⠀⠀⠀⠀⠀⠀⠀⢱⡈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠸⡄ I never quite realized...
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢿⡀ how beautiful this world is.
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣧⡀⠀⣀⠤⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⠊⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⢠⣴⣿⣿⡟⠁⠈⠙⢍⠉⠀⢠⢦⠀⢠⡄⠀⠰⣇
⠀⠀⠀⢰⣿⣿⣿⠏⠀⠀⠀⠀⢨⠀⠐⣿⠀⢧⡘⣷⣄⠰⣿⡀
⠀⠀⠀⢺⣿⣿⣧⠀⠀⠀⠀⠀⣩⠀⢸⢳⡀⠀⠛⠈⢿⣦⠙⢧⡄
⠀⠀⠀⠈⢿⣿⣿⣿⣦⢤⢈⣶⢋⣿⡞⠶⠁⠀⠀⢰⣿⣟⣷⡄⡙⠦⡀
⠀⠀⠀⠀⠀⠉⠻⡿⠋⠀⣽⣥⣿⡿⣧⠔⢢⠀⠀⠘⡟⣿⣾⡋⢢⣄⠈⡆
⠀⠀⠀⠀⣀⠤⠀⢈⢲⡾⠋⠀⠉⢻⢾⡈⠀⠀⠀⣰⣁⣽⡄⠹⡀⡛⢷⣅
⠀⠀⠀⠀⠀⠀⠠⣲⣻⣾⠲⣄⠀⡎⣹⣿⣿⣿⣿⣿⣯⡀⠈⢣⡙⢴⢄⠿⣝⡦⠄
⠀⠀⠀⠀⠀⡐⡩⣹⡿⠁⠀⡿⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣧⢈⠱⣄⣷⣕⢮⠛⢶⣄⣂
⠀⠀⠀⢀⣞⡜⣹⡟⠀⠀⢸⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠞⢿⣿⣧⠠⣀⠛⢝⠛⢿⣶⣄
⠀⠀⢀⡾⠋⢠⡟⠀⠀⠀⡏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡻⣤⣀⣈⣿⠻⣧⡈⠻⢶⣴⡄⠈⢿⡻⢦
⠀⠀⡼⠁⠀⣾⠀⠀⠀⠀⡇⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣇⣷⢻⣿⣿⣿⣀⠉⠻⣄⠀⡉⢻⣄⠀⢻⠀⠁
⠀⡰⠁⠀⢠⡇⠀⠀⠀⠀⣇⢿⣿⣿⡌⣿⣿⣿⣿⣿⣿⣿⣗⣿⣮⣿⣿⣿⡟⣆⠀⠘⢦⠀⡄⠹⡆⠀⠇
⠈⠀⠀⠀⢸⠃⠀⠀⠀⠀⢱⠸⣿⡿⢱⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣿⣿⣞⢧⡀⠈⢳⡘⠀⠘⡄
⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠸⡆⠘⢣⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣟⣿⣿⣿⣎⢻⣄⠠⣷⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠿⣧⠙⠋⠻⣿⣿⡄⠿⠆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⣤⣷⣿⣿⣿⣟⣿⡿⣟⣻⣿⣿⣷⣿⣷⠀⠀⠀⠈⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣴⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣧⠀⠀⣀⣀⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠉⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⡟⣆⠀⠻⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡜⢿⣿⣿⢟⠻⣅⠀⠀⠀⢈⡇⣿⡆⠀⠙⢿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠠⣿⣤⣤⣴⣿⣾⡇⢿⣾⣾⣿⣦⣀⣀⣼⡇⣿⣿⡄⠀⠘⠿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢸⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣸⠈⢵⣿⡀⠀⠀⠙⢿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣾⣿⣿⣿⣿⣿⠀⣸⣿⣿⡿⢿⣿⣿⣿⠇⠀⠈⣿⣷⡀⠀⠀⠈⠛⢻⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⣿⡿⣿⣁⣼⣿⣿⡟⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠈⢻⣧⡙⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡄⡿⠏⠀⠉⠙⣿⣿⠁⠀⠀⠀⠀⢹⢿⣧⡄⠀⠀⠀⠀⠉⢿⣦⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣗⡇⠀⠀⢰⣿⢻⠃⠀⠀⠀⠀⠀⠈⢛⣿⣵⣄⠀⠀⠀⠀⠀⠀⠁⢆⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠀⠀⣼⢏⠇⠀⠀⠀⠀⠀⠀⡴⣾⣿⣿⣽⣧⢀⠀⠀⠀⠀⠀⠀⠑⠀⣿⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠀⢀⣼⢛⡎⠀⠀⠀⠀⠀⠀⢠⡟⣿⣿⣿⣯⣸⢿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠓⣕⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⢸⣷⣼⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⡏⠀⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣕⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣞⢁⡙⣿⣿⣷⡀⣤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⢕⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⡀⢀⡿⣺⡀⠀⠀⠀⠀⠀⠀⡏⢠⡾⠗⠈⠻⣿⣆⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠷⡾⣷⣹⡇⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠙⢿⡿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⣿⣿⣿⣿⠀⠀⣿⣮⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⢀⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⣹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⢼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠇