⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⠲⡶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣯⣿⣿⡟⢿⣶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣿⣿⣿⣿⠻⣿⣿⣇⢳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⣿⢿⣯⣶⠳⣾⣿⡯⢿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⣿⣿⣧⢻⣿⣷⣾⣳⣿⣿⣀⢸⣾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣾⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⣿⣿⣿⠟⢋⣙⣉⠉⣻⣿⣿⣿⣿⡤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⣿⣿⣿⣤⣀⣠⣾⣿⣿⣿⠿⠯⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣾⣿⣶⣶⣶⡆⠎⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣶⣾⡿⣻⣻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⢛⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⢿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣼⣾⣿⣿⡿⣿⠛⠉⠀⠉⢻⠟⠉⠉⠙⢻⡿⢿⣿⣿⣧⣀⠀⠀ ⠀⠀⠀⢻⣥⣿⣿⡿⢡⣾⣿⡄⠀⠀⠀⢸⠀⠀⠀⠀⣸⣿⣦⠙⣿⣿⣯⡂⠀ ⠀⠀⠀⣰⣏⢱⣽⣧⣿⣿⣿⣿⡄⠀⠀⢸⡇⠀⠀⢰⣿⣿⣿⣧⣸⠟⢡⣿⠀ ⠀⠀⠀⣿⣿⠸⠿⣿⣿⣿⣿⣿⣿⣄⣀⣼⣇⣀⣠⣿⣿⣿⣿⣿⡏⠀⣘⣿⡆ ⠀⠀⠀⠙⣇⢑⠲⠿⣿⢟⡿⠿⠛⣙⣿⣿⣿⣟⡉⠉⠉⣉⣽⣿⣧⡐⢛⣵⠃ ⠀⠀⠀⠀⠈⠒⠒⠛⠁⢸⣿⡿⠿⠋⠉⠿⠏⠙⠟⠟⢛⣿⠙⠛⠯⠷⠛⠁⠀ ⠀⠀⠀⢀⣀⣀⡀⠀⡠⠋⢿⡗⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⣿⣿⣿⡞⠀⠠⣼⣷⠀⠀⠀⢤⡄⠀⠀⢀⣿⢀⢖⠞⡄⠀⠀⠀⠀ ⠀⣰⣾⣿⠿⣿⣿⡀⠀⠰⠈⣿⠀⠀⠀⠀⠀⠀⠀⣼⣏⣀⠀⢀⣷⡄⠀⠀⠀ ⢰⣿⣿⣿⣾⣾⣿⣿⣦⣌⣓⣿⣶⣤⣀⠀⢀⣠⣶⣿⣿⣒⡪⣭⡶⢳⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣟⣂⣩⣬⡭⢿⣿⠀⠀⠀ ⠸⢿⣿⣿⣿⣿⠀⠉⠲⠶⠚⠉⠉⣿⣿⣿⣿⠟⠏⠉⠙⠻⢶⠔⠉⠸⠀⠀⠀ ⠀⠈⠛⠛⠻⠿⡇⠀⠀⠀⠀⠀⠀⠀⠻⣿⠉⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⡟⡄⠀⠀⠀⠀⠀⠀⣠⡎⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⢰⡇⡟⠾⢤⣤⣤⣤⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢸⠁⡇⠀⠀⠀⠀⠈⣻⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠁⣻⠈⠀⠀⠀⠀⡇⠁⢸⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡿⣿⣤⣤⣤⢤⠾⡟⡇⢰⠀⠀⠀⠀⠀⡀⢳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡎⣠⠀⠀⠀⠀⠀⠀⡄⡟⠀⠀⠀⠀⠀⠀⠀⡀⢹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠇⢠⠀⠀⠀⠀⠀⠀⠀⠉⣿⠻⠀⠀⠀⠀⠀⠀⠀⡇⠿⠻⠛⠛⠈⠀ ⠀⠀⠀⠸⠉⠔⢶⠻⠙⠉⠏⠟⣿⣿⣿⣿⠉⠉⠚⠶⠲⠉⠀⣿⣿⣿⣿⢿⠸ ⠀⠀⠀⣿⢿⡭⣬⣩⣂⣟⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸ ⠀⠀⠀⢳⡶⣭⡪⣒⣿⣿⣶⣠⢀⠀⣀⣤⣶⣿⣓⣌⣦⣿⣿⣾⣾⣿⣿⣿⢰ ⠀⠀⠀⡄⣷⢀⠀⣀⣏⣼⠀⠀⠀⠀⠀⠀⠀⣿⠈⠰⠀⡀⣿⣿⠿⣿⣾⣰⠀ ⠀⠀⠀⠀⡄⠞⢖⢀⣿⢀⠀⠀⡄⢤⠀⠀⠀⣷⣼⠠⠀⡞⣿⣿⣿⣿⢀⠀⠀ ⠀⠀⠀⠀⠀⣄⠳⡏⣾⠀⠀⠀⠀⠀⠀⠀⠀⡗⢿⠋⡠⠀⡀⣀⣀⢀⠀⠀⠀ ⠀⠁⠛⠷⠯⠛⠙⣿⢛⠟⠟⠙⠏⠿⠉⠋⠿⡿⣿⢸⠁⠛⠒⠒⠈⠀⠀⠀⠀ ⠃⣵⢛⡐⣧⣿⣽⣉⠉⠉⡉⣟⣿⣿⣿⣙⠛⠿⡿⢟⣿⠿⠲⢑⣇⠙⠀⠀⠀ ⡆⣿⣘⠀⡏⣿⣿⣿⣿⣿⣠⣀⣇⣼⣀⣄⣿⣿⣿⣿⣿⣿⠿⠸⣿⣿⠀⠀⠀ ⠀⣿⢡⠟⣸⣧⣿⣿⣿⢰⠀⠀⡇⢸⠀⠀⡄⣿⣿⣿⣿⣧⣽⢱⣏⣰⠀⠀⠀ ⠀⡂⣯⣿⣿⠙⣦⣿⣸⠀⠀⠀⠀⢸⠀⠀⠀⡄⣿⣾⢡⡿⣿⣿⣥⢻⠀⠀⠀ ⠀⠀⣀⣧⣿⣿⢿⡿⢻⠙⠉⠉⠟⢻⠉⠀⠉⠛⣿⡿⣿⣿⣾⣼⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⣷⣿⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⢛⢰⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣷⣿⣿⣿⣿⣻⣻⡿⣾⣶⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⠎⡆⣶⣶⣶⣿⣾⣾⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠯⠿⣿⣿⣿⣾⣠⣀⣤⣿⣿⣿⡿⣿⠙⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡤⣿⣿⣿⣿⣻⠉⣉⣙⢋⠟⣿⣿⣿⣿⢿⠰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡟⣾⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⢸⣀⣿⣿⣳⣾⣷⣿⢻⣧⣿⣿⡇⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣆⢿⡯⣿⣾⠳⣶⣯⢿⣿⡿⣿⣿⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⢳⣇⣿⣿⠻⣿⣿⣿⣿⣷⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣶⢿⡟⣿⣿⣯⣼⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡶⠲⡗⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀