⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣺⣿⣿⣯⡽⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⠏⣿⣗⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣻⣯⠀⠷⠟⠁⠀⠀⠀⠀⢀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣤⢟⡹⣖⣄⠀⠀⠀⠀⢀⣴⡿⣟⣿⢿⣿⣷⣄⠀⠀⠀⠀
⢠⣶⣶⣦⣤⡀⢀⣌⣲⣙⢣⣿⢴⣷⣷⣾⡵⣶⣴⣿⣿⡽⣯⣟⣯⢷⣟⣿⢷⡄⠀⠀
⢾⡿⣯⣟⢟⣩⣾⣿⡝⣿⣻⡿⣟⣯⣫⢅⡻⣜⡹⢿⣷⣿⣳⣟⡾⣟⣾⣽⣻⣟⣦⡀
⠸⣟⠗⣱⣚⣧⠵⠿⠽⠷⠯⠷⣟⣿⢯⣚⢭⢓⡽⣏⢮⢗⣿⡞⠋⠻⢳⣯⢷⣻⢯⡿
⠀⢇⣸⡾⣈⠁⠀⡀⠄⠀⢤⠥⢤⠉⠳⣿⣯⢾⢻⣾⢲⣯⠵⣖⡀⠀⠀⠉⠛⠉⠉⠀
⣐⣲⡗⠁⠡⠂⠄⠠⠐⠈⣓⣠⢀⡤⠃⡙⣿⣾⣧⣷⣟⣭⣯⣾⣗⡀⠀⠀⠀⠀⠀⠀
⢆⣿⣰⡵⣿⡧⢀⢁⠂⣴⣾⣿⡟⢟⢯⠖⠸⣿⣯⡞⣿⣞⣱⣟⣿⡿⢦⠀⠀⠀⠀⠀
⡾⣽⠸⢴⣿⡃⠀⠐⢀⠘⣟⡿⣿⡃⠬⠀⠆⣿⣷⣿⣟⣯⣷⣾⣷⣿⡟⠓⠀⠀⠀⠀
⠰⡿⣈⡉⠋⠁⡐⠈⠀⠂⢉⠳⠊⢈⠠⠐⡈⣿⡷⣿⣷⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀
⠀⢻⣷⣄⠘⢀⠠⠔⢨⠀⢠⠀⡑⢀⠂⠅⣴⡿⣿⣿⣿⣿⡿⢿⣿⡛⣏⢆⠀⠀⠀⠀
⠀⠀⠈⠙⣻⢤⢦⣈⣐⣈⡄⣰⣤⣦⣷⣾⣾⣿⣿⣿⣿⣿⣿⣿⢣⠟⣜⣎⠆⠀⠀⠀
⠀⠀⠀⢠⡚⣎⢧⠻⣏⡟⣾⣿⣭⣽⣺⡿⣿⢿⡽⣷⣫⣷⣿⡗⢯⢺⡱⣎⡻⠀⠀⠀
⠀⠀⠀⢰⠹⣘⠮⣝⣡⠻⣏⣷⣩⠗⣟⡾⣯⣟⡽⣽⠯⣷⢫⡟⢧⣫⠗⣼⠱⡇⠀⠀
⠀⠀⠀⢠⠛⣬⠹⡜⣜⢳⡜⣹⢥⡻⣜⡴⣹⢮⠿⣵⢛⣖⣯⣽⣙⠶⣫⢧⢻⣱⠀⠀
⠀⠀⠀⢠⢛⢖⡹⣚⡥⢷⡘⢗⡎⡷⣌⡳⣹⢮⢷⢺⣝⠾⣸⣧⢏⡿⣱⣚⡵⡛⠀⠀
⠀⠀⠀⠘⡽⢪⠴⣣⡝⣲⠹⣎⠵⣓⢞⡵⢣⢟⢮⣗⡞⣿⣵⣳⢟⣼⢣⡟⣴⢣⠀⠀
⠀⠀⠀⠀⠘⣱⡛⣤⠻⡬⡗⣮⠳⣥⢻⡜⣯⢹⣲⢻⣜⡳⣞⡵⣏⣾⡵⣹⣾⣿⡄⠀
⠀⠀⠀⠀⠀⣾⣷⣞⡽⣳⣭⢳⡟⣮⢳⣟⣼⣷⢻⣳⢾⡽⣞⣷⣿⣾⣽⣿⣿⣿⡇⠀
⠀⠀⠀⠀⠀⣿⣿⠿⠟⠑⠋⠷⠾⢷⣿⣼⣷⣯⣿⣿⣿⣾⣿⣿⣿⠁⠈⠻⠿⠿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀