⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⣀⠀⠀⣾⠏⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣎⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⣰⡟⠀⣸⡏⠀⠀⠀⣤⠀⣼⣳⡆⠀⠀⠀⠀⠀⢠⡄⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⣴⠆⣼⡿⠀⠀⠀⢠⣿⠁⢰⣿⠁⠀⠀⣸⡇⢠⡏⢻⡅⠀⠀⠀⠀⠀⣿⠃⠀⠀⣿⣷⠀⠀⣀⠀⠀⠀⠀⠘⣿⡄⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⢿⡇⠀⢿⣆⠈⣿⣜⣷⡀⣿⡆⠘⣷⠸⣧⢻⣞⣧⠘⢳⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⡍⠀⣾⠟⣿⣿⡿⢁⣾⠏⠀⡇⠀⣿⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠈⢻⣆⢹⡏⠙⣿⣼⣿⣄⢿⡆⣿⣆⠻⣿⣤⣿⡟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢺⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⣿⣿⡀⠀⢰⣿⣟⣵⣿⠁⠀⠀⠁⠀⢸⠀⣀⣤⡾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⡄⠀⠀ ⠀⠀⠀⠀⠀⢸⡟⠶⣦⣄⡀⠀⠀⠀⠀⠀⠘⠃⠀⢀⣽⣯⣷⡀⠈⢿⣿⣿⣮⢿⡽⣿⡆⠙⣿⣿⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣿⣿⡇⢠⣿⣿⠟⢻⡟⠀⠀⠀⠀⠀⢸⡟⠋⠉⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⢹⡇⠀⠀ ⠀⠀⠀⠀⠀⠸⣯⠻⢦⣍⠻⢶⣤⡀⠀⠀⠀⠀⠀⣼⠃⠈⠻⣧⠀⣾⠙⢿⣿⣿⣿⣿⣿⡘⠛⣿⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣿⡿⠿⠿⠛⢿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣼⠏⠘⠷⢿⡏⠁⢠⡿⠀⠀⠀⣸⠀⠀⢸⡇⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⢀⣠⡶⢟⣩⣶⢾⣿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣷⣦⣍⠻⢦⣌⡛⠷⣦⣄⡀⢸⡏⠀⠀⠀⠀⢸⡏⠀⠀⢻⡟⠻⣿⣿⣧⢀⡘⠻⣎⡻⣟⣋⣁⣀⣀⣼⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠏⣷⣶⡶⠾⣿⣿⣿⣿⡿⢛⣿⡿⠁⠀⠁⠀⠀⢀⡿⠁⢀⣿⠁⠀⠀⢀⡟⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣯⣶⣿⠿⣫⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣷⣍⠻⢶⣍⡛⠷⠦⢉⠛⢾⣤⣀⠀⠀⠀⣿⠁⠀⢠⡿⠁⠀⠈⠛⢿⣎⠁⠀⠀⠙⠋⠻⠿⣿⣯⣭⣭⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⢯⣿⡥⠶⠾⠛⠋⠀⠀⠀⠀⠀⢠⡾⠃⢀⣾⠃⠀⠀⢀⣾⠃⠀⠀⠀⣧⠀⠀⠀⣀⣤⡴⠟⠋⠿⢿⣿⡷⠛⢡⣼⡟⠁⠀⠀⠀⠀ ⣦⡀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀⠉⠛⢶⣄⡈⠳⠆⠈⠙⠳⢦⣼⡏⠀⢀⣾⠃⠀⠀⣾⠃⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⢀⣾⠃⠀⠀⣀⢸⡟⠀⢤⡀⠀⣧⣠⡴⠞⠋⠁⠀⣀⣤⡶⠛⠉⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀ ⠈⠻⣦⡀⠀⠀⠀⠀⠀⣼⣛⣿⣦⡀⠀⠈⠛⠶⣤⡀⠀⠀⢀⣿⠀⠀⣸⠇⠀⠀⣼⠇⠀⢠⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⢠⣿⢣⡾⢀⣼⠃⣾⠃⠀⢸⡇⠀⣿⠁⢀⣀⣤⡶⠟⠋⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣦⣠⣤⠶⠞⠛⠉⠛⢿⡿⢶⣄⡀⠀⠈⠙⠷⣦⣸⠇⠀⢠⡟⠀⠀⢰⡏⠀⠀⢸⠉⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⣰⣿⠳⠟⠀⠘⢁⢰⡟⠀⠀⠸⡇⠀⣿⠾⠛⠉⠁⠀⠀⠀⢀⣤⡾⠛⢿⡀⠀⠀⠀⠀⠀⠀⣀⠾ ⠀⠀⠀⠀⠈⠻⣦⠀⣀⣠⣤⠶⠚⣷⠀⠉⠛⠷⣤⣀⠀⢠⡟⠀⠀⣼⢁⡤⠀⣾⠁⠀⠀⣾⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠁⠀⢀⣴⣿⠃⠀⠀⠀⠀⣹⣿⠁⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⣀⣤⡾⠿⣏⣠⡶⠟⠛⠶⠶⢤⣤⣤⡾⠃⠀ ⠀⠀⠀⠀⠀⠀⣿⣈⠉⠉⣀⣀⣰⡏⣀⣀⣀⣰⣿⣙⣻⣾⣃⣀⣰⣏⣘⣃⣠⣏⣀⣀⣀⣏⣀⣀⣹⣧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⢤⣤⣤⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣯⣀⣠⣾⣿⣃⣀⣀⣀⣀⣰⣿⣟⣀⣀⡀⠀⣷⠀⣿⣠⣴⣶⠟⠋⠁⠀⠀⢻⣿⠀⠶⢤⣄⠀⢀⣾⠋⠀⠀⠀ ⣄⠀⠀⠀⠀⢸⡿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡁⢀⣠⣭⣽⣿⢻⣿⣫⣥⣄⡈⣻⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⢿⣿⣿⣷⣶⣶⣶⣦⣤⣿⣤⣤⣀⣀⣀⣸⡇⠀⠀⠀⠀ ⠙⠻⢶⣄⣀⡿⠀⠀⠀⠀⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⢙⡁⠈⣛⣿⣿⣿⡛⠣⣍⠃⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠛⠛⣧⢀⣠⡴⠞ ⠀⠀⠀⠉⢻⡟⠳⠶⢶⣤⣤⣀⣙⠻⠶⢦⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⢊⣵⠿⢫⡿⠉⢿⡿⣷⣌⠛⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠟⠉⠀⠀ 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⠀⠀⠀⠀⠰⠟⠁⢀⣼⢃⡀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⣼⣷⠀⠀⠀⣿⠈⠙⠻⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠛⣽⠇⣿⠀⣧⣿⡇⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠘⣷⣸⡏⠙⠻ ⠀⠀⠀⠀⠀⠈⢀⣼⠏⣼⠃⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⣴⠿⠶⠶⠶⠶⠟⢛⣿⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠟⠛⠉⠈⣷⣴⡿⠶⠿⠶⠶⠞⠻⡆⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⢹⣆⠀⠀⠀⠘⢿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠏⣼⠏⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢹⡷⠶⠶⠶⣶⠶⠻⣇⠀⠀⠉⠻⠿⣶⣦⣄⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠿⠛⠉⢻⡆⠀⠀⠀⣿⠿⣶⣤⣤⣤⡤⣶⢾⡇⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠘⣷⡀⠀ ⠀⠀⠀⠀⠀⣼⠏⣼⡏⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⣾⠁⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠿⠛⠛⠶⣤⣄⡀⠈⣿⠀⠀⠀⣿⠀⣿⠘⣷⠙⠀⣿⢸⡇⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠈⢻⣦ ⠀⠀⠀⠀⣼⠏⣸⡟⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇⠀⣰⡏⠀⢸⡇⠀⣾⠀⢸⣿⡀⠀⣀⣀⣀⣤⣤⡴⠶⠾⠛⠛⠻⢿⣶⣤⣀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠉⠛⠻⢿⣤⣀⡀⢸⣸⡇⠀⣿⠀⠀⣿⢸⡇⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠻ ⠀⠀⠀⣼⠏⢰⡟⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⢀⣠⣤⠶⠞⠛⠛⠋⠉⠉⠉⢹⡇⠀⣸⠃⠀⣾⠀⢸⣿⣏⣿⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠛⠛⠛⠒⠒⠒⠒⠒⠒⠚⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠏⠛⢳⣾⠃⠀⣯⠀⠀⣿⠘⣷⠤⠤⠶⠤⠬⢿⣦⣤⣤⣤⣀⣀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀ ⠀⠀⣼⠏⢠⡿⠀⠀⠀⠀⠀⠀⢠⡟⢀⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣿⠀⠀⣿⠀⢸⢹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⢿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢶⣤⣀⠀⢹⣧⣀⣀⣀⣀⡀⠹⣷⡀⠀⠀ ⢀⣼⠃⣠⡾⠁⠀⠀⠀⠀⠀⣀⣸⡷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡏⠀⠀⣿⠀⣾⣾⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⢸⡆⣿⠀⠀⠀⠀⠀⣿⡿⣿⠿⣿⣿⠟⣾⣿⡿⠿⠿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷

⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠿⠿⡿⣿⣾⠟⣿⣿⠿⣿⡿⣿⠀⠀⠀⠀⠀⣿⡆⢸⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⣾⣾⠀⣿⠀⠀⡏⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⡷⣸⣀⠀⠀⠀⠀⠀⠁⡾⣠⠃⣼⢀ ⠀⠀⡀⣷⠹⡀⣀⣀⣀⣀⣧⢹⠀⣀⣤⢶⠻⠙⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢿⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⢹⢸⠀⣿⠀⠀⣿⠀⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠾⣴⢀⡟⢠⠀⠀⠀⠀⠀⠀⡿⢠⠏⣼⠀⠀ ⠀⠀⠀⡀⣧⠹⠀⠀⠀⠀⠀⣧⢻⠀⠀⠀⠀⣀⣀⣤⣤⣤⣦⢿⠬⠤⠶⠤⠤⣷⠘⣿⠀⠀⣯⠀⠃⣾⢳⠛⠏⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠚⠒⠒⠒⠒⠒⠒⠛⠛⠛⠿⠿⠿⠿⠿⣿⣿⣿⣿⠿⠛⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⣿⣏⣿⢸⠀⣾⠀⠃⣸⠀⡇⢹⠉⠉⠉⠋⠛⠛⠞⠶⣤⣠⢀⠀⠀⠇⣸⠀⠀⠀⠀⠀⠀⡟⢰⠏⣼⠀⠀⠀ ⠻⠀⠀⠀⠀⣧⠹⠀⠀⠀⠀⠀⣇⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢿⠈⠀⠀⠀⡇⢸⣿⠀⠀⣿⠀⡇⣸⢸⡀⣀⣤⢿⠻⠛⠉⠀⠀⠀⠀⠀⠁⠋⠟⡿⣶⣤⣤⣤⣦⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣀⣀⣀⠀⠀⠀⣀⣤⣶⢿⠻⠛⠛⠾⠶⡴⣤⣤⣀⣀⣀⠀⡀⣿⢸⠀⣾⠀⡇⢸⠀⡏⣰⠀⡇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⣾⠀⠀⠀⠀⠀⠀⡟⣸⠏⣼⠀⠀⠀⠀ ⣦⢻⠈⠀⠀⠀⣆⠻⠀⠀⠀⠀⠀⣧⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢿⠀⠀⠀⡇⢸⣿⠀⠙⣷⠘⣿⠀⣿⠀⠀⠀⣿⠈⡀⣄⣤⠶⠛⠛⠿⣿⣶⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣄⣦⣷⠿⠛⠉⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠁⣾⠀⠀⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠁⡿⢠⠀⠀⠀⠀⠀⡏⣼⠏⣼⠀⠀⠀⠀⠀ ⠀⡀⣷⠘⠀⠀⠀⣧⢻⠀⠀⠀⠀⠀⣷⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢻⠀⠀⡇⢾⣶⡤⣤⣤⣤⣶⠿⣿⠀⠀⠀⡆⢻⠉⠛⠿⣿⣾⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⣄⣦⣶⠿⠻⠉⠀⠀⣇⠻⠶⣶⠶⠶⠶⡷⢹⠀⠀⡇⣿⢸⠀⠀⠀⠀⠀⠀⠀⡟⢰⠀⠀⠀⠀⠀⠏⣼⠏⣼⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⢿⠘⠀⠀⠀⣆⢹⠀⠀⠀⠀⡄⣷⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢹⠀⡆⠻⠞⠶⠶⠿⠶⡿⣴⣷⠈⠉⠛⠟⣿⣾⣴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⣿⢛⠟⠶⠶⠶⠶⠿⣴⠀⠀⡏⣿⠀⠀⠀⠀⠀⠀⠀⡏⣰⠀⠀⠀⠀⠀⠃⣼⠏⣼⢀⠈⠀⠀⠀⠀⠀ ⠻⠙⡏⣸⣷⠘⠀⠀⠀⣦⠹⠀⠀⠀⠀⡀⣷⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠘⠀⡇⣿⣧⠀⣿⠇⣽⠛⡿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⢿⠻⠙⠈⣿⠀⠀⠀⣷⣼⠀⠀⠀⠀⠀⠀⠇⣼⠀⠀⠀⠀⠀⠀⡀⢃⣼⢀⠁⠟⠰⠀⠀⠀⠀ ⠀⡀⣄⣦⠻⣧⠘⠆⠻⠀⣧⠹⠀⠀⠀⠀⡀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⠀⡇⢹⡏⠛⠿⣾⣴⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣷⠻⠛⠉⡟⢠⠀⠀⠀⠀⠀⠃⣾⢀⠀⠀⠀⠀⠀⠀⠃⣾⢀⠀⡀⢀⠀⠀⠀⠁⡾ ⠀⡄⢷⠙⣇⠀⣧⠹⣆⠻⠀⣧⠹⠀⠀⠀⠀⡆⢻⠀⠀⠀⠉⠉⠛⠛⠿⠿⡿⣿⣶⣴⣤⣀⠀⠀⠀⠀⠀⡄⣤⣤⣤⣤⠶⠶⠶⠶⠶⠓⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠚⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⣶⢿⠻⠛⠉⠀⠃⣾⢀⠀⠀⠀⠀⠀⠀⠁⣾⢀⠀⠀⠀⠀⠀⠀⠃⣼⠋ ⠀⠀⠀⣄⣧⢸⠀⣯⠹⡍⢹⠉⣯⠻⠛⠛⠛⠿⣷⣿⣿⣿⣿⣾⣶⣴⣤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠋⠛⠛⠒⠖⠶⠶⠶⠤⠤⡤⣤⣤⣠⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣶⣷⢿⠛⠙⠉⠀⠀⠀⠃⣾⢀⠀⠀⠀⠀⠀⠀⠋⣿⣼⢀ ⠛⠛⠉⠋⣿⣤⣤⣤⣤⣤⣥⣭⣫⣛⣟⠿⡾⣶⣴⣤⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠋⠛⠛⠛⠛⠾⠶⠶⠶⠤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠳⠛⠙⠉⣈⣤⣤⣶⠿⠻⣿⢙⠉⠀⠀⠀⠀⠀⠏⣼⡿⠀⠀ ⠀⡀⣀⣀⣦⠿⡶⣶⣶⣤⣤⣤⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠶⠴⠤⣤⣤⣠⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣤⢤⠶⠶⠒⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⢤⠶⠲⡛⣛⣍⣭⣦⣶⠷⠿⠟⣿⠙⣿⠙⠉ ⠀⠀⠀⠃⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠋⠛⠛⠛⠒⠶⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠟⣿⠈⠀⠀⠀⠁⠿⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣄⣤⣤⢶⠶⠲⠛⠛⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⢶⠶⡲⣿⣾⣠⠀⣀ ⠀⠀⠀⡀⢷⡿⠋⠛⠛⠛⠛⠛⠛⠛⠒⠒⠒⠒⠶⠶⠶⠴⠤⡤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠟⣿⢙⡌⢿⠈⠀⠁⡿⢠⣥⢿⠻⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⠒⠛⠛⠛⠛⠉⠉⠉⠉⡉⣀⣀⣤⣤⠦⠶⠓⠛⠙⠉⠉⠀⠀⠀⠀⠀⠃⣾⠀⠀⠀⠀ ⠀⠀⠉⠟⡿⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⠛⣌⣷⡿⢿⠉⡿⢫⠿⣵⢊⡃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣤⣤⣤⣤⣤⣤⢦⠶⠻⣙⣀⣤⣤⢶⠶⠳⡟⢻⠉⠀⠀⠀ ⠞⡴⣠⢀⣧⠛⠛⠛⠛⠙⠉⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⠃⣍⠣⡛⣿⣿⣿⣛⠈⡁⢙⣷⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠀⠀⠀⠀⡿⣀⣄⢶⠻⠙ ⠀⠀⠀⠀⡇⣸⣀⣀⣀⣤⣤⣿⣤⣦⣶⣶⣶⣷⣿⣿⢿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡏⣻⡈⣄⣥⣫⣿⢻⣿⣽⣭⣠⢀⡁⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠟⠿⠿⠿⡿⢸⠀⠀⠀⠀⣄ ⠀⠀⠀⠋⣾⢀⠀⣄⢤⠶⠀⣿⢻⠀⠀⠁⠋⠟⣶⣴⣠⣿⠀⣷⠀⡀⣀⣀⣟⣿⣰⣀⣀⣀⣀⣃⣿⣾⣠⣀⣯⣿⣿⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣤⣤⢤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣧⣹⣀⣀⣏⣀⣀⣀⣏⣠⣃⣘⣏⣰⣀⣃⣾⣻⣙⣿⣰⣀⣀⣀⡏⣰⣀⣀⠉⠉⣈⣿⠀⠀⠀⠀⠀⠀ ⠀⠃⡾⣤⣤⢤⠶⠶⠛⠟⡶⣠⣏⠿⡾⣤⣀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠁⣿⣹⠀⠀⠀⠀⠃⣿⣴⢀⠀⠁⣟⣴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠸⠀⣾⠀⠀⠁⣾⠀⡤⢁⣼⠀⠀⡟⢠⠀⣀⣤⠷⠛⠉⠀⣷⠚⠶⣤⣠⣀⠀⣦⠻⠈⠀⠀⠀⠀ ⠾⣀⠀⠀⠀⠀⠀⠀⡀⢿⠛⡾⣤⢀⠀⠀⠀⠁⠉⠛⠾⣿⠀⡇⠸⠀⠀⡟⢰⢁⠘⠀⠟⠳⣿⣰⠀⠀⠏⣾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠉⢸⠀⠀⡏⢰⠀⠀⡟⢠⠀⠇⣸⣦⠷⠙⠈⠀⡀⣄⢶⡿⢿⠛⠉⠛⠞⠶⣤⣠⣦⠻⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠟⣾⣠⠀⠀⠀⠋⠟⡶⣤⣀⢀⠁⣿⠀⡇⢸⠀⠃⣾⠃⣼⢀⡾⢣⣿⢠⠀⠋⡾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⢠⠀⠇⣼⠀⠀⠇⣸⠀⠀⣿⢀⠀⠀⡀⣤⠶⠛⠈⠀⡀⣦⣿⣛⣼⠀⠀⠀⠀⠀⡀⣦⠻⠈ ⠀⠀⠀⠀⠀⠀⠋⡾⣠⠀⠉⠛⡶⣤⣀⠀⠁⠋⠞⡴⣠⣧⠀⡀⢤⠀⡟⢸⣀⠀⠀⠃⣾⢀⠁⠟⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠃⣾⠀⠀⠃⣾⢀⠀⡏⣼⢦⠳⠙⠈⠆⠳⡈⣄⢶⠛⠉⡀⣧⢻⠈⠀⠀⠀⠀⠀⠀⡀⣦ ⠀⠀⠀⠀⠁⡟⣼⢡⠛⡷⣿⢿⠿⠋⠟⡴⣤⣀⠀⠀⠀⣧⠀⠀⠀⠃⣾⢀⠀⠀⠃⣾⢀⠃⡾⢠⠀⠀⠀⠀⠀⠋⠛⠾⠶⡥⣿⢯⠶⠻⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠟⡿⣿⣭⣭⣯⣿⠿⠻⠋⠙⠀⠀⠁⣎⢿⠛⠈⠀⠁⡿⢠⠀⠁⣿⠀⠀⠀⣀⣤⢾⠛⢉⠦⠷⡛⣍⢶⠻⣍⣷⠙⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⡿⣫⠿⣿⣶⣯⣿⣾⣤⣀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⡟⢀⠀⠀⠁⣿⢀⠁⡿⢀⠀⠀⠁⠀⠁⡿⣿⢛⡿⣿⣿⣿⣿⠾⡶⣶⣷⠏⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣿⣿⣿⣿⣿⣼⣀⣀⣁⣋⣟⡻⣎⠻⡘⢀⣧⣿⣿⠻⡟⢻⠀⠀⡏⢸⠀⠀⠀⠀⡏⢸⡀⣄⣦⠷⡛⣌⢦⠻⣍⣦⣷⠹⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⣿⢾⣶⣩⢟⡶⣠⢀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⡇⢸⠀⠀⣸⠀⠀⠀⡿⢠⠁⡏⢿⠷⠘⠏⣼⠀⡿⣿⣿⣿⣿⣿⣿⣿⢿⠛⠿⠿⡿⣿⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡀⣿⠛⡘⣿⣿⣿⣿⣿⢿⠙⣾⠀⣧⠻⠈⠃⣼⠀⠀⠀⠀⠀⡀⣤⢶⠻⣍⢦⠻⣯⠸⠀⠀⠀⠀⠀ ⠀⠀⡇⢹⠟⡶⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠋⡟⢸⠀⠀⠀⠀⠀⡟⢻⠟⣿⣿⢠⡇⣿⣿⢀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⠙⡆⣿⡽⢿⣮⣿⣿⢿⠈⡀⣷⣯⣽⢀⠀⠃⠘⠀⠀⠀⠀⠀⡀⣄⣦⠶⡟⢸⠀⠀⠀⠀⠀ ⠀⠀⡄⣷⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡾⣤⣀⠀⢸⠀⠁⠀⠀⠁⣿⣵⣟⣿⢰⠀⡀⣿⣿⠈⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢺⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡟⣿⣤⣿⠻⣆⣿⡆⢿⣄⣿⣼⣿⠙⡏⢹⣆⢻⠈⡄⣿⠘⠀⠀⠀⠀⠀⠀⠀⠏⣾⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡿⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀