⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⣀⣠⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈ ⠀⠀⠀⠲⣿⢿⡽⣿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣾⢿⣻⡿⣟⣿⢿⣧⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠐ ⠀⠀⠀⣾⣟⣯⡿⣯⣿⣟⣶⣄⣤⣄⣀⣠⣀⠀⠀⣰⣿⣻⣽⢷⣯⢿⣯⣟⡿⣽⣯⢿⣽⣻⣷⣤⣶⣄⡀⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⣤⣾⡿⣟⣿⢿⣷⣀⠀⠀⠀⠀⠘ ⠀⠀⣾⣟⣾⣯⢟⡀⠁⠀⠉⠁⢻⣏⣿⢿⣽⡿⣿⣻⢷⣻⣽⣟⣾⣟⡷⣯⣿⣻⢾⡿⣽⣳⡿⣾⣽⣻⣟⣯⣷⢶⣾⢿⡿⣟⣷⡶⣿⣟⣯⣷⢿⣯⣟⡿⣞⣿⡤⠀⠀⠀⠘ ⡃⣠⢠⣾⣷⣾⣦⣬⣧⣤⣤⣽⣿⣻⣽⢿⡾⣽⡷⣿⣻⡯⠗⠛⠓⠫⢿⣟⣾⡽⣿⣽⣻⢷⣟⣷⣿⣿⣿⣻⢾⡿⣽⣯⣟⣿⣳⢿⣳⣯⣟⣾⣟⣾⣽⣻⢯⣿⠀⠀⠀⠀⢸ ⠃⠡⢼⣿⣿⣿⢿⣽⢾⣯⣟⡷⣯⣟⣾⢿⣽⢯⣟⡗⠁⢀⣴⡾⣟⣿⣻⣮⣿⣟⡷⣯⣟⣿⣾⣿⣿⣻⢾⣽⢿⣽⣷⣻⣾⡽⣯⡿⣯⡷⣟⣷⣯⣟⣾⣻⣯⣟⣿⣻⣷⡄⢘ ⠀⠀⠘⠋⣩⣿⣻⢾⣟⣾⣽⣻⣽⣻⡾⣯⣟⣯⡏⠀⢠⣿⢯⣟⣿⣳⣯⡷⣟⣾⢿⠹⡿⢿⡿⣽⣞⣯⡿⣯⢿⣞⡷⣟⣾⣽⡷⣟⣯⣿⣻⣞⣷⣯⣟⣷⣻⡾⣷⣻⠺⠁⢸ ⠀⠀⠀⠀⢘⣿⡽⣿⣞⡿⣾⡽⣷⣻⣽⣟⣾⣻⡇⠀⢸⣯⣟⡿⣾⣽⣳⣿⣻⢯⣅⠀⡀⢿⣽⣟⣾⢯⣿⡽⣿⣽⣻⢯⣟⣾⣽⣟⡷⣯⣷⣟⣷⣻⣾⡽⣷⢿⣽⣻⡁⠀⢸ ⠀⠀⢀⣲⣘⣿⣟⣷⣻⣽⡷⣿⢯⣟⣾⣽⣳⣟⣧⡀⠈⢷⣟⣿⣳⣯⣟⣾⡽⣟⣯⣴⡿⣷⣻⡾⣯⣿⣞⣿⣳⣯⣟⡿⣽⣻⡾⣽⣻⣽⡾⣽⡾⣷⢯⣿⡽⣯⡿⣽⣇⠀⢸ ⠀⠀⠀⠈⠙⢻⣾⣯⡟⣾⣽⣯⣿⣯⣷⢻⣽⣾⣯⣷⡄⠀⠙⢺⣯⣷⢻⣯⣿⣿⣽⣯⣿⣽⣷⣿⣽⣾⣽⣾⣯⣷⡟⣿⣽⣷⡟⣿⣽⢳⣿⣯⣿⣽⣿⡞⣿⣽⢻⣽⡏⠀⢸ ⠀⠀⠀⠀⠀⠒⣿⣞⣿⣻⣽⡾⣷⢯⣟⣿⣽⣳⡿⣞⡿⣷⣦⣤⣤⣴⣾⣻⣽⢾⣳⡿⣞⣿⣞⡷⣟⣷⣟⡷⣯⣷⣟⣯⣷⢿⣽⡷⣟⣿⣳⢿⣞⣿⣾⡽⣿⣽⣻⢯⣿⡆⢸ ⠀⠀⠀⠀⠀⠀⣝⣿⣾⣽⣳⡿⣯⢿⣻⣞⣷⢿⣽⢿⣽⣿⣿⢯⣟⣾⢷⣻⣽⣟⣯⢿⣻⢷⣯⢿⣻⣾⣽⣻⣽⡾⣽⣳⣯⡿⣾⣽⡟⠷⠟⠫⠟⠋⠿⠋⠁⠉⠙⠋⢷⡿⢸ ⠀⠀⠀⠀⠀⠀⠰⠖⣺⠋⠹⡟⣿⣻⣽⣻⣾⠉⠉⠛⠿⢯⣟⣯⡿⣾⣻⣟⡾⠋⠘⠿⡯⠋⣸⣿⠉⠓⠯⠟⠉⠉⠙⠋⠗⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠟⠃⠃⠀⠀⠀⠀⠈⠻⢽⠻⠷⠿⠛⠀⠀⠀⠀⠀⠻⣿⡝⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠