⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠂⣹⣶⣶⣶⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⢨⢿⣿⣿⣿⣻⣽⢯⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⢶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠟⠀⠀⢀⢴⣿⣿⣿⣻⢾⣽⡾⣿⣽ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⡿⣿⣧⣤⣠⠖⠀⠀⢀⣴⣶⣿⠿⠄⠀⠀⠀⠀⣀⣤⣶⣿⢿⡿⡏⠀⠀⠀⢨⣿⣿⣻⢾⡽⣟⣷⢿⣳⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣷⣻⢿⣯⣤⣴⣾⣿⢿⣻⡿⣿⣿⠤⢤⣶⣿⡿⣟⣯⣟⡿⣷⣤⠀⠀⠀⠿⠿⠾⠻⣿⣻⣟⠞⠋⠉⠀ ⠀⠀⠀⠀⣰⣶⣶⡦⣼⣿⣿⣾⣿⢯⣟⣿⣻⢿⣽⡾⣟⣯⣟⣿⣻⣿⣾⣻⣯⣟⡿⣽⡾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⣿⣟⣿⢿⣻⣾⣽⣾⣿⣿⣾⣽⡿⣾⣽⢿⣽⡾⣷⣻⣾⡽⣿⣻⢾⣟⣯⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⡿⣞⣯⠿⠛⠉⠀⢀⣽⣤⡀⠈⠙⠛⢯⣿⡾⣽⡷⣟⡷⣟⣯⣟⣯⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠛⣿⣿⠟⠁⠀⠀⢀⣴⣿⣿⠟⠁⢀⡀⠀⠀⠙⢿⣯⣟⡿⣽⡿⣽⣾⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⣰⣾⣿⠃⠀⠀⢠⣴⣿⣿⠟⠁⠀⢀⣴⣿⣄⠀⠀⠀⢻⣿⣽⢯⣿⣳⣯⣷⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣿⣿⡇⠀⣀⠀⠈⠻⣿⣿⣷⣄⣴⣿⣿⣿⣿⣷⣄⠀⠀⣿⣯⢿⣳⣟⡷⣯⣿⢾⣽⢿⣷⣾⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⣿⣟⣾⠅⣼⣿⣦⡀⠀⠈⢻⣿⣿⣿⣿⠋⠀⠙⢿⣿⣷⡶⢼⣿⣻⣽⡾⣿⣽⢾⣻⣽⣟⣾⣽⣻⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣯⣿⡇⠈⠻⣿⣿⣦⣴⣿⣿⡿⣿⣿⣷⣄⠀⠀⠙⠏⠁⣼⣿⣽⣾⣻⣷⠿⢿⣯⣷⣻⣽⢾⣯⢿⡾⣽⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣻⣷⣻⣧⠀⠀⠈⠻⣿⣿⡿⠋⠀⠈⣻⣿⣿⡷⠀⠀⠀⢰⣿⣿⠋⠉⠉⠀⠀⠀⠀⠉⠿⣯⣿⢾⡿⣽⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣿⣿⣽⣻⣷⡀⠀⠀⠈⠋⠀⠀⣠⣾⣿⡿⠋⠀⠀⠀⣰⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠻⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢼⣿⣷⣻⣽⢿⣦⣄⠀⠀⠀⠻⣿⡿⠋⠀⠀⢀⣠⣾⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠿⣷⣿⢯⣟⡿⣿⣶⣦⣤⣬⣤⣤⣶⣾⡿⣿⢯⣷⣿⣷⣤⣀⡀⠀⠀⣷⣤⣀⣀⣼⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣹⣿⣟⣷⢯⡿⣽⣻⢿⣽⣳⣯⢿⣽⣻⢷⣻⣞⣿⣻⢿⣦⣴⣿⢿⣻⣟⣿⣻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣟⣾⢯⣿⣻⣽⢯⣿⡽⣷⣻⣯⢿⣽⣻⢯⣟⣾⣻⣯⣟⣯⢿⣻⣽⡾⣯⣟⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⡿⣞⣯⣿⣳⡿⣽⣻⢷⣻⣯⡷⣟⣯⡿⣽⣻⢯⣷⣟⡷⣯⢿⣻⣽⢷⣻⣽⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⠿⠟⠿⠉⠛⠳⢿⣿⣽⣻⣟⣾⣽⢿⣽⣻⣽⣟⣯⡷⣿⡽⣟⣿⡽⣯⡿⣯⣷⢿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⣳⣯⢿⡾⣽⣟⣾⣯⣷⢯⣿⡽⣷⢿⣻⢷⣻⣯⣟⣷⣯⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠙⠻⠿⠉⠉⠁⠘⠿⣻⣞⣿⣽⣻⢯⣿⣻⠾⠽⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠞⠽⠾⣻⣿⢯⣻⣽⣿⣞⣻⠿⠘⠁⠉⠉⠿⠻⠙⠛⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣯⣷⣟⣯⣻⢷⣻⢿⣷⡽⣿⢯⣷⣯⣾⣟⣽⡾⢿⣯⣳⣿⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠿⢿⣷⣯⡿⣯⡽⣿⣟⡽⣿⡷⣯⣟⣽⣻⣽⢿⣽⣾⣟⣻⣽⣿⢿⠳⠛⠉⠿⠟⠿⠸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣽⣻⢷⣽⣻⢿⣯⡷⣟⣷⢯⣻⣽⡿⣯⣟⡷⣯⣻⢷⣻⣽⡿⣳⣿⣯⣞⡿⣿⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣟⣯⡾⣽⣻⢿⣯⣟⣯⣻⣾⣟⢯⣻⣽⢿⣯⣻⣷⡽⣿⢯⣽⣻⣿⢯⣾⣟⣿⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⣻⣿⣟⣻⢿⣿⣴⣦⢿⣻⣿⣞⣻⢷⣻⣽⢿⣯⣳⣽⢿⣻⣽⡿⢯⣷⣟⣿⣹⠈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣼⣀⣀⣤⣷⠀⠀⡀⣀⣤⣷⣿⣷⢯⣿⡿⣾⣶⣤⣤⣬⣤⣦⣶⣿⡿⣟⢯⣿⣷⠿⠛⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡟⣿⣾⣠⢀⠀⠀⠋⡿⣿⠻⠀⠀⠀⣄⣦⢿⣽⣻⣷⣿⢼⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠿⠿⠻⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠁⡏⣿⣰⠀⠀⠀⠋⡿⣿⣾⣠⠀⠀⠋⠈⠀⠀⡀⣷⣻⣽⣿⣿⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⡿⣽⡿⢾⣿⣯⠿⠉⠀⠀⠀⠀⠉⠉⠋⣿⣿⢰⠀⠀⠀⡷⣿⣿⣻⠈⠀⠋⡿⣿⣿⠻⠈⠀⠀⣧⣻⣷⣻⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣽⡾⢿⣯⢾⣽⣻⣷⣯⢿⠿⣷⣻⣾⣽⣿⣼⠁⠏⠙⠀⠀⣄⣷⣿⣿⡿⣿⣿⣴⣦⣿⣿⠻⠈⡇⣿⣯⣿⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⣷⢿⣻⣽⣾⣟⣽⣻⢾⣽⣿⡾⣽⣻⣿⢼⡶⣷⣿⢿⠙⠀⠋⣿⣿⣿⣿⢻⠈⠀⡀⣦⣿⣼⠅⣾⣟⣿⣰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣾⣷⢿⣽⢾⣿⣯⡷⣟⣳⢿⣯⣿⠀⠀⣄⣷⣿⣿⣿⣿⣴⣄⣷⣿⣿⠻⠈⠀⣀⠀⡇⣿⣿⣿⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣷⢿⣷⣯⣳⣿⢯⣽⣿⢻⠀⠀⠀⣄⣿⣴⢀⠀⠁⠟⣿⣿⣴⢠⠀⠀⠃⣿⣾⣰⣀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣻⣾⣽⡿⣽⡿⣟⣯⢿⠙⠀⠀⡀⢀⠁⠟⣿⣿⣴⢀⠀⠀⠁⠟⣿⣿⠛⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡟⣯⣟⣯⣟⡷⣟⡷⣽⡾⣿⢯⠛⠙⠈⡀⣤⣽⢀⠀⠉⠛⠿⣯⣞⡿⣾⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⣯⣟⢾⣻⣿⡽⣾⣻⣷⡾⣽⢿⣽⣾⡿⣽⣾⣿⣿⣾⣽⣾⣻⢿⣿⣟⣿⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠁⡟⣿⡾⣽⡿⣟⣯⣻⣾⣿⣻⣿⣟⣯⣟⡾⣽⢿⣻⣿⣟⢯⣿⣾⣿⣿⣼⡦⣶⣶⣰⠀⠀⠀⠀ ⠀⠉⠋⠞⣟⣻⣿⠻⠾⠿⠿⠀⠀⠀⣤⣷⡿⣟⣯⣟⡿⣿⣶⢤⠤⣿⣿⡿⣻⢿⣿⣾⣴⣤⣯⢿⣻⣷⣿⣿⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⣳⢿⣷⣟⡽⢾⣻⣿⣿⢨⠀⠀⠀⡏⡿⢿⣿⣶⣤⣀⠀⠀⠀⠀⠄⠿⣿⣶⣴⢀⠀⠀⠖⣠⣤⣧⣿⡿⣿⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣽⣿⡾⣽⢾⣻⣿⣿⣿⢴⢀⠀⠀⠟⣿⣿⣴⣠⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⣶⢶⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢯⣽⣻⣿⣿⣿⢿⢨⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⣶⣶⣶⣹⠂⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀