⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣟⡿⣝⣻⠉⠉⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢻⣮⢷⣻⣯⡟⣷⢦⡀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣿⣿⣶⣄⡀⠀⠀⠀⣰⣿⣛⣾⢻⣼⣳⣿⣳⣻⣭⡟⣿⡄⠀⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⠋⢢⠁⠀⠀⣼⣟⡾⣝⡾⣻⡼⣿⣳⡽⣳⢾⡽⣳⡟⣿⣻⡿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡤⠤⣄⠀⠀⠸⣇⣠⣿⣦⣀⡀⣿⣞⣽⣫⢷⢯⡽⣿⣳⡟⣽⣳⣻⢳⣟⣳⢷⣻⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣏⠀⠀⢹⠀⠀⠀⠉⠙⣿⠋⠁⠀⠙⢾⣧⣟⢯⣯⣟⣽⣷⣻⣳⡽⣳⣟⢾⡽⡾⣽⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡄⠀⢸⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⢠⣿⣿⣿⡿⣿⢿⣿⣧⡟⣧⢿⡼⣟⣼⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⠿⡿⠟⠛⢦⣌⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣟⡾⣷⣟⣯⣿⣞⡿⣿⣯⣷⣿⣽⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⠦⣄⣀⡠⣼⠃⣸⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿⣾⣿⣷⣯⣿⣾⣽⣿⣳⡿⣽⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢧⣄⣀⣀⣀⡼⠁⢿⡆⠀⠀⠀⠀⠀⠀⣸⣿⡿⠛⣻⣿⣽⡻⠿⣿⣿⢯⣟⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣧⣈⣉⣀⡝⢂⡼⣧⡀⠀⠀⠀⠀⢠⣿⡟⡠⢲⣿⣿⡟⠀⣴⣿⣿⣿⣟⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⠓⠶⣯⣴⣿⣿⣶⣤⣄⡀⢸⣿⡇⠈⣬⣿⣿⡁⠀⣹⣿⣿⣿⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣷⡀⠹⣿⣿⣇⠀⢿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣷⣻⢿⣶⣿⡿⣿⣷⣾⣿⣿⢯⣿⣿⡿⠿⠿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⢿⣿⣷⣯⣟⣷⣯⣿⣿⣿⣯⣿⡇⠀⠀⠀⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⡿⣽⣿⣿⣿⣿⣿⣿⣿⣳⣯⣿⡇⠀⢀⣼⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣽⣻⣿⠿⢿⠟⠛⣿⣟⣷⢯⣿⣧⣴⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣞⡿⣿⡀⠛⢀⣼⣿⣟⣾⣿⢻⣿⣿⣿⣿⣹⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣯⣟⡿⣿⣿⡿⣿⣻⣾⡏⣼⣦⠍⠛⠛⢺⣀⣸⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣞⣿⣳⣯⢿⣷⣻⣽⣷⡀⠻⠀⠀⣀⡼⠁⠀⢈⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⢀⣼⣿⣻⣾⡽⣯⣿⢾⣽⣳⡿⣿⣦⣄⡀⠉⠀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣷⣾⡿⣟⣿⣿⡾⣽⡷⣯⣿⡽⣷⢿⣷⣻⣟⣿⡿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣽⢻⣯⣿⣽⡟⣯⣿⣷⣯⣿⣽⣿⣿⢳⣿⣾⣽⣿⡅⠉⠛⣿⣶⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡀⠀⢠⣾⣿⣻⢷⣻⣾⡽⣿⣞⣯⡿⣽⣿⣞⣷⣯⢿⣽⣻⢯⣿⣳⣯⣟⣷⣷⣦⣄⡈⠙⢿⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⢩⣿⣿⣳⣿⣻⣽⢾⣻⢷⣯⣷⢿⣻⣟⣿⣿⣾⣿⣳⣿⣻⢷⣯⡷⣿⣾⢷⣯⣟⣿⣦⣼⣿⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣳⡿⣾⣿⣽⣟⣯⣿⢾⣽⣻⢿⣻⣿⣷⣿⣷⣿⣞⣯⣿⣞⡿⣿⣟⡿⣾⣽⢾⣯⣟⣿⣿⠚⠃ ⠀⠀⠀⠀⠀⠀⠸⣿⣷⣻⡷⣿⣟⣾⣽⢾⣻⣽⢯⣿⣻⢾⣿⣟⣾⢷⣻⣽⡾⣽⣻⢷⣯⢿⡷⣯⣿⣾⣽⣾⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣷⣿⣽⣷⡿⣽⡾⣿⣿⡿⣟⣷⢿⣯⣟⡿⣯⣿⢯⣷⣿⣿⣿⡿⣽⣯⢿⣽⣿⣿⣞⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢾⣿⣽⣯⢿⣽⡷⣟⣿⣽⠿⠟⠉⠀⠈⠛⠿⣷⣻⣞⣷⢿⣻⣾⣟⣷⣯⡷⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠁⠋⠛⠛⠛⠛⠛⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠟⡷⣯⣷⣟⣾⣻⢿⣷⣞⣻⣷⠿⠛⠈⠀⠉⠟⠿⣽⣿⣟⡷⣽⢿⣯⣽⣿⢾⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠃⣿⣞⣿⣿⣽⢿⣯⣽⡿⣿⣿⣿⣷⢯⣿⣯⡿⣟⣯⢿⣷⣟⡿⣿⣿⡾⣽⡿⣷⣽⣿⣷⠙⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣾⣽⣾⣿⣯⡷⢿⣯⢷⣻⣽⡾⣽⣻⢷⣾⣟⣿⢾⣻⣿⢯⣽⣻⢾⣽⣾⣟⣿⡷⣻⣷⣿⠸⠀⠀⠀⠀⠀⠀ ⠃⠚⣿⣿⣟⣯⢾⣽⣾⡿⣟⣿⡿⣞⣿⣯⣞⣿⣷⣿⣷⣿⣻⢿⣻⣽⢾⣿⣯⣟⣽⣿⣾⡿⣳⣿⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⣇⣿⣼⣦⣿⣟⣯⢷⣾⣿⡷⣯⢷⣻⣿⣳⣿⣾⣿⣿⣟⣻⢿⣷⣯⢷⣻⢾⣽⣻⣿⣳⣿⣿⢩⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⣦⢿⠙⡈⣄⣦⣷⣷⣟⣯⣳⣿⢯⣻⣽⢿⣯⣷⣞⣿⣽⡿⣯⣞⣿⡽⣾⣻⢷⣻⣿⣾⢠⠀⡀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⡄⣶⣿⠛⠉⡅⣿⣽⣾⣿⢳⣿⣿⣽⣿⣯⣷⣿⣯⡟⣽⣿⣯⢻⣽⣿⣿⣿⣾⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⣷⣿⡿⣿⣟⣻⣷⢿⣷⡽⣿⣯⡷⣽⡾⣿⣿⣟⡿⣾⣷⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠞⡤⣀⠀⠉⡀⣄⣦⣿⡿⣳⣽⢾⣿⣯⡽⣾⣻⣿⣼⢀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⢈⠀⠁⡼⣀⠀⠀⠻⡀⣷⣽⣻⣷⢿⣯⣳⣿⣞⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣆⣸⣀⢺⠛⠛⠍⣦⣼⡏⣾⣻⣿⡿⣿⣿⡿⣟⣯⣿⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣆⣹⣿⣿⣿⣿⢻⣿⣾⣟⣿⣼⢀⠛⡀⣿⡿⣞⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⠿⣿⣿⣿⣴⣧⣿⢯⣷⣟⣿⠛⠟⢿⠿⣿⣻⣽⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠇⣿⣿⣿⣼⢀⠀⡇⣿⣯⣳⣿⣿⣿⣿⣿⣿⣿⣽⡿⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡿⣿⣿⣾⠀⠀⠀⡇⣿⣯⣿⣿⣿⣯⣷⣟⣯⣷⣿⢿⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⠿⠿⡿⣿⣿⢯⣿⣿⣾⣷⣿⡿⣿⣶⢿⣻⣷⣿⠿⠻⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⣦⣷⣿⣿⣿⣿⣿⢷⣿⣿⣿⢿⠀⣇⣿⣿⠹⡀⣷⣿⣿⣿⣿⣿⣿⣿⠻⠙⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⣿⣿⣹⠀⡁⣿⣿⣬⠈⡇⣿⢸⡀⣄⣤⣶⣿⣿⣴⣯⠶⠓⠛⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⣟⣿⣿⣿⣴⠀⡟⣿⣿⢲⡠⡟⣿⢠⠀⠀⠀⠀⡀⣧⡼⢂⡝⣀⣉⣈⣧⠸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣷⣟⢯⣿⣿⠿⡻⣽⣿⣻⠛⡿⣿⣸⠀⠀⠀⠀⠀⠀⡆⢿⠁⡼⣀⣀⣀⣄⢧⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣾⣽⡿⣳⣿⣽⣾⣿⣯⣷⣿⣾⣿⣾⠀⠀⠀⠀⠀⠀⠀⡇⣸⠃⣼⡠⣀⣄⠦⣿⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣽⣿⣷⣯⣿⡿⣞⣿⣯⣟⣷⡾⣟⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⣧⣌⢦⠛⠟⡿⠿⣴⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣼⣟⡼⢿⣧⡟⣧⣿⢿⣿⡿⣿⣿⣿⢠⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⠀⡄⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠃⣽⡾⡽⢾⣟⣳⡽⣳⣻⣷⣽⣟⣯⢯⣟⣧⢾⠙⠀⠁⠋⣿⠙⠉⠀⠀⠀⢹⠀⠀⣏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⣻⢷⣳⣟⢳⣻⣳⣽⡟⣳⣿⡽⢯⢷⣫⣽⣞⣿⡀⣀⣦⣿⣠⣇⠸⠀⠀⣄⠤⡤⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⡿⣻⣿⡟⣳⡽⢾⣳⡽⣳⣿⡼⣻⡾⣝⡾⣟⣼⠀⠀⠁⢢⠋⡿⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⠀⡄⣿⡟⣭⣻⣳⣿⣳⣼⢻⣾⣛⣿⣰⠀⠀⠀⡀⣄⣶⣿⣿⣾⣤⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡄⣷⠙⠀⡀⢦⣷⡟⣯⣻⢷⣮⢻⣿⣴⢀⠀⠀⠀⠀⠀⠀⠀⣇⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⢿⠛⠉⠉⣻⣝⡿⣟⣾⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀