⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣀⣀⣠⡤⣤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢶⣶⣿⣾⣭⣿⢿⣿⢿⣷⣾⣟⣿⣿⣷⣾⣿⣿⣿⣿⣿⠏⣀⣠⣤⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣠⣶⣿⡿⣿⣻⣯⣷⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣾⣿⣿⣿⣿⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⡟⣤⣾⣿⣿⣛⣧⣿⣷⣿⣿⣿⣿⣿⣿⡿⣿⣟⠿⣯⢻⣝⡯⡽⣝⡾⣹⣝⢯⣟⡻⣟⡿⣿⢿⣿⣿⣿⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣟⡷⣯⣿⣿⣿⣿⡿⣟⢿⣹⣏⢛⣿⢷⣞⣯⣝⣳⢮⣝⢷⣫⢞⡷⣺⢏⡾⣝⢧⡟⣮⢟⡾⣽⢿⣿⣿⣽⣳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⢿⣻⣽⢺⣵⢻⣞⡿⣡⢏⡼⣩⣛⣿⢮⣳⢯⢾⣹⢮⢯⣗⣯⢯⣳⣏⣾⣹⢎⡿⡼⣭⡟⡿⣿⣿⣿⣿⣯⣳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣭⣗⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡿⣞⣯⢷⣞⣯⣞⡿⢾⣷⣧⣞⡴⢣⣾⣟⣯⢾⡹⣏⣞⢯⣳⠾⣜⣳⡝⣮⢳⣏⠿⣷⢿⣵⣫⡽⣳⡻⣿⣿⣿⣿⣿⣿⣲⣄⡀⠀⠀⠀⠀⣼⣻⣿⣿⣿⣿⣷⡎⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣟⣾⣟⣾⣳⡿⣽⣻⡼⣏⡿⣿⡿⣿⢻⣜⣳⢯⣝⡾⣹⢮⡿⣽⣳⣿⣷⣯⣾⣝⣮⣳⡭⣏⢷⢯⡷⣝⡾⣻⣿⣿⣿⣿⣷⣽⡦⣄⢀⡼⣵⣿⣿⣿⣿⣿⡿⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣷⢯⣿⣽⣟⡷⣽⡳⣟⣮⢽⢾⣱⢯⡽⣞⡽⣳⡟⣿⢿⣿⣿⣿⣿⢿⣿⣿⣮⣷⡹⣝⢾⣳⢯⣟⣿⣿⣿⣿⣿⣿⣽⣛⣷⡻⢟⣻⢿⣿⣹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣯⣟⣷⣻⡽⣮⣛⣮⢷⣏⡾⣵⣫⢷⣹⢏⡿⣽⣿⣿⣾⣿⣯⣿⣿⣿⣿⣞⣧⣛⢾⣹⣞⡿⣿⣿⣿⡿⠿⠿⠟⠃⠀⠉⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⣷⣿⣽⣿⣻⣽⣿⢾⣽⡷⣯⢿⡽⣾⡽⣞⣽⣿⣯⣿⣿⣷⣿⣿⣿⣿⣿⣻⣯⣶⢫⢿⡽⣿⣿⣿⣲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣟⣷⡿⣷⣿⢿⣝⡾⣹⢯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⡾⣽⣿⢿⣻⢿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣷⡻⣽⣻⣿⣿⣾⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣾⣿⣿⣿⣟⡿⣾⡽⣯⣿⣾⣿⣯⣟⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣟⣯⣟⣿⣿⣿⣿⣿⣿⣿⣽⣾⣟⣷⣻⣽⣿⣿⣿⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⢷⡿⣷⣿⣿⣿⣷⣯⢿⡽⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣻⣾⢿⣿⣿⣿⣿⣿⣿⣻⣾⢷⣯⢿⣿⣿⣿⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⡿⣿⣿⣿⣿⣿⣿⣯⢿⡽⣟⡷⣯⣿⣿⣿⣿⡿⣟⡹⢆⡳⢎⠶⣑⢎⠶⡱⣊⢭⠛⡽⢻⡿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣻⣿⣿⣿⣿⣿⣿⣿⢿⣾⣻⣿⣿⣿⣿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⣯⢿⣻⣽⣿⣿⣿⡿⢏⢶⣡⢛⡬⢓⡎⠳⡜⡘⡖⢥⠩⢆⡛⡜⡱⣌⢇⡛⡟⣿⣿⣿⣿⣿⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣯⣷⢿⣿⣿⣿⣿⡇⠀⠀⠀⣤⣤⣤⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⢯⣿⢯⣿⣿⣿⡿⣙⠞⣦⢣⠏⡴⣋⢜⢣⡱⢩⠜⣌⠣⣍⠲⣡⠳⣌⠲⣍⡜⢦⡙⢿⣿⣿⣿⣿⣿⣿⣟⡿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣷⠀⠀⢸⡇⠄⠀⠀⠁⡀⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣿⣿⣿⣿⡱⡭⢞⢦⣋⢞⡱⢜⡊⢦⡑⢣⢚⠤⣋⡔⡣⣅⠳⣌⢓⠦⣙⢦⡙⣦⢍⠿⣿⣿⣿⣿⣿⣽⢻⣿⣿⣿⣿⣿⣷⡿⣿⣿⣿⣾⠇⠀⣾⠁⡁⠀⠂⠀⡅⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⢧⣳⡙⡞⢦⡙⢦⡙⢦⡙⢦⡉⢧⠪⡕⢲⠬⡱⣌⠳⡜⣪⠵⣩⢖⡹⢆⡯⣝⢮⢿⣿⣿⣿⢯⣟⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠐⣿⢀⣤⣐⣠⢁⡗⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣳⠲⣝⣹⢲⡙⢦⡙⢦⡙⢦⡙⢦⣙⣬⢣⣞⡱⣌⡳⡹⣔⢫⠖⣭⡚⣵⢺⡜⣯⢞⡽⣿⣯⣟⡾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠙⠳⠾⠿⠭⠭⠬⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢟⡼⣒⢧⡹⢲⣙⣦⣽⣶⢿⡻⢯⠟⡿⢞⡿⣟⣿⣷⣾⣧⣛⢶⡹⣎⢷⣹⢮⣻⡽⣯⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢯⢶⡹⢆⢿⡷⣟⢫⠧⣍⠶⣙⠮⣙⢎⠷⢮⢵⡺⣜⢧⡳⣝⢮⡳⡽⢮⣳⢯⣷⣻⡷⣿⣿⢿⣿⣻⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡮⣇⣛⠮⣖⡱⢎⡵⢚⡤⣋⢖⡹⢜⡪⡝⣎⢧⡝⣮⢳⡽⣹⡞⣽⣹⢯⣽⣻⣞⣷⡿⣟⣾⢯⡷⣿⣻⢿⣿⣿⠘⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⡷⣏⢾⡱⣝⠺⡴⣙⠶⣨⠓⡴⢃⡞⣌⠧⢳⡹⡜⣮⡝⣮⢷⡹⢧⣛⣮⢳⢯⣞⣷⣻⣯⣿⣻⡽⣯⣟⣷⣻⡿⣿⣻⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣮⠷⣝⣮⢳⡭⣳⠱⣍⠶⣡⠛⡴⢋⡴⢪⡝⣣⢳⡝⣶⣹⢞⣧⡟⣯⢳⣭⣛⢮⡽⣞⣿⡷⣯⢷⣻⢷⣻⣞⡷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣼⢻⡵⣎⢷⢣⡇⡟⣬⢳⣡⢛⡬⢳⡘⢧⣚⡵⣣⢟⡶⢯⣻⢮⣽⢣⡟⡴⢫⡞⣽⢯⣿⡿⣽⢯⣟⣾⣳⢯⡿⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣟⣧⣳⢲⣌⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢷⡭⣷⢻⡜⡯⢶⡹⣜⢣⠷⣬⢳⣜⣧⣛⣧⣿⣼⣳⣯⣟⣿⣽⣻⣎⠷⡹⣜⢣⡝⣾⣻⣿⣟⣯⡿⣞⣷⣯⣿⣿⣟⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡽⣾⣿⣿⣾⣧⢩⣿⣿⣿⣿⣿⣿⣿⣟⡾⣫⢷⣭⢳⣝⣣⢗⡳⡌⢧⢛⡛⢏⠭⡹⢍⢯⡹⣹⢛⡿⣻⣿⣿⡷⢎⡽⠱⡌⢶⡙⣶⣻⣿⣿⣿⡿⢿⣛⢿⡻⣟⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⡹⢣⢯⡽⣻⣿⣷⢾⣿⣿⣿⣿⣿⣟⡾⣝⣳⢏⣞⣳⣚⡜⢮⡱⣙⢎⡱⢚⡌⡣⢝⡸⢆⡳⣍⢏⡾⣱⢏⠿⣱⢋⡔⢫⠜⣡⠝⡶⢯⣿⣯⢖⡜⢦⣛⢮⡽⣝⣻⣽⡿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣹⠣⣇⡻⣵⢻⣯⢿⣿⣿⣿⣿⣟⡾⣽⣹⢎⡿⣜⡲⣕⠺⣥⢓⣍⢲⡙⢦⣘⠱⣊⠖⣩⠖⡭⢎⡵⣋⢎⡳⣡⠎⡜⣡⠞⣤⣛⡼⣛⣾⣽⢮⡝⣧⢛⣎⢷⣫⢷⣻⣷⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⡙⢦⡝⣮⣛⣾⣻⣿⣿⣿⣟⡾⣽⡞⣵⡻⣜⢧⣓⢎⡳⢆⢏⡴⢃⠞⡰⢌⠳⡌⢎⡱⢎⡵⣋⠶⣍⢮⡱⢦⡙⠴⣡⠞⣴⢣⡻⢵⣫⢿⣟⡾⣱⠯⣜⠶⣹⢞⣳⢿⣏⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣎⡱⠜⣥⣛⠶⣯⣟⣿⣾⣽⣻⢷⣛⣧⢟⣮⢳⢎⢮⡱⣋⠮⣔⢫⡜⢥⢋⡖⡍⡎⢵⣊⠶⣩⠗⡮⢖⡹⢆⡭⢓⠴⣻⡜⣧⡙⢦⠣⢏⡿⣿⣱⠻⡜⣏⢷⣫⢯⣟⣾⣞⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣲⣶⣤⣤⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣎⠽⡰⣩⢛⡼⣯⣿⣾⣷⣟⣯⣟⡾⣝⡮⣏⢾⣡⠳⣍⠞⡴⢣⡜⣊⠶⣘⣌⡓⣣⢜⡣⢇⣏⢳⣫⢵⣋⠶⣉⠶⣹⣿⣶⣍⠶⣹⣎⣷⣿⡧⢏⡽⣘⢮⢳⣏⢾⣳⢿⣽⡆⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣯⣷⣄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣣⡕⣫⡜⣿⣽⣿⣾⣿⣽⡾⣽⣻⡼⣝⠾⣌⡗⢮⡙⢦⠓⡼⣐⠣⡕⢢⢱⢊⠖⣩⠞⣬⡓⣮⢳⣎⠷⣩⠒⡭⢿⣿⣿⣿⣷⣿⣿⣿⡝⣎⠶⣩⢎⡳⣎⣟⢾⣯⣷⣿⡀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⣻⣍⢷⡀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠷⠿⣿⣿⣿⣿⣿⣿⣿⢷⣯⣟⡾⣹⢞⣜⡣⡝⣎⠽⣰⢡⢋⡜⠥⢎⡜⢪⡑⡞⡴⣹⢎⡷⣎⢿⡡⢏⠴⣋⢜⡻⢻⡟⣿⢻⡿⣼⡘⢮⡱⢎⡵⣹⢎⡿⣞⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣫⣽⣿⣿⣿⣷⡽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣷⣯⢿⣝⡾⣼⡱⡝⡜⢮⡱⢎⡱⣊⡝⣢⢚⢥⡓⡽⣸⢧⣻⢞⡽⣎⡷⣩⢒⢥⢪⡵⣫⣞⣳⣯⣿⣷⡹⢧⣛⢮⣳⢽⣺⡽⣿⣿⣿⠄⠀⠀⠀⠀⠀⠹⣿⣿⣿⣾⣟⣧⣾⣿⣿⣿⣿⣿⣿⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣿⣿⣿⣿⣿⣿⢟⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣻⣞⡷⣧⣻⢭⡻⣼⢱⣋⢶⡱⢎⡵⣊⢶⡹⣞⡵⣯⢷⣯⢿⣽⣻⣵⣿⣾⣿⣿⣿⣿⣿⣿⣿⣳⣽⣳⣽⣺⣵⣯⣷⣿⣿⣟⣏⣀⣀⣀⣀⣀⣀⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢿⡿⢿⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⣿⣿⣿⣿⣿⣽⡷⣯⢷⣻⣼⢣⡟⡶⣭⢳⣞⡹⣎⡷⣽⣻⣽⣻⣞⡿⣞⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣟⣯⣷⢯⡿⣽⣳⢯⡷⡾⣝⣯⣟⣷⣿⣳⣿⣽⣻⣽⢳⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⢿⣯⣿⣽⣿⣳⣿⣿⣟⣿⣽⡾⣷⣏⡷⣹⢿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠛⠛⠛⠻⠻⠛⠛⠛⠛⠛⠛⠛⠛⠟⡏⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣯⣟⡷⣾⣝⣷⣻⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⠟⠉⠁⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣿⡽⣷⣻⣾⣽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣯⠟⠋⠁⠀⠀⠀⠀⠀⠀⢀⣄⣀⣴⡴⠶⠶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣳⣿⣟⣷⣿⣾⣿⣿⣿⣿⣿⣿⢿⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣦⡍⢧⡓⡦⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠞⣜⡣⣝⣹⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣞⣿⣿⣷⣝⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠓⢛⣿⣟⣻⣝⣗⣒⣲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣞⣛⣻⠿⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣻⣽⣿⣿⣿⣯⣿⣷⣍⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣝⢿⣯⣿⣿⣿⣻⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⠁⠘⠂⠝⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢺⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢿⣟⡷⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢋⡀⠐⠀⡀⠉⢓⡞⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣟⣛⣻⣛⣿⣻⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣝⡳⣄⢠⣸⢟⡽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢮⣋⣱⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠄⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
🤱╰⋃╯ (◕ε◕*)😖👩🏼🦲╰⋃╯ (◕ε◕*)👩🏼🦲👩🏼🦲
ᴼˡⁱᶠ ᶜʳᵒⁿᑫᵘⁱˢᵗ ᵐᵃʳʳⁱᵉᵈ ʰⁱˢ ʷⁱᶠᵉ ᴶᵘˡⁱᵃ ᶜʳᵒⁿᑫᵘⁱˢᵗ⸴ ʷʰᵒ ᵈⁱᵉᵈ ᵒⁿ
ᴶᵃⁿᵘᵃʳʸ ⁸ᵗʰ⸴ ¹⁹¹⁴ ᶠʳᵒᵐ ᵛᵃˡᵛᵘˡᵃʳ ʰᵉᵃʳᵗ ᵈⁱˢᵉᵃˢᵉ⸴ ᵐᵒˢᵗ ˡⁱᵏᵉˡʸ
ᶜᵃᵘˢᵉᵈ ᵇʸ ˢᶜᵃʳˡᵉᵗ ᶠᵉᵛᵉʳ‧ ᴼˡⁱᶠ ʷᵃˢ ᵒⁿᵉ ᵒᶠ ᵗʰᵉ ᶠⁱʳˢᵗ ᶜᵒᵘⁿᵗʸ
ᶜᵒᵐᵐⁱˢˢⁱᵒⁿᵉʳˢ ⁱⁿ ᶜᵃᶜʰᵉ ᶜᵒᵘⁿᵗʸ ᵃⁿᵈ ʷᵃˢ ᵃˡˢᵒ ᵃ ʷᵉˡˡ⁻ᵏⁿᵒʷⁿ ᵈᵃⁱʳʸ ᶠᵃʳᵐᵉʳ‧
ᵀʰᵉⁱʳ ᶠⁱʳˢᵗ ᶜʰⁱˡᵈ⸴ ᴹᵃʳᵍᵃʳᵉᵗ ʷᵃˢ ᵇᵒʳⁿ ⁱⁿ ¹⁸⁸⁰⸴ ᑫᵘⁱᶜᵏˡʸ ᶠᵒˡˡᵒʷᵉᵈ ᵇʸ ᵗʷⁱⁿˢ
ᴼˡⁱᶠ ᵃⁿᵈ ᴼˡⁱᵛᵉʳ ⁱⁿ ¹⁸⁸³‧ ᴼʳˢᵒⁿ ʷᵃˢ ᵇᵒʳⁿ ⁱⁿ ¹⁸⁸⁸ ᵃⁿᵈ ᵉᵛᵉʳʸᵗʰⁱⁿᵍ
ˢᵉᵉᵐᵉᵈ ᶠⁱⁿᵉ ᵘⁿᵗⁱˡ ᵗʰᵉ ᶠⁱʳˢᵗ ᵇᵒᵘᵗ ᵒᶠ ˢᶜᵃʳˡᵉᵗ ᶠᵉᵛᵉʳ ʰⁱᵗ ᵗʰᵉ ᶠᵃᵐⁱˡʸ
ⁱⁿ ᴹᵃʳᶜʰ ¹⁸⁸⁹‧ ᴮʸ ᴹᵃʳᶜʰ ²²⸴ ¹⁸⁸⁹⸴ ᵗʰᵉ ᵗʷⁱⁿˢ ᴼˡⁱᶠ ᵃⁿᵈ ᴼˡⁱᵛᵉʳ ʷᵉʳᵉ
ᵇᵒᵗʰ ᵈᵉᵃᵈ⸴ ˢᵘᶜᶜᵘᵐᵇⁱⁿᵍ ᵗᵒ ᵗʰᵉ ᵉᶠᶠᵉᶜᵗˢ ᵒᶠ ˢᶜᵃʳˡᵉᵗ ᶠᵉᵛᵉʳ‧
ᵀʰᵉʸ ʷᵉʳᵉ ⁵ ʸᵉᵃʳˢ ᵒˡᵈ‧ ᵀʰⁱˢ ʷᵃˢ ᵃˡˢᵒ ʷʰᵉⁿ ᴶᵘˡⁱᵃ ᶜᵒⁿᵗʳᵃᶜᵗᵉᵈ
ˢᶜᵃʳˡᵉᵗ ᶠᵉᵛᵉʳ ʷʰⁱᶜʰ ʷᵒᵘˡᵈ ᶜᵃᵘˢᵉ ʰᵉʳ ᵖʳᵒᵇˡᵉᵐˢ ᶠᵒʳ ᵗʰᵉ ʳᵉˢᵗ ᵒᶠ
ʰᵉʳ ˡⁱᶠᵉ⸴ ᵃⁿᵈ ʷᵒᵘˡᵈ ᵘˡᵗⁱᵐᵃᵗᵉˡʸ ˡᵉᵃᵈ ᵗᵒ ʰᵉʳ ᵈᵉᵃᵗʰ‧
ᴬⁿᵒᵗʰᵉʳ ᶜʰⁱˡᵈ⸴ ᴱˡᵃᵐ⸴ ʷᵃˢ ᵇᵒʳⁿ ⁱⁿ ¹⁸⁹¹ ᵃⁿᵈ ᵗʰⁱⁿᵍˢ
ʷᵉʳᵉ ˢᵗᵃʳᵗⁱⁿᵍ ᵗᵒ ˡᵒᵒᵏ ᵘᵖ ᶠᵒʳ ᵗʰᵉ ᶜʳᵒⁿᑫᵘⁱˢᵗ ᶠᵃᵐⁱˡʸ‧ ᴵⁿ ¹⁸⁹⁴⸴
ᴸⁱˡᵉᵃⁿ ʷᵃˢ ᵇᵒʳⁿ ᵃⁿᵈ ⁱᵗ'ˢ ᵘⁿᶜˡᵉᵃʳ ʷʰᵉᵗʰᵉʳ ˢʰᵉ ʷᵃˢ ˢᵗⁱˡˡᵇᵒʳⁿ ᵒʳ
ᵒⁿˡʸ ˡⁱᵛᵉᵈ ᶠᵒʳ ᵃ ˢʰᵒʳᵗ ᵖᵉʳⁱᵒᵈ ᵒᶠ ᵗⁱᵐᵉ‧ ᴵⁿ ᵃ ᵐᵃᵗᵗᵉʳ ᵒᶠ ⁵ ʸᵉᵃʳˢ⸴ ᵗʰᵉ
ᶜʳᵒⁿᑫᵘⁱˢᵗ ᶠᵃᵐⁱˡʸ ʰᵃˢ ˡᵒˢᵗ ³ ᵒᶠ ᵗʰᵉⁱʳ ⁶ ᶜʰⁱˡᵈʳᵉⁿ‧
ᴶᵘˡⁱᵃ ᵃⁿᵈ ᴼˡⁱᶠ ʰᵃᵈ ᵃⁿᵒᵗʰᵉʳ ᵈᵃᵘᵍʰᵗᵉʳ ⁱⁿ ¹⁸⁹⁶ ⁿᵃᵐᵉᵈ ᴱᵐᵉˡⁱᵃ⸴ ᵃⁿᵈ
ⁱⁿ ¹⁸⁹⁹ ᴵⁿᵉᶻ ʷᵃˢ ᵇᵒʳⁿ‧ ᴴᵃᵖᵖⁱⁿᵉˢˢ ʷᵃˢ ᵃᵍᵃⁱⁿ ˢʰᵒʳᵗ ˡⁱᵛᵉᵈ ᵃⁿᵈ
ˢᶜᵃʳˡᵉᵗ ᶠᵉᵛᵉʳ ˢᵗʳᵘᶜᵏ ᵗʰᵉⁱʳ ᶠᵃᵐⁱˡʸ ᶠᵒʳ ᵗʰᵉ ˢᵉᶜᵒⁿᵈ ᵗⁱᵐᵉ ⁱⁿ ˡᵃᵗᵉ
ᶠᵉᵇʳᵘᵃʳʸ ¹⁹⁰¹‧ ᴼⁿ ᴹᵃʳᶜʰ ¹ˢᵗ⸴ ¹⁹⁰¹ ᵗʰᵉⁱʳ ᵗʷᵒ ᵈᵃᵘᵍʰᵗᵉʳˢ ᵈⁱᵉᵈ
ᶠʳᵒᵐ ˢᶜᵃʳˡᵉᵗ ᶠᵉᵛᵉʳ; ᴱᵐᵉˡⁱᵃ ʷᵃˢ ⁴ ᵃⁿᵈ ᴵⁿᵉᶻ ʷᵃˢ ²‧ ᵀʰᵉʸ ʷᵉʳᵉ
ᵇᵘʳⁱᵉᵈ ᵗᵒᵍᵉᵗʰᵉʳ ⁱⁿ ᵃ ˢᵖᵉᶜⁱᵃˡˡʸ ᵇᵘⁱˡᵗ ᶜᵃˢᵏᵉᵗ‧
ᴵⁿ ᵃ ᵐᵃᵗᵗᵉʳ ᵒᶠ ¹² ʸᵉᵃʳˢ⸴ ᶠⁱᵛᵉ ᵒᶠ ᵗʰᵉⁱʳ ⁸ ᶜʰⁱˡᵈʳᵉⁿ ʰᵃᵈ ᵈⁱᵉᵈ‧
ᴬᶜᶜᵒʳᵈⁱⁿᵍ ᵗᵒ ᶠᵃᵐⁱˡʸ ʰⁱˢᵗᵒʳʸ⸴ ᴶᵘˡⁱᵃ ʷᵃˢ ⁱⁿᶜᵒⁿˢᵒˡᵃᵇˡᵉ ᵃⁿᵈ ʷᵒᵘˡᵈ
ᵒᶠᵗᵉⁿ ᵛⁱˢⁱᵗ ᵗʰᵉ ᵍʳᵃᵛᵉˢ ᵒᶠ ʰᵉʳ ᶜʰⁱˡᵈʳᵉⁿ‧ ᴾᵃˢˢᵉʳˢᵇʸ ʷᵒᵘˡᵈ ʳᵉᵐᵃʳᵏ
ᵗʰᵃᵗ ᵗʰᵉʸ ᵒᶠᵗᵉⁿ ˢᵃʷ ᴹʳˢ‧ ᶜʳᵒⁿᑫᵘⁱˢᵗ ʷᵉᵉᵖⁱⁿᵍ ᵃᵗ ᵗʰᵉ ᵍʳᵃᵛᵉˢ‧ ᔆʰᵉ
ᵖʳᵒᵍʳᵉˢˢⁱᵛᵉˡʸ ᵍᵒᵗ ʷᵉᵃᵏᵉʳ ᶠʳᵒᵐ ᵗʰᵉ ᵈᵃᵐᵃᵍᵉ ᵈᵒⁿᵉ ᵇʸ ˢᶜᵃʳˡᵉᵗ
ᶠᵉᵛᵉʳ ᵃⁿᵈ ᵖᵃˢˢᵉᵈ ᵃʷᵃʸ ᵃᵗ ³ᵃᵐ ᵒⁿ ᴶᵃⁿᵘᵃʳʸ ¹⁴ᵗʰ⸴ ¹⁹¹⁴‧
https://usustatesman.com/tag/olif-cronquist/
⢣⠚⠄⡓⠌⠒⡅⠢⠀⠄⡠⢀⠄⡄⢐⠀⠄⣘⣾⣷⣦⣤⣀⠄⡐⠀⠄⠠⠀⠄⠠⠀⠄⠠⠀⠄⢠⠀⠄⢠⠀⠄⢠⠀⠄⠠⠀⠄⡠⠀⠄⢠⠀⡄⢠⠀⡄⠠⢀⠄⡠⢀⠄⡠⠀⢄⠠⠀⢄⠠⡀⢄⠠⡀⠄
⡂⠅⠒⡈⠄⠃⡄⠡⢉⠐⠄⠢⠐⡀⠆⡈⠄⣿⣻⣿⣿⣿⣿⣷⣶⣥⣈⣤⣅⡈⠄⠡⠈⠄⠡⠈⠄⡘⠠⢁⠌⠠⠁⠌⠠⠁⡌⠐⠠⢁⠘⡀⢂⠰⠀⠂⠤⠑⡀⠂⠔⡀⠂⠄⠡⠂⠄⡉⠄⢂⠰⠀⠂⠍⡀
⠌⠌⡐⠠⢈⠐⠠⢁⠂⠌⣀⠃⠤⢁⠒⢠⠐⡈⠙⠿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣷⣿⠿⣿⢿⣶⣆⡀⡁⠢⠘⠠⢁⡘⠠⠡⢐⠈⠂⠔⡀⠂⠄⢂⠘⡀⢂⠐⠠⢁⠂⠄⠡⢈⠐⡈⠔⠠⠈⠄⠂⠌⡐⠂⠄
⠎⡒⢁⠃⠎⡘⢑⠊⠰⠀⡄⢈⠐⠠⠈⠄⢂⣤⣵⡶⠾⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣷⡎⣶⡜⣬⠛⢿⣶⡁⡈⢁⠂⠄⡁⠂⢄⡈⢁⠂⠄⡉⠄⡁⢂⠐⡈⠄⡁⠂⢌⠠⢁⢂⠐⡠⠈⠄⠡⠈⠌⡐⠠⡉⠀
⠐⠐⠂⠌⡐⢀⠊⠄⡁⠒⡐⠂⠌⢠⣵⡾⠟⠋⢠⠐⠤⡑⢨⠐⡠⠠⣹⣿⣿⣿⣿⡿⢐⣾⠏⣸⣇⢺⡿⣷⣔⠂⡉⠐⠠⠑⠠⠐⠂⠡⠂⠔⡐⠈⠄⢂⢁⠢⠐⡁⢂⠢⠐⠠⢂⠐⠡⠊⠄⡑⠠⢂⠡⠄⠁
⠀⣉⠰⢀⡁⠢⢈⡐⢈⠐⢠⣡⣾⣿⣽⣦⣬⣀⠡⢈⠐⡠⢁⠂⢄⠡⢘⣿⣿⣷⣽⣿⣿⣇⣦⣿⢡⣾⠇⣿⣿⣤⣠⣷⠶⣿⣶⣧⣬⣀⢁⠂⡌⠰⠁⡌⢀⠂⢡⠐⢄⡈⢄⢡⣀⡌⠠⢁⠂⠌⡐⣀⠂⢌⠀
⠀⠄⠂⠤⢀⢁⠂⡐⣢⣾⡿⣟⢯⣝⣾⡿⢿⡿⡛⣿⣷⣴⣶⢿⡾⢿⠿⣿⢻⢿⣻⢿⣷⣯⣻⣾⡛⣷⣾⣿⣿⣿⣿⣷⡎⢄⠰⢈⢋⠻⣷⣔⠠⠑⢂⠐⠠⠌⠄⠨⠄⠔⣼⣿⣿⣿⣿⣷⣮⣔⣠⠀⠌⡀⠂
⠀⡘⢈⠐⠠⢈⡐⣴⣿⣯⢳⡝⣾⣾⢏⡰⣡⣶⣿⣛⢯⡳⣝⢮⡳⣏⡟⣶⢫⢾⣱⢏⡾⣭⣛⡽⢿⣿⣿⣿⠿⣿⣿⣿⠐⡬⢂⠇⡌⢂⠍⣻⣧⠐⡁⠌⡐⣀⠊⢄⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠁
⠀⠰⠈⠄⡁⢂⣼⣿⠷⣭⢧⣻⣟⢢⣶⡿⢟⡽⣲⡝⣮⡳⣝⢮⡳⣝⢾⡱⣏⢷⡹⣎⢷⣣⢟⣼⢳⢮⣝⢻⢿⣯⣝⣿⡔⢠⠃⡌⠰⢡⢈⠣⣿⣦⣔⠠⠁⠄⡈⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡑⢈⠐⠠⢸⣿⢯⣛⢶⡹⢾⣿⣿⡗⣻⣽⣾⣷⡹⣎⢷⡹⣎⢷⡹⣎⢷⡹⣎⢷⡹⣎⣧⢻⡜⢯⡞⣼⢫⢞⡭⣟⣿⣿⣿⣿⣿⣿⣶⣆⣽⣿⣿⣿⣿⣷⣦⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢌⠠⠈⠄⣻⣿⢧⣻⣖⢯⣿⣿⣟⣾⡿⣿⢫⣟⣷⡝⣾⡱⣏⢾⡱⣏⡾⣱⣛⢮⣳⣽⣿⣿⣞⣣⢟⣼⣏⢾⡱⣿⣿⡿⠿⠟⠿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠢⢀⠁⢂⢹⣿⢿⡿⣭⣿⢿⣿⢋⠡⡘⣿⣿⠞⢻⣿⡖⡽⣎⢷⡹⣎⣷⣧⡿⠻⣿⣏⢿⣿⣿⣷⣋⢾⣟⢮⣽⣿⡉⠄⢂⡰⠀⠆⠰⢀⠡⠙⣿⣿⡟⢿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⡑⠠⠈⠤⢺⣿⠾⠛⣿⣟⣿⡇⢌⣶⣵⣿⣿⣯⣤⣌⠻⢷⣏⣾⣽⠟⣛⠡⠌⢡⢸⣿⣿⡇⣈⠻⢿⣞⣿⣞⡲⡽⣷⣎⠠⢀⠥⠘⢠⠁⠲⣿⣿⠻⡗⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠠
⠀⠤⠁⠌⡐⢹⣿⠠⢱⡿⣭⣿⠐⣹⣿⣿⠟⢉⠙⠻⢿⣿⡲⠉⣍⠰⣈⡤⢷⣾⣾⣿⣿⣿⣶⣔⡰⢈⠩⣿⣧⢏⡷⣹⣿⡄⠨⠠⠑⠂⡌⠠⢹⣿⠗⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠄⡁
⠀⢂⠁⠂⠄⢹⣿⠠⣸⡿⢶⡟⡰⣼⣿⣥⡆⠠⢈⠡⡉⣿⣧⠑⢌⠓⠤⠄⣿⠿⢃⠀⡀⠌⢿⣿⣖⠨⠡⢼⣿⢎⡷⡭⣿⣇⠂⠅⢊⠐⡌⡐⢈⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀⠂⠄
⠀⢌⠠⠁⠌⢘⣿⡄⣿⡟⣿⡇⢼⣻⣿⣿⣀⠂⠄⢂⣿⣞⣿⠈⠦⡙⠰⣸⣿⣷⠀⡂⠐⠠⣦⡹⣿⢂⡑⢺⣿⣝⡺⡵⣿⡧⠈⠌⠢⢈⠄⡁⢂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠐⡄⠈⠄
⠀⠢⢀⠡⢈⠠⣿⣷⣿⣝⣿⠐⣸⣿⣿⣿⣿⣿⣶⣿⣿⣿⡦⢉⡒⠡⢣⣷⣿⣿⣶⣤⣁⣦⣿⣿⣔⠢⡑⢸⣿⢎⡷⣹⣯⡷⠁⠌⡑⠠⢂⡁⠂⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀⠡⠠⢁⠂
⠀⣁⠂⡐⢀⠂⠼⣿⣿⣾⣟⠰⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠠⣉⠒⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⡝⠠⣿⣫⢼⣣⣿⡗⡈⢄⠡⡘⠠⠄⡁⢺⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠐⠊⠄⡁⠂⠄
⠀⠄⢂⠐⠄⠨⢀⣿⣿⣏⢡⠂⡅⢻⣇⡜⡻⣿⡿⢟⣻⣿⠅⡱⢀⠣⢐⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠐⠭⡐⣿⢧⡻⣼⢿⡇⠐⡂⠡⢐⠁⠆⠰⣿⡇⢀⠩⠛⠿⣿⣿⣿⣿⣿⣿⣿⠟⠡⢀⢉⠐⠂⠤⠁⠂
⠀⡘⠠⢈⠤⠑⠠⠹⣿⣯⣇⠰⡈⠔⡙⠛⠷⠾⠿⠾⡛⡁⢆⠱⡎⠰⡁⠌⠿⣦⣍⡛⣭⣹⣴⡿⢣⠘⡴⠠⣿⢧⣻⣼⣿⠀⠱⢈⡁⠎⡐⣈⠰⣿⠃⠄⠒⠌⠄⡐⠈⢉⠛⠛⠛⠉⠄⡁⠂⠄⢊⠐⢂⠁⠂
⠀⡐⢁⠂⡐⢈⠂⡁⠼⣿⣷⣇⠰⡉⠖⣩⠂⡅⢊⠔⢡⢸⣦⡑⣸⣧⠘⣌⣷⡭⠙⠛⣉⠋⡍⡰⢁⠎⠰⣑⣿⢧⣳⣿⡇⢈⠅⠢⠐⡈⠔⡀⣾⡟⠠⢈⠰⢈⠐⠠⢁⠂⡐⢈⠄⢃⠐⡠⢉⠐⡠⠡⠈⠄⡁
⠀⡐⠂⠄⣁⠂⡐⠠⢈⠻⣿⣿⣷⣄⡃⠔⡉⠜⡡⢊⡔⢂⡙⠻⠞⡛⠟⠞⡋⠔⣉⠒⠤⢃⡔⡉⢆⠊⡅⣼⣿⢎⣷⡟⠀⡌⢂⢁⡃⠰⠐⣲⣿⠁⠄⢃⠐⠠⢈⠂⡁⢂⠌⡀⠢⠀⠆⡐⠀⠆⠠⢁⠌⠠⠀
⠀⡐⡉⠄⠄⠒⠠⢁⠂⡐⢻⣿⣿⠉⢻⢷⣬⣆⡱⢀⠒⢄⠢⠑⢢⠑⠌⢢⠑⡊⢄⠋⡔⠡⢂⠜⣠⣃⣴⣿⣿⢾⠟⢀⠩⢄⠡⠂⠄⢃⣷⡿⠁⢌⠐⠠⢊⠁⡂⠌⡐⡀⢂⠌⡐⡁⠒⡀⠉⠄⠃⢄⡈⠄⡁
⠠⠐⡐⢈⢂⢁⠂⡔⠠⠐⡀⠉⢿⣷⡟⠱⣿⣿⣿⣿⣷⣾⣤⣭⣦⣬⣜⣤⣊⣴⣌⣶⣬⣷⣾⣾⣿⣿⡟⣻⣿⠋⡐⠢⠡⠂⠌⣰⣼⡿⢋⠠⠉⡄⡈⢁⠢⠐⡀⠆⡐⢀⠂⡐⠠⠀⠅⠠⠉⠄⡁⠂⠄⠂⠄
⢂⠡⢈⠄⠂⠌⠠⠄⠡⠑⡀⢁⢲⡿⢀⢁⢻⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⠒⢛⠁⠒⠠⣁⣢⣵⡾⠟⡉⢄⠂⠄⠡⠐⠠⢁⠂⢡⠐⠠⠐⣀⠂⠄⠡⢁⠊⠄⡑⢀⢂⠡⢈⠂⠄
⢂⠐⠂⠌⢌⠠⠁⠌⠤⢁⡐⣰⣿⠑⠄⠂⠄⢿⣿⡿⣿⣿⣿⣿⣦⣁⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢢⠘⢠⠸⡾⣿⡟⠋⠡⡐⡈⠰⠀⠌⢂⠡⢈⢁⠂⠌⢠⠈⠄⠡⢀⠌⠠⢁⠂⠌⡐⠀⠆⡀⠢⠀⡅⠂
⠠⠘⣈⠐⠂⠤⠁⡌⠐⡂⢀⣿⠏⢠⠉⡜⢀⠂⡙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡿⠟⠋⣀⢊⠰⢈⠄⢂⠐⢸⣧⠈⡐⠠⡀⠡⠌⡐⢂⠐⠂⠤⢈⠂⠄⡈⠄⡁⠂⠌⡐⠠⢈⠐⠠⢁⠂⡐⢁⠂⠔⠀
⠀⢌⢀⠂⣉⠐⡀⢂⠡⠀⣽⡿⢀⠂⡌⢠⠁⠎⢄⡁⢂⠀⣀⣾⣿⣿⣿⣷⡀⠄⡠⢀⡐⠄⣃⠠⢂⢁⠢⠘⠠⢈⢸⣿⠐⡀⠡⢀⠁⡂⢐⠠⢈⠂⠰⠀⠌⡐⢀⠂⢡⠈⡐⠠⢁⠂⠌⡐⠠⢁⠰⠀⠌⢂⠁
⠀⢂⠂⡐⢀⠂⠄⢃⠠⢱⣿⢁⠂⠌⡐⠄⢊⡐⠠⠌⢂⠐⣾⣿⣿⣿⡷⣿⣧⠈⠤⣁⠰⠈⠄⢂⠂⠰⡀⣉⠂⠄⠨⣿⡄⠠⢁⠂⠌⡐⢀⠂⠂⠌⢠⠁⢂⠰⢀⠊⠄⠂⠄⡁⠂⠌⡐⠠⢁⠂⠄⡁⠊⠄⠠
⠀⠌⡐⡀⢂⠌⡐⢀⢂⣼⣿⣿⣶⣥⣐⡈⠄⠠⠑⡈⠄⠾⢿⣿⣿⣿⣟⣿⣿⡌⡐⢄⠂⡅⢊⠄⡡⠡⡐⠠⠈⡄⠡⣿⡃⡐⠠⠌⡐⢀⠂⠌⣈⠐⠂⠌⡀⠂⠄⡈⠄⡉⠐⠠⢁⠂⠄⡁⠂⠌⡐⠠⢁⠊⡀
⠀⡘⠠⢀⢉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣦⣔⣈⡔⠠⢀⡘⢛⠛⡛⢛⠃⡐⠠⠈⠄⢂⠐⢠⢡⣤⣱⣶⣾⣿⣿⣷⣄⠁⠒⡀⠆⡈⠐⠠⢈⠐⡈⠄⡁⢂⠁⠂⢌⠠⢁⠂⠌⡐⠠⢁⠂⠤⢁⠂⠔⠀
⠀⡐⢁⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⣐⡀⠂⠌⡁⢂⠂⡐⠐⡈⠐⠠⢈⠒⡀⢂⠂⠌⡐⠠⢁⠂⠌⡐⠠⢈⠂⡐
⠀⡐⠂⠌⡐⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠐⣀⠂⠄⡑⠠⢉⠐⡀⢂⠰⠀⠌⡐⠠⢁⠂⠌⡐⠠⢁⠂⡁⠄
⢀⠐⠡⡈⠔⣀⣿⠟⠻⠿⣿⣿⣿⡿⣿⣿⣷⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣻⣿⣿⢿⣯⣿⣿⣿⣿⣿⠇⠐⠠⢈⠐⠠⢁⠂⡐⢀⠂⠄⢃⠐⠠⢁⠂⠌⡐⠠⢁⠂⡐⠄⠂
⠀⢌⡐⢀⠂⣾⡟⢈⠅⡒⢠⠙⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⢿⣻⣿⣿⣷⣿⣿⣿⣽⣿⣿⣿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⠛⡉⠰⢈⠐⠠⢈⡁⢂⠐⡀⠂⠌⡐⡀⢊⠐⠠⡈⢐⠠⢁⠂⡐⢀⠊⡀
⠀⢢⠐⠠⣸⡿⠛⠷⣮⣴⣁⣮⣾⠛⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣟⣿⣿⡿⣿⣿⣿⣻⣯⣿⣿⣿⣿⣿⣿⣽⡿⠟⠋⡄⢃⠆⣻⣇⠠⠁⠆⡈⠔⠠⢐⠀⠢⠀⠅⢂⠐⠄⠂⠌⡐⢀⠢⠐⡀⠆⠐⠂⠡⠀
⠀⡂⠄⣡⣿⠇⡈⡔⠠⠂⣵⣿⠃⠌⡀⠄⡈⢉⠉⠉⢉⠠⢈⠙⠻⠿⢿⣿⣿⣿⣿⣿⠿⠛⠉⡉⠉⡉⠍⡉⢿⣧⣑⡌⣐⣁⣎⣼⡧⢀⠁⠆⡐⢈⠐⢂⠁⢂⠡⠈⢄⠨⢀⠃⡐⢀⠂⠄⠡⠐⡈⠐⠡⢁⠂
⠐⢠⣦⣿⣯⣐⠠⠐⠡⣼⡟⠁⠰⡈⠄⠡⢀⠃⠌⡈⠤⠈⠄⠢⠐⣀⠂⡠⠈⢄⠀⡂⢄⠡⠒⡈⡐⡐⠂⢄⣿⠋⠙⠛⠛⡉⢩⣿⠃⠄⡨⠐⡀⢂⡁⠂⠌⡀⢂⠁⢂⠰⠀⠂⠌⠠⠌⡈⠄⠡⠠⢉⠐⠄⠂
⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡁⠂⡔⠈⠄⡡⢈⠐⠄⢂⠡⠊⠄⡡⢀⠂⠡⠌⡀⠎⠐⡀⢂⠡⠐⠠⠄⡑⣾⠏⠄⡉⠁⠆⣰⣿⠋⢀⠘⠠⢁⠐⠄⡠⢁⠂⠰⢀⠊⠄⢂⠡⢁⠘⡀⢂⠐⡈⠄⡁⠂⠌⡐⠀
⠀⠙⠛⠿⠻⠟⠛⠛⠉⡀⠂⠤⠁⠄⡡⢈⠐⡠⢈⠌⢠⠁⡘⠠⠐⣀⠊⡐⡐⢠⠈⡡⠈⠄⢂⠉⡐⢰⣿⣷⣶⣧⣤⣥⣾⣿⡀⠐⡈⠄⡁⠂⢌⠐⣀⠂⠌⡐⠠⢈⠐⠠⠂⠌⡐⠠⢁⠂⡐⠠⠁⠌⡐⠠⠁
⣀⢡⣈⣄⣰⣀⣌⡄⠁⠄⠡⢀⠁⢂⠐⡀⢂⠐⡀⠌⢀⠂⠄⡁⠂⠄⡐⠠⠐⢀⠂⠄⠡⢈⠐⠠⢀⠩⣹⣟⠿⣿⣿⣿⣿⣿⠟⠠⠐⠠⢀⠁⢂⠐⡀⠐⠠⢀⠁⢂⠡⠘⢀⠡⢀⠁⢂⠐⡈⠄⠃⡈⠄⡁⠂
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