⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣠⣤⣤⡶⠾⠟⠻⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀ ⠀ ⠀⠀⠀⠀⣀⣤⣴⠶⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠈⠙⠛⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀
⠀ ⠀⠀⢀⣤⣶⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⡀⠀⠀⠀⠀⠀
⠀⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀
⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⣤⡄⠀⠀⣤⠀⠀⣀⡀⠀⣤⡀⠀⠀⠀⠀⠀⠘⢿⣆⠀
⢠⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⠀⣰⣿⠀⠀⣿⠃⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⢻⡇
⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⢻⣇⢰⡏⢀⣼⣯⣿⡄⢠⡿⠞⢻⡏⠀⢀⡀⠀⠀⠀⠀⠀⢸⡇
⢸⡟⠀⠀⠀⠀⠀⠀⠸⠃⠀⠙⠋⠀⠟⠁⠀⠘⠃⠾⠀⠀⠛⠀⢀⡾⠁⠀⠀⠀⠀⠀⢸⡇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡶⣆⡞⢀⣠⣤⣶⣶⣦⠀⠈⠁⠀⠀⠀⠀⠀⠀⢸⡇
⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠁⠀⠋⠀⠀⣿⠁⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣏⣀⡀⠀⠀⢰⣏⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠁⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⢸⡇⠀⠀⠀⠀⠀⠀⢴⡆⢀⡀⢸⡿⢠⣶⣶⡿⠿⠃⣶⡆⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⠇
⢸⡇⠀⠀⠀⠀⠀⠀⣼⢇⣾⣇⢸⠇⠀⠀⣼⠀⠀⠀⣿⣷⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀
⢸⡇⠀⠀⠀⠀⠀⢀⣿⠟⠉⢿⡟⢀⣀⣠⣯⣤⡄⢸⠏⠹⣧⡾⠀⢠⡤⠀⠀⠀⠀⠀⣿⠀
⢸⣷⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣾⠋⠀
⠀⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀
⠀⠀⠀⠉⠛⠿⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡿⠃⠀⠀⠀⠀⠀
⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠀⠀⠀⣠⣶⣶⣶⣶⡶⠾⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠃⢀⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣟⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⠇⣿⡹⡄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢳⣿⡾⣟⣷⣾⡏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣯⣼⢟⣽⣛⣞⣳⢧⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡠⣪⣿⡻⣝⣮⢳⢯⡖⣯⢞⡽⢮⣳⢏⣿⣳⣵⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣸⣼⣟⣶⢻⡵⣞⢯⣳⣛⣮⢟⡞⣯⢳⣛⡶⢯⣟⣎⡆⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⡼⣇⣿⣸⣻⣼⢣⣟⣼⣻⡼⢧⡿⢧⣿⢿⡼⣿⣧⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣯⡿⢋⣧⣭⣷⣯⣻⢞⡶⣏⣾⣫⣴⣆⠌⢿⣻⣽⡇⠀⠀⠀⠀
⢠⣾⣿⣿⣿⢋⣰⠾⠿⣿⣿⣿⠹⣯⣳⡏⣿⣿⣿⠿⠮⣐⠻⢿⣿⢿⣯⢢⠀
⢳⡿⡟⢉⣿⣰⠁⠀⠀⠀⠈⢻⡐⢹⡟⣠⠏⠁⠀⠀⠀⠀⡇⣾⢋⢻⣽⣿⠁
⠈⢿⣿⣄⣿⣾⠀⠀⠀⢀⣿⣓⡇⠆⢆⢽⢾⣟⠀⠀⠀⠀⣧⣿⣐⣾⣿⠏⠀
⠀⠈⠻⠿⡿⣿⣦⠀⠀⠀⠛⢫⠣⣉⠆⣺⡜⠛⠀⠀⢀⣴⣿⠿⣿⠿⠏⠀⠀
⠀⠀⠀⠀⠀⠈⠻⢿⣷⣶⣾⡥⡓⣞⡚⢧⢸⣽⣾⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣬⣿⢿⣿⡿⣟⡿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣰⣿⢿⣽⣿⣽⣷⠭⣙⣾⡿⣷⣿⣿⣿⣿⣖⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣴⣿⣟⣿⢻⣿⣻⢃⠞⠰⡘⣿⣿⡄⠙⢾⣻⢿⣿⡄⠀⠀⠀⠀
⢀⡄⠴⢋⢎⣿⣟⣾⡏⢸⣷⣿⠈⡌⠱⠰⣹⣿⡇⠀⠈⣿⡿⡾⡿⣆⠀⠀⠀
⠀⢱⣾⣧⠞⠿⣾⡿⠀⣸⣷⣻⣌⠔⡡⢣⣿⡷⣇⠀⠀⡟⡰⢄⠡⢹⡆⠀⠀
⢠⣿⣿⣧⣾⣿⡟⠁⠀⣿⣿⣽⣿⣾⣶⣿⣿⣽⣿⡄⢸⣽⣦⡍⡖⢡⣷⠀⠀
⠀⢿⣿⡿⣿⡏⠀⠀⠀⣿⡿⣟⣿⣿⣿⣿⣿⣟⣿⣿⣶⣧⡼⣟⡱⠛⠋⠀⠀
⠀⠀⠙⢣⡏⠀⠀⠀⠀⣿⣿⣽⡇⠀⠀⠀⢻⣾⣽⡯⠉⠛⠻⢿⣿⣵⣄⠀⠀
⠀⠀⠀⠈⠿⠀⠀⠀⢠⣛⠛⢾⡀⠀⠀⠀⢸⠻⠛⣷⠀⢀⣤⣤⣼⡷⣿⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⡙⡢⣇⠀⠀⢀⡏⡌⡓⣌⣇⠘⠿⠯⡷⠿⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠶⠗⠋⠀⠀⠀⠛⠷⠷⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀