⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣀⣀⣀⣀⣀⣀⣤⣠⣄⣠⣠⣄⣀⣄⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⢿⡛⢿⣋⠿⣛⢻⡛⣟⢻⡛⢿⡻⣿⢷⣶⣄⡀⠀⠀⠀⢠⣿⣿⡿⢿⢟⡻⢟⡻⡟⢿⠻⣟⠻⣟⠻⢿⠻⢿⢟⡻⣛⠿⢿⣿⣧⠀⠀⠀
⠀⠀⠀⠀⣠⣴⣿⣿⡿⢏⡷⣎⢧⡹⢦⣙⢮⡙⢶⡹⣌⢧⡹⢲⡱⢭⣚⣼⣿⠃⠀⠀⠀⣼⣿⢻⡛⡜⢮⡱⣋⠶⣙⣎⠳⣎⠽⣌⢻⡌⡟⡜⢮⡱⣍⠾⣱⢾⣿⠀⠀⠀
⠀⠀⠀⣰⣿⡿⢏⡳⣜⢣⡝⣚⢦⡛⢦⣙⢦⣋⢧⠳⣜⠲⣍⢧⡹⣒⢧⣿⡏⠀⠀⠀⠀⣿⡧⢧⡹⣙⠶⣱⢋⣞⡱⢎⡳⢬⣓⢎⡳⣜⡱⢻⣌⢳⢬⠳⣭⣿⣿⠀⠀
⠀⠀⣰⣿⠿⣝⣎⢳⢬⠳⣜⢣⡎⡝⢮⡜⣦⣙⣮⣳⣎⣽⣘⣦⢳⣭⣾⡿⠀⠀⠀⠀⠀⣿⡟⢦⠳⣍⠞⣥⣋⠶⣙⢮⡱⢳⡜⢮⡱⢮⡕⡳⢎⡳⢎⡳⢣⣿⡇⠀⠀
⠀⢰⣿⣿⡹⢇⣮⡓⣎⢳⢎⡳⣜⣹⣶⡿⠟⠛⠙⠋⠛⠛⠛⠻⠿⣿⠟⠁⠀⠀⠀⠀⠀⣿⣿⡌⣗⢮⣙⢦⣙⢮⡱⢮⣱⠳⣜⢣⡝⢶⣩⢓⢯⡱⢫⡜⣻⣿⠁⠀⠀
⠁⣿⣿⣧⡝⣎⠶⡹⣌⡳⢎⡵⣊⣿⡟⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠾⠿⠾⠿⠿⠿⠿⣿⣿⡜⣣⢞⡳⣎⣝⡲⢭⠳⡜⣿⡟⠀⠀⠀
⣦⣿⣯⠳⣜⢬⢳⡙⡦⡝⣎⠶⣹⣿⣇⣠⣴⣶⡾⣿⢿⣛⢟⡻⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢣⡓⣎⢷⡩⢖⡽⢣⣛⣼⣿⠃⠀⠀⠀
⢸⣿⣯⢛⣬⢣⢇⡻⢴⡹⣌⡳⡱⣿⣿⣿⡟⢮⡱⢣⠞⡜⣮⢱⢫⡜⣹⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣟⡣⡝⣜⢮⡱⢫⣜⣳⣬⣿⡟⠀⠀⠀⠀⠀
⢸⣿⡿⡸⢭⡚⣜⢣⢎⢧⣋⠧⢧⡹⢽⣿⣷⣎⠳⣎⢖⡳⣍⠞⣬⠳⣍⢞⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢏⢧⢳⡹⢬⡓⣎⠿⡽⣿⣿⠇⠀⠀⠀⠀⠀
⢸⣿⣿⢱⢣⡝⣬⢓⡞⢦⣙⢎⢧⣻⣿⠛⠻⣿⡳⡜⢮⡱⢎⡝⢦⡛⡜⣎⡳⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢓⢮⣙⠦⡝⡶⡹⣌⠷⣽⣿⡿⠀⠀⠀⠀⠀⠀
⢿⣿⡿⣌⡳⣜⢲⡹⣜⢣⠞⣎⠶⣿⡏⠀⠀⢿⣿⡙⡦⡝⣎⠞⣥⢛⣜⠲⣍⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡧⣋⠶⣩⣛⠼⣱⠳⣬⠳⣾⣿⡇⠀⠀⠀⠀⠀⠀
⡜⣿⣿⡲⡱⢎⢧⡳⢬⢣⣛⢬⠳⣿⡇⠀⠀⢸⣿⣽⢲⡹⣌⠻⣔⢫⡜⡹⢆⡳⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢲⣍⠳⣇⢏⡞⣥⡛⡴⣻⣼⣿⠀⠀⠀⠀⠀⠀⠀
⠰⢿⣿⣷⡙⢮⡖⣭⢣⠗⣎⠮⡝⣿⡇⠀⠀⢸⣿⣟⢦⠳⣜⡹⢬⠳⡜⣭⢣⡝⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢏⡳⣌⢻⡬⢳⡞⣥⢛⡴⣭⣿⡏⠀⠀⠀⠀⠀⠀⠀
⠀⠘⣿⣿⣟⠧⣞⠲⣍⠾⣌⡳⢭⣿⣧⠀⠀⣼⣿⢏⣎⠳⣎⠵⣋⠷⣙⢦⣓⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣏⠮⡕⢮⢳⡜⣣⡝⢦⢫⢼⣽⣿⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣿⣿⣳⢬⡛⡼⣓⢮⡱⢣⢞⣿⣦⣼⣿⡝⢮⡜⡳⢬⠳⣍⢞⡱⢎⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢎⡳⣍⡟⣣⠝⣦⠹⣎⢧⢻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⢿⣷⣧⡟⣴⢋⡶⣏⠳⣎⢽⡻⢟⡳⣜⢣⢞⡱⣋⠗⣎⠮⣵⣻⣿⠏⠀⠀⠀⠀⠀⠀⠀⡜⣴⣿⣏⢮⡱⢎⡼⢥⡛⡴⢫⡜⣎⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠙⠿⣿⣦⣏⢶⣩⢓⢮⢲⡙⢮⡱⢎⡳⢎⡵⣩⢞⣥⣿⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⣯⠜⡦⣝⠺⣜⢣⡝⣜⣣⢾⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣷⣿⣾⣧⣯⣧⣽⣮⣷⣿⣶⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠿⡿⠿⠿⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀