⡷⠀⢀⢽⣛⠚⠁⠀⣀⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⣿⣿⣿⣽⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣻⣿⣿⣿⣿⣿⡿⠿⣠⣽⠿⣿⣿⣯⣿⣿⣿⢋⣹⣼⣿⣿⣏⣀⣶⣾⣿⣿⣿⣿⣿⠏⠃⣼⣿⣿⣿⣟⣿⣿⣽⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⠿⠛⢱⣾⣿⣿⣄⡉⠈⠋⠘⢟⣽⣿⣿⣿⣿⣷⣿⡧⣿⣿⣽⣿⣿⠿⠋⠀⠀⠀⠀⠉⠉⠋⠹⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠃⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⣦⡀⢾⣿⣿⣿⣿⣿⣯⣿⠎⠻⠿⠛⠯⠀⠀⠀⢰⣶⣤⣤⣤⣶⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣟⣿⠅⢿⣿⣿⣿⣿⣿⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣾⣿⢿⡟⠃⠀⠀⠛⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀
⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃
⠀⠀⠀⠀⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠀⣾⣿⠟⠋⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀