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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⡿⠿⠿⢿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠿⠿⠿⣿⣷⣶⣄⠀⠀⠀⠀ ⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠁⠀⠀⠀⠀⠈⠙⢿⣿⣆⠀⠀⠀⠀⠀⢀⣼⣿⠟⠉⠀⠀⠀⠀⠀⠉⠻⣿⣷⡄⠀⠀ ⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⠀ ⠀⣸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⣴⣦⠄⠀⠀⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣴⣦⡄⠀⠀⢸⣿⣷⠀ ⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢠⣿⡿⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⣸⣿⣿⡇ ⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠃⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⣿⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣶⣤⣀⣀⣀⣀⣤⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣄⣀⣀⣀⣠⣴⣾⡿⠟⠀⣿⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠿⠛⠉⠀⠀⠀⣿⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇ ⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀ ⠀⠈⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣇⠀⠀⠀⠀⢀⣾⣿⠃⠀ ⠀⠀⠈⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⢠⣾⣿⠃⠀⠀ ⠀⠀⠀⠈⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⡿⠁⠀⠀⣠⣿⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⣠⣾⣿⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣀⣇⣄⠀⠀⠀⠀ ⠀⠀⠠⠚⠉⠀⠈⠙⠻⢶⣤⣤⣤⡀⡀⢠⠀⣤⣤⣤⣴⢾⠛⠉⡇⠉⠑⢲⠀⠀ ⠀⠀⠀⠀⠀⣀⠠⠄⠀⠤⢍⠙⠋⠐⠁⠀⠑⠉⠛⢉⠤⢼⣶⠤⡇⡇⠀⠘⠀⠀ ⠄⣀⣀⡒⢠⡽⠚⠉⠉⠑⢧⡕⠀⠀⠀⠀⠀⠀⠒⣭⠟⠉⠉⠛⠫⣧⣗⣧⣀⣠ ⠐⠒⠒⣻⡏⠀⠀⠀⠀⠀⠀⣻⡁⠀⠀⠀⠀⢀⡽⠁⠀⠀⠀⠀⠀⠘⣿⣟⠒⠛ ⠀⠀⠈⠩⠷⣄⣀⠀⠀⠀⠀⠂⠋⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⢀⣠⡴⠍⠉⠀⠀ ⠀⠀⠀⠀⠀⡇⣿⠠⡏⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠃⠣⠈⠂⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⡟⠀⠇⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢀⣀⣉⣁⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠓⠒⠀⠐⠒⠐⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⠿⠛⠋⠉⠉⠀⠀⠀⠈⠉⠉⠛⠻⣽⡛⠿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠛⢿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠟⢀⠤⠚⢉⣀⠉⣁⣀⣀⣀⡠⠤⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⢀⡤⠒⠊⠉⠉⠀⠀⠉⠉⠁⢀⣀⡀⠀⠀⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⣏⠀⣫⣶⣶⣶⣦⡀⠀⠀⠀⠐⣫⣥⣤⣈⡙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣟⣡⣾⡿⠛⠉⠉⠀⠁⠀⠀⠀⠈⠙⠛⠛⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⠟⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠙⢿⣦⣤⣄⡀⠀⠀⠀⣰⢿⣷⠈⣿⣸⣧⠀⣄⢻⣷⣖⣄⢹⣿⣿⣿⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⣀⠴⠋⠙⠺⢷⡄⠀⢀⣶⢯⣴⣒⣚⠒⠦⣀⠀⠉⠉⠹⢿⣆⠀⢰⢹⣏⣿⣧⣹⣿⣿⣷⣽⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⡇⣾⡟⠛⠛⢦⣄⢸⡗⠀⢸⢏⣹⡟⠉⠉⠙⢷⣌⢧⠀⠀⠀⠀⠙⠀⢸⣬⣿⣞⠿⣿⣞⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⠀⢸⡄⣾⣷⡆⢈⡿⠃⠀⢸⣾⣸⠇⣴⣶⣦⠀⠙⢮⣷⠄⠀⠀⠀⠀⠈⢿⣿⣿⡶⡌⢿⣷⢶⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⣾⣿⣿⠀⠞⠳⡿⣚⣵⠟⠀⠀⠀⠀⠙⣿⡠⠿⠿⠟⢀⣠⠴⣊⢙⣣⠤⠤⡀⠀⠈⢿⣿⣷⡘⢯⣿⣯⡿⡟⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀ ⠀⠀⠀⣼⣿⣿⡏⠀⠀⠒⠦⣼⠏⠀⠀⠀⢤⡀⠀⠈⢻⡆⠀⠀⠀⢠⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣽⣿⡟⢠⣾⣭⡕⣆⠻⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠉⠳⣄⠀⠈⠓⢦⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⠛⢦⣾⡙⠿⠹⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⣿⣿⣿⣿⠀⢀⡼⢹⣇⠀⠠⠾⢯⣀⣀⡀⠈⣿⣦⡀⠀⠉⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢹⣿⡇⠸⢿⣿⣦⠀⠹⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⣿⣿⣿⣿⣇⠘⠀⢈⣯⣛⢦⠀⠀⣉⣻⣇⠴⠃⠙⢻⣦⡀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⢸⣿⠇⠘⢳⣿⣿⠀⣤⣰⣿⣿⣿⣿⣿⣿⣿⣿⡀ ⢀⣀⣀⣿⣿⣿⣿⠙⠀⢀⣿⣿⣷⣿⡇⣼⢿⣿⣿⣿⣷⣤⣀⢹⣧⠀⠀⢳⠀⠀⠀⠀⠀⢀⣾⡿⠃⢀⣿⡟⠀⠰⠾⠟⣁⡼⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁ ⠀⠬⣽⠿⢫⣿⣿⠀⠀⢸⣿⣿⣿⣿⢤⣿⣄⣿⣿⣯⢿⣿⣿⣦⡙⠀⠀⠈⣇⠀⠀⠀⢠⡾⠟⢀⡴⣫⠞⠀⠠⠤⠴⠞⢉⣴⣿⣿⣿⣿⣿⣿⣏⣿⣿⠏⠀ ⠀⠀⠀⠾⠿⠟⣿⡇⠀⣿⣿⣿⡿⠟⠈⢿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣆⠀⠀⢻⠀⠀⢠⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⡇⠀⣿⣿⣿⣧⡤⢤⣤⣬⠭⢭⣘⣷⠹⣿⣿⣿⣿⡀⠀⣾⠀⠀⠀⣇⠀⠀⠀⠀⠀⠈⣷⣤⣶⡿⣻⣿⣿⣿⣿⡿⠿⠟⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⡄⢻⣧⠋⢿⢷⣄⢙⣁⡀⣨⣍⣹⣦⣿⡇⡇⣿⡇⢠⠃⠀⠀⠀⡏⠀⠀⠀⠀⠀⢀⣿⠋⠁⠀⠉⠀⢩⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⢿⡃⠈⢻⣿⠯⠽⡿⢛⡽⠟⠛⠿⡖⢱⠛⡷⠈⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠉⢀⠀⣗⣚⣾⡤⠈⠀⠔⣲⠞⠁⠀⢸⡇⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⡀⠈⣇⠉⠉⠉⠙⠒⠚⠉⠀⢀⡴⠃⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡇⠈⠳⠶⠶⠶⠶⠦⠶⠚⠁⠀⠈⠀⠀⠀⠀⠀⢀⡀⢀⣠⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣀⣤⡾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣤⣤⣤⣤⣤⣴⣾⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⣀⣤⢤⣶⣶⣿⣥⣄⣐⠀⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣶⣿⣿⠿⣉⠉⠁⠶⠚⡎⠉⡿⣻⢭⣉⠉⠉⠻⠯⣙⡒⠒⠻⠿⠭⣗⣶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠹⣹⣿⣿⣦⣼⡃⣀⣠⠶⠿⡎⠳⣌⠀⠈⠲⣄⠀⠀⠀⠉⠲⢆⡀⠀⠀⠉⢉⡻⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣝⡿⣿⣈⡽⣿⣆⠀⠀⠻⣄⠈⢄⠀⠀⠘⢄⠀⠀⠀⠀⠀⠉⠳⢄⠀⠀⠻⡄⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⣻⣿⣅⣽⣿⡆⠀⠀⠈⢦⠀⢢⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⢘⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣡⣄⡉⢻⣷⡄⠀⠀⠀⠑⣄⠳⡀⠀⠀⠈⠱⢄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠘⣿⣟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠿⠋⠙⠳⣆⢿⣿⣆⠀⠀⠀⠈⠳⡵⡄⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠘⡶⠛⢿⡞⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⢀⠀⠀⠘⢧⣻⡝⣧⡀⠀⠀⠀⠘⢾⡆⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⠀⢻⡆⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠸⣿⣷⣄⠀⠀⠙⢿⣽⣄⠀⢄⡀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢸⡇⠀⠸⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⡇⠀⣸⠻⣿⡗⠀⠀⠀⠙⣮⣤⣀⠈⠂⠠⠘⢻⣢⡀⠀⠀⠀⠀⠀⠙⠄⠀⠀⣿⠇⡆⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣷⢠⣿⣟⠘⣿⠆⠀⠀⠀⠈⠓⠮⣟⢲⣤⣀⡈⣻⡷⣤⡀⠀⢠⠀⠀⠀⠰⢼⡇⢰⠇⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡿⠘⣿⠉⣠⡶⠀⠀⠀⠀⠀⠀⠀⠈⢳⣿⠽⣿⣷⡋⠟⣿⣦⣤⢀⠀⠀⢠⡟⣄⡜⠀⠀⠀⣯⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⠁⢠⣵⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢈⣣⡹⣿⢽⡇⠉⠙⢦⣀⡟⢀⡼⡇⠀⠀⠀⢿⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⠋⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠻⡯⠴⣆⡾⢿⠀⠀⣤⣿⡤⠊⠀⠸⡄⠀⠀⠘⡏⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⣷⣀⣠⡴⢻⣿⠈⣦⣴⡿⠘⠀⠀⠀⠀⠱⡄⠀⠀⣿⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⢿⣷⣶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠉⠁⠀⠈⣿⣶⠻⡏⠀⢠⡀⠀⠀⠀⠀⡱⠀⠀⢹⠀⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⣴⣿⡆⠀⢧⠀⠀⠱⣆⠀⠀⠀⢣⠀⠀⠸⡄⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠿⢶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢰⡟⠈⣷⠀⠈⣆⠀⠀⠘⢆⠀⠀⠸⡆⠀⠀⣧⢻⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⢸⣧⢀⡿⣆⢀⠙⡀⠀⠀⠈⢇⠀⠀⣇⠀⠀⣿⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⢸⣿⢏⡼⠛⣆⢧⣷⠀⠀⠀⠘⢆⠀⢻⠀⠸⢹⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠨⣿⣿⢁⠀⠉⢾⠈⢧⡀⠀⠀⠸⡄⠘⠀⠀⢿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣫⠟⠁⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠾⣿⣻⣀⠀⠈⢷⡀⠙⡄⠀⢀⢳⡀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠛⣧⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣡⡄⠀⠀⢻⡆⠘⡆⠀⠎⣇⠀⠀⢸⣿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⠶⠖⢋⣿⡇⠀⠀⠀⢀⡴⠂⠀⠀⠀⠈⢿⣿⣗⡀⠂⠀⢻⡀⠘⡆⠰⣹⠀⠀⠈⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⠀⢀⡴⠋⠀⠀⢀⣴⣶⣶⣼⣿⣿⣷⠄⠀⠀⢿⡀⢹⡄⢼⠀⠀⠰⣿⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡴⠋⠀⠀⢀⡾⠛⠓⠒⣒⣿⣯⣟⣿⣿⠇⢀⣸⡇⠈⠇⢸⡇⠀⠈⡟⠰⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⢀⡼⠋⠘⢁⣴⡯⠅⣈⠀⠈⢿⣿⣯⣄⠀⢿⠀⢸⠀⠁⠀⠀⠀⠀⢱⡝⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⢠⡿⠁⢀⡼⣫⠇⠀⠀⠀⠀⠀⠀⠸⣿⡎⠀⢸⠀⠀⡆⠀⠀⠀⠀⠀⠀⠱⡌⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⠀⢀⣿⠃⢠⡎⡼⠃⠀⠀⠀⠀⠀⠀⠀⠈⢿⢿⡖⠘⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢱⡄⠙⢦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡿⠀⠀⢀⣼⡏⢖⡏⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⣿⡄⢸⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢣⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠁⠀⢀⡾⣼⠁⣼⠁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⡇⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠙⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⣻⣿⠗⠂⣠⢛⠊⢸⠀⡟⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣹⣿⡆⢠⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠙⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠈⠙⠚⢧⠁⠀⠸⡄⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⢻⡇⠘⡆⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠘⣆⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⡇⢸⡇⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠹⡄⠀ ⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠎⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣸⡇⣸⠃⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢷⠀ ⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⡟⢠⡏⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠘⡄ ⠀⠀⠀⠀⠘⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡿⣾⠃⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡟⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀

⠙⣿⣿⡿⡏⠉⢻⡏⠉⠉⢻⣿⣏⡍⠉⠉⢹⢻⢻⢹⢻⠉⠉⠉⡏⢿⠋⠉⠉⠉⠉⢹⣟⡟⡿⠋⠉⣙⡛⢟⡟⠋⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠚⠛⠛⠛⢳ ⠀⢸⣼⣷⣃⠀⠸⣿⡀⠀⠸⣿⣾⠃⠀⠀⢈⣸⣘⣸⣼⢤⣄⣀⣁⣼⣀⣀⣤⣀⣀⠒⠾⠶⠀⠀⠀⠒⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠉⠋⠉⠀⠀⢻⡇⠀⠀⠃⠉⢀⣤⠶⠛⠋⠁⠀⠀⢀⣀⣈⣉⣷⣍⠳⣄⠀⠉⠙⠶⣄⣀⡀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⣠⡴⠋⢁⡴⠊⠀⠀⣠⣴⡿⠉⠀⠀⠀⢻⠀⠙⣦⣀⠀⠀⠈⠑⣝⠲⣤⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡾⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣴⠋⠀⠀⣠⢞⡷⠋⠀⢀⠀⠀⢀⡿⠀⢀⡇⠈⠳⣄⠀⠀⠈⢦⣹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⣠⠞⠁⠀⣠⠞⠁⠙⠀⠀⣠⠟⢀⡴⣻⠁⠀⣼⠀⢤⡀⠘⢧⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⢠⡞⠀⢀⡾⠁⠀⠀⠜⠁⠀⠀⣀⣤⣺⠵⢛⡿⣡⠋⠀⣰⠏⠀⠀⡿⣦⠀⢻⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⢀⡞⠀⢠⡞⠁⠀⠀⠀⠀⢀⣤⠾⠛⠋⠀⣠⠟⣠⠋⠀⣠⠋⠀⠀⣰⢣⠈⠷⡀⠻⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⣼⠁⢀⡞⠀⠀⠀⢀⡤⠚⠉⠀⠀⡼⠁⣴⠋⠰⠁⠀⣴⠃⠀⠀⣴⠃⠘⢀⠀⣿⡄⢻⡸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⢰⡟⠀⡸⠁⠀⠀⡀⠀⠀⡖⠀⢀⡾⢁⡼⠁⠀⠀⣠⠟⠀⠀⣠⠞⢰⠀⠀⣿⠀⣿⠻⡄⢿⣷⠀⠀⠀⠀⠀⠀⠀⣴⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⡼⡇⢰⣧⠆⢀⡞⠁⠀⡾⠀⢀⡞⣠⠞⠀⠀⣠⠞⠁⢀⣠⣾⠃⠀⣾⠀⢸⡇⠀⡏⠀⣿⠘⡏⢧⠀⠀⠀⠀⠀⠚⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⣼⣷⡇⠸⡜⠀⡼⠁⠀⢸⠃⢀⡞⠀⠀⠀⣠⠞⢁⣤⠞⠋⢠⠏⠀⠀⡏⠀⡿⠀⣼⠀⢀⡟⣧⣿⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⡸⣧⣿⣧⢠⡇⢸⡇⠀⠀⡆⢀⡞⠀⣀⣴⣾⠵⠚⣹⠁⠀⠀⣾⠀⠀⢰⠁⣼⠁⠀⣽⠀⣼⡀⠸⣸⠀⠀⢿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⣸⡿⢻⣿⠉⢸⢃⣿⠀⠀⠸⠁⣾⣠⠞⠛⠉⠀⣠⣾⡿⠀⠀⣸⣿⠀⠀⣿⣴⠃⠀⣠⠏⣾⡿⣷⠀⡇⡆⠀⠘⡄⠙⢷⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸ ⠀⠉⠀⣸⢹⠀⢸⢸⢻⡆⠀⢀⢸⣿⠁⠀⠀⢠⣾⠟⠋⡇⠀⢠⠏⠞⠀⣸⡟⠁⠀⣰⣯⣾⠟⠚⠙⣇⢸⠃⠀⠀⣷⠀⢸⢻⣯⠙⢛⡷⢲⣶⡄⠀⢰⠂⠀⠀⠀⠀⠀⢸ ⠀⠀⢀⡏⢸⡀⢸⡘⢸⡇⠀⢈⣯⡇⠀⠀⣴⠻⠴⠶⣦⡇⢀⠟⠀⠀⢠⠟⠀⣠⡞⣵⣿⡽⠶⡶⣄⣽⡼⡄⢠⠀⣿⠀⢸⢿⠹⣆⠀⠀⠀⢸⠃⣰⠏⠀⠀⠀⠀⠀⠀⢺ ⠀⠀⠸⢣⡿⡇⢸⡇⠈⡇⠀⢸⡟⠀⢀⡾⠁⠀⣴⣤⡌⣿⡞⠀⠀⢀⡟⡠⢚⣿⠟⣽⠃⣠⣶⣆⢹⣿⡗⡇⣸⢀⡟⡆⢸⣿⠀⠘⠆⠀⢠⣏⡵⠃⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠉⣿⠁⠘⡇⠀⢱⠀⢸⠃⢠⠟⢷⣄⠀⠙⠋⠀⣾⣷⠀⢀⡿⠈⣠⠟⠁⠸⣇⣀⠈⢉⣅⣨⠟⣿⠀⡿⣸⠁⡇⣾⣿⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⢸⠀⠀⠣⠀⠈⠃⡿⢀⣿⠀⠀⠈⠛⠒⠒⠒⠉⠈⣠⠟⢀⠛⠁⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⣿⣰⡷⡟⣸⣧⠇⠹⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⢸⡆⠀⢸⡄⠀⠀⣿⡼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢤⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢡⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠸⡇⠀⣼⡇⠀⠀⢸⣇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠇⣾⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘ ⠀⠀⠀⠀⠀⣧⢸⣿⣿⡄⠀⣼⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⡇⣿⠿⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠀⠀⠀⠀⠀⠹⡾⢸⠀⢳⡀⣿⠀⡿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠦⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣸⣿⠋⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⢧⣿⠀⠈⢳⡿⣇⢷⡹⡻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣿⠉⣿⠈⠀⠀⠀⠀⠀⠸⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠉⠹⣇⢷⡳⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠀⠀⠛⠀⢹⡀⠀⠀⠀⠀⠀⠀⢹⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠀⠀⠀⠀⠀⠀⠀⣼⣷⠀⠀⠀⠀⠙⠈⢷⡀⠀⠀⠙⠿⣷⣦⣀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡟⠀⠀⠀⠀⠀⠀⣧⠀⠀⡀⠀⠀⠀⠈⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⢸⣻⣇⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠈⠛⢿⣿⣷⣶⣶⣿⣿⣿⣿⠏⢀⣀⣀⣀⣠⣤⣤⡿⣻⠋⠙⠳⢤⡀⠀⠈⠻⣿⣾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠸⡆⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡿⣿⠏⣰⠋⢥⡤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡐⢯⣿⡌⢧⡀⠀⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣽⢦⡀⠀⠀⠀⠀⣼⡿⠛⠁⢀⡟⡼⠁⠀⠘⠀⠀⡏⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣮⣻⡄⠳⣄⠀⠀⠀⠀⠀⠸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⡟⠈⠳⡄⠀⠀⠉⠁⠀⠀⠀⣿⠾⣅⢀⠀⠀⠀⡌⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠙⠻⣆⠹⣦⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⣴⣿⠇⢸⠁⠀⠀⠙⣶⠦⠄⠀⠀⠀⣴⣿⣼⣥⢫⠀⣀⡤⡀⢀⣼⡿⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠈⢷⡌⣗⠀⠀⠀⠈ ⠸⡄⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠉⠉⣿⠁⠀⢺⣷⣄⠀⠀⠈⢷⣀⠀⠀⣾⠟⠀⠰⣷⣿⠞⣿⣶⡽⠋⣿⣵⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠈⣆⠀⠹⣾⡆⠀⠀⢈ ⡀⠘⣆⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠹⠀⠀⠀⠙⣿⣷⣦⠀⠀⢻⣦⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠸⡆⠀⠘⣿⡀⠀⢠ ⠹⡄⠘⢦⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣦⠀⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⡄⠀⠸⣧⡀⠈ ⠀⠹⣆⠘⢧⡀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠈⡇⠀⠀⡏⢧⡀ ⠀⠀⠘⢦⡈⢧⡀⠀⠐⡆⠀⠀⠙⢦⠀⠀⠀⠀⠀⡀⠀⠀⠹⣿⣿⣿⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⢿⣻⣿⣯⠀⠀⢸⠃⠀⢐⡇⠈⢷ ⠀⠀⠀⠈⢳⣎⢧⡀⠀⢳⠀⢸⡆⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠈⢻⣿⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠙⣿⣄⣴⡏⠀⠀⠀⠃⠀⢘ ⠀⠀⠀⠀⠀⠙⣾⣧⠀⢸⡇⠈⣇⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⢻⡄⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⢿⡏⠀⠀⠀⠀⠀⠀⢼ ⠀⠀⠀⠀⠀⠀⢸⣿⣇⣾⡇⠀⢹⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⠁⠀⠀⠀⠲⣄⠀⠐ ⠀⠀⠀⠀⠀⠀⠈⢻⡻⣿⣿⠀⢸⡇⠳⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⣆⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡆⠀⠀⠀⢈⠊⠑⢠ ⠀⠀⠀⠀⠀⠀⠀⠈⢷⣿⣿⡇⠀⣷⣄⡈⠈⠉⠀⠀⠀⠐⠒⠒⠶⠾⣧⡘⢷⣀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣀⠀⠸⠆⢧⠀⠀⠀⠠⠑⢄⢰ ⠤⠤⠤⠤⠶⠶⠶⠶⣾⣿⣿⠷⠶⢿⠿⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⠾⠷⣶⡿⠷⡾⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠷⠿⠶⠶⠶⠾⠶⠶⠶⢶⠶⡶⠾

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠿⠟⠛⠋⠉⠉⠙⠛⠻⢿⡿⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠙⠻⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⠟⣀⠄⠂⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⠏⣠⠔⠒⠛⠃⠈⠉⠉⣀⣀⡀⠀⠙⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⡿⣨⣷⣿⣷⠦⠀⠀⠀⣨⣵⣦⣬⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣧⣀⠀⠀⠀⠀⢀⢰⡆⣤⣤⡀⠀⢀⡄⣀⢸⣿⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⠁⣀⠔⠒⠺⣦⠀⢀⣴⣯⣤⡶⠤⣀⠈⠛⠻⢷⡄⢠⢸⡾⣷⡸⣿⣷⣼⣾⣯⣿⣿⣿⣿⣿⣷⡀⠀⠀ ⠀⠀⠀⠀⢀⡿⢺⠟⢛⠲⢄⣹⠂⢸⣉⣿⠋⠉⠙⢮⢦⠀⠀⠀⠑⠘⣾⣿⡝⢿⣾⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀ ⠀⠀⠀⢠⣾⡇⢸⣼⣿⡇⡰⠃⠀⠘⢷⡟⣸⣿⡆⠀⢹⠷⣄⠀⠀⠀⠹⣿⣿⠢⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣷⠀ ⠀⠀⢠⣿⣿⠃⠀⠬⣭⡿⠁⠀⢀⠀⠈⠻⡌⠉⠀⢈⡴⠖⠊⠉⠁⠀⠀⠘⢿⣷⣿⣿⠏⣵⣒⢌⢻⣿⣿⣿⣿⣿⣿⡆ ⠀⠀⢸⣿⣿⡀⠀⢀⣼⠁⠀⠀⠀⠙⠢⣀⠈⠒⢤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⣼⡛⠛⢣⠀⣿⣿⣿⣿⣿⣿⠃ ⠀⠀⢸⣿⣿⣇⠠⠊⢳⣄⡐⠛⠦⣤⡀⣸⢷⣄⠀⠙⣆⠀⠀⠀⠀⠀⠀⢀⣾⠛⣿⡇⣻⣿⡇⠀⠂⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⢸⣿⣿⡿⠄⢠⣾⣿⣿⣄⣴⣿⣷⣧⣀⠙⣷⠀⠘⡄⠀⠀⠀⠀⣠⣾⠃⢰⡿⠀⣸⡿⢃⡔⣼⣿⣿⣿⣟⣿⣿⡇ ⠨⠭⡿⢿⣿⡇⠀⣸⣿⣿⣿⣽⣿⣿⣿⣿⣿⣷⣜⠃⠀⢱⠀⠀⠀⡰⠟⢁⢔⡽⠁⠠⠤⠖⢋⣼⣿⣿⣿⣿⣏⣿⡿⠀ ⠀⠀⠘⠛⠛⣿⠀⣿⣿⡏⠏⠘⠿⣿⡿⣿⢻⣿⣿⣧⠀⢀⡇⠀⢠⠀⠀⠀⠀⠀⡀⠀⣀⣴⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀ ⠀⠀⠀⠀⠀⢿⡀⣿⡿⢷⣖⠲⠖⠒⢒⠻⣌⣿⡿⣿⡆⢸⠃⠀⢨⠇⠀⠀⠀⠀⣿⠿⠛⠛⠛⢿⣿⠋⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣧⠘⡷⠈⢿⣿⠿⡷⢟⡿⠿⢿⡖⠿⡧⠀⠀⠀⣸⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣧⠈⠀⡸⣗⣻⡥⠅⢠⡲⠎⠀⢰⡇⠀⠀⠀⠃⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠳⣀⣀⡈⠉⠁⣀⠔⠃⠘⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢀⣴⡦⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⣠⡾⠶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣶⣶⣶⣶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠛⠫⡉⢛⢛⡷⠶⠦⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡏⠀⠀⠀⠀⠀⢈⣼⣁⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⡀⠀⡠⠒⠉⠉⠀⠀⠉⠙⠢⠀⠀⡎⠈⢧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠏⠀⠔⠳⣤⠁⠀⠀⠀⠀⠀⠀⠀⣔⡠⠚⣦⠀⠸⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠃⢀⠌⢀⠴⢶⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠘⢧⠀⢿⠀⠀⠀ ⠀⠀⠀⠀⢀⠏⢀⠆⠐⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠛⠋⠉⠙⠂⠘⡄⢸⡀⠀⠀ ⠀⠀⣀⠀⡸⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⡇⠀⠀ ⠀⡜⠉⠑⢧⡘⠀⠀⠀⡠⢒⡦⡀⠀⠀⠀⠀⠀⢀⠠⢄⡀⠀⠀⠀⠘⠄⡇⢀⡀ ⠸⠀⢧⡀⠀⠀⠀⠀⣆⠱⢽⡥⠃⠀⠀⠀⠀⠀⢸⣜⣓⡝⢀⠀⠀⠀⢸⠞⠁⢱ ⡆⠀⡨⣇⠀⠀⠀⠀⠀⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠊⠀⠀⠀⠀⢀⡄⠈ ⣇⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠘⢦⣧⣀⣀⣀⣄⡠⠀⠀⠀⠀⠀⠀⠀⠀⡏⠇⢸ ⠘⠶⠖⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⡀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣶⣾⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⣾⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣿⠿⣛⠭⡥⠤⠤⠬⣭⣛⠿⡀⠀⠀⠀⠀⠀⡟⠀⠀ ⠀⠀⠀⣿⡀⠀⠀⠀⠀⠸⣕⣹⣀⠠⠷⠲⠤⢧⣀⡉⠛⡇⠀⠀⠀⠀⣰⡇⠀⠀ ⠀⠀⠀⡟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⣠⠃⡇⠀⠀ ⠀⠀⠀⢧⠈⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⢰⠀⠀⠀ ⠀⠀⠀⢸⡀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⡜⠀⠀⠀ ⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠶⠶⠖⠒⠊⠉⠀⠀⠀⠀⢰⠃⠀⠀⠀ ⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⡾⠿⠿⠿⠟⠻⠿⠿⠿⢶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠛⣉⠡⠠⢀⡠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⣁⠄⢊⡡⠔⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢉⠔⢊⠤⠂⠁⣠⡶⠟⠛⠓⠦⠀⠀⠀⠀⠀⠀⠀⠴⠞⠛⠛⢶⣤⠀⠀⠀⠀⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⠟⢁⠔⡡⠊⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⡿⠃⣠⡡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀⠀⠀⠀ ⠀⠀⢀⣾⡟⠁⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠿⣿⣶⣤⡀⠀⠀⣠⣶⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀ ⠀⠀⣾⡟⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠁⠀⠀⠀⠈⠻⣷⣤⣾⡿⠋⠁⠀⠀⠉⠻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀ ⠀⣸⣿⠁⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⠏⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀ ⢠⣿⡇⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄ ⣸⣿⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢠⣼⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⡆⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠙⠋⠁⠀⠀⠀⢠⠀⠀⠀⠀⠈⠛⠁⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣀⠀⠀⠀⣀⣴⡿⠙⣿⣦⣀⠀⠀⠀⢀⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⡿⠟⠋⠀⠀⠘⣿⠿⠿⣷⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏ ⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣼⣿⠃ ⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣰⣿⡟⠀ ⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣠⣿⡿⠀⠀ ⠀⠀⠈⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⣰⣿⡿⠁⠀⠀ ⠀⠀⠀⠈⢻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⣾⣿⡟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢁⣴⣿⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⣠⣴⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣷⣍⡀⠒⠤⠤⢀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⠠⠄⠒⠈⢁⣠⣴⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣶⣦⣤⣀⣀⣈⣉⠈⠀⣀⣀⣀⣀⣤⣤⣶⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣠⣤⣿⣤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠛⠛⠛⠛⠛⠿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⠿⠛⣿⠛⠛⡟⠻⢦⣀⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣷⣶⣤⣤⣤⣤⣤⠀⣀⣀⠀⠀⣦⠀⢀⣦⣤⣤⣦⣴⣾⣿⣿⣿⡿⡟⠉⢸⠀⠀⣿⠀⠀⡇⠀⠀⠈⢻⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⡟⠀⣼⠟⠀⠀⢻⣆⠀⢿⣿⣿⣿⣿⣿⠿⠋⠁⢀⣷⠀⢸⠀⠀⣿⠀⢰⠃⠀⡀⠀⣾⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⠶⠶⠶⠦⣄⣀⠈⠉⠉⠉⠉⠀⠞⠉⠀⠀⠀⠀⠙⠆⠀⠉⠉⠉⠉⢀⣀⣤⠶⢾⣿⡶⣿⠦⢄⣿⠀⢸⠀⠀⠃⠀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣋⡉⢀⣠⣴⣶⣤⣤⣀⠈⣹⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣍⠁⣠⣬⣿⣧⣿⣆⡀⣿⣃⣾⠀⢸⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠲⣤⣤⣄⣠⣽⣿⠟⠛⠉⠉⠉⠉⠻⢿⣧⣄⣨⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣅⣠⣽⡿⠛⠋⠉⠉⠉⠛⠻⣿⣯⣽⣧⣼⡦⠖⣿⡀⠀⠀⠀⢀ ⠉⠛⠓⠲⢶⣶⣤⣤⣤⣤⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣧⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣼⡟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣿⣤⣼⣿⣶⣶⠿⡿⣿ ⠐⠶⠦⠤⣤⣤⣤⣤⣬⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣿⣿⣾⡶⠷⠿⠿ ⠀⠀⠀⠀⠀⢀⣀⣠⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣌⣿⣠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠉⣹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⣽⢹⠠⠦⡀⠀⠀⠀⠠⠀⠄⠀⠿⢻⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠋⠉⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⠋⢹⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣿⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡏⢸⣿⣿⡇⠀⣶⡇⢶⡆⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠴⣦⠸⣧⠀⠉⢿⡋⠀⠛⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠈⡇⠈⡇⢸⣟⠸⢿⡇⢸⣧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠻⠀⠻⣶⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠰⠇⠀⡇⢸⡇⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠸⡇⠀⢸⡇⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⡇⠀⠀⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣠⣤⡴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠁⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣴⠞⠛⠓⠲⠶⠖⠛⠛⠉⠙⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣠⡤⠶⠶⠶⢦⣤⣀⣀⣀⣀⣠⡾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⣀⣀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠉⠁⠀⠉⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⣀⣤⣤⡀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣵⣄⠩⢖⠍⠂⠌⠉⠩⢉⠙⢳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⣳⢿⣇⠈⠂⠀⠀⠂⠀⠀⠁⠀⠳⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠟⠑⢽⣦⠀⠑⢦⠀⠈⠠⡀⠀⠀⢱⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡄⣲⣌⠙⢷⡄⠄⠱⡄⠀⠈⠢⠀⢸⣧⢻⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⡧⢙⠀⠀⠙⠳⣦⣽⠶⣄⠀⠀⡎⡀⠈⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⡠⠀⡻⠁⠀⠀⠀⠀⡇⠜⣙⣧⢉⣞⠜⠂⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⠸⢤⡤⠀⠀⠀⠀⠀⠀⢸⠒⠙⡿⡞⢀⠀⠈⠀⢠⢷⠀⠀⠀⠀⠀⠀ ⠀⠸⢄⠀⠀⠀⠀⠀⠀⡸⠀⡜⣇⠰⠀⠣⠀⠄⠸⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢱⡀⠀⠀⠀⡰⠁⠀⢿⡙⢖⢆⠀⢡⠐⢰⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢾⡃⠀⠀⡜⠀⠀⠀⠘⣦⠀⠢⠢⠀⠆⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⠒⠈⡇⢀⠔⠀⣀⣹⣧⡀⢣⢡⢨⠀⡏⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡶⠁⡠⢏⣩⠛⠻⣷⡈⡆⠈⠀⠁⢱⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡾⠁⡼⡠⡟⠀⠀⠀⠸⣇⢃⢠⠀⠀⠀⢎⢂⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⠁⡸⢃⠹⠀⠀⠀⠀⠀⢸⡌⠨⠀⠀⠀⠀⢂⠁⡀⠀ ⠀⠀⠀⣴⠟⠙⠊⠀⢼⣇⠀⠀⠀⠀⠀⢸⠃⠀⠆⠀⠀⠀⠀⢂⠡⡀ ⠀⠀⢸⠃⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢸⡌⡆⠀⠈⢂⠀⠀⠀⠀⡆⢡ ⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢺⡙⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀

⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣤⣶⣿⠿⠟⣛⣷⠾⣬⣿⠶⠶⠶⣶⢶⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢾⣿⣿⣬⣷⢀⣠⡼⣖⠫⡙⠙⠢⡀⠈⠉⠒⢤⡀⠉⠙⢛⡿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠻⣿⣯⣭⢿⣆⠀⠘⢆⠑⡄⠀⠘⢄⠀⠀⠀⠈⠑⠄⠀⠙⣌⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡿⠷⠾⣿⡄⠀⠈⠳⡘⢄⠀⠀⠱⢄⠀⠀⠀⠀⠀⠀⠈⢦⢻⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⡿⠛⠷⡼⣿⣆⠀⠀⠈⢮⣦⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠈⣧⠿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⠀⣀⡀⠘⠾⢟⣧⡀⠀⠀⠙⢷⡀⠀⠀⠀⠑⢤⡀⠀⠀⠀⢹⡆⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡄⢙⣿⣦⡀⠀⠻⣿⣄⠒⠄⠈⠻⣤⠀⠀⠀⠀⠙⢦⠀⠀⣸⡇⡆⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⡇⣸⡇⢻⡧⠀⠀⠈⠻⢷⡦⣤⣁⡙⣷⣄⠀⠀⡀⠀⠁⢤⡿⢸⠁⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⡇⢻⡏⣰⠆⠀⠀⠀⠀⠀⠘⣿⡿⣿⣿⣛⣿⣦⣅⠀⠀⡼⢥⡞⠀⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡼⠀⠺⡿⠁⠀⠀⠀⠀⠀⠀⠀⢿⡇⣮⠧⡙⣻⣇⠈⠑⣾⢡⠞⢇⠀⠀⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⠚⠁⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠞⣧⡈⣉⣿⣯⢻⣠⡿⠛⠁⠀⠘⣆⠀⠘⡟⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⢷⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡉⠁⠈⣿⡞⣿⠀⢄⠀⠀⠀⢘⠀⠀⣷⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣴⢻⡆⠸⡄⠀⠱⡀⠀⠘⡆⠀⢹⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣿⢸⣷⠀⢳⠀⠀⠙⡄⠀⢷⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣷⡄⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⣿⣎⠞⢧⣫⣇⠀⠀⠹⡄⢸⠀⢾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡸⣿⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⢻⣯⡄⠀⢻⡈⢧⡀⠀⢱⡈⠀⠘⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⠿⡅⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠈⣿⣷⡀⠀⠹⣄⠱⡄⢠⢧⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠦⠴⠖⣻⣿⠀⠀⢀⡴⠂⠀⠀⠈⣿⣿⡢⠂⠸⡆⢱⡀⣼⡀⠀⣿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢀⡴⠋⠀⣠⣴⣿⣿⣿⣿⣿⣂⠀⢹⡄⢷⢸⡇⠀⣿⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⢀⡶⠯⢊⣤⡛⠋⠛⣿⣿⣖⠚⣧⢸⡌⠃⠀⠋⠈⢽⢆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⣰⡏⢀⣴⡿⠁⠀⠀⠀⠈⢹⣿⠀⣿⠀⢰⠀⠀⠀⠀⠈⢎⠳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⢠⡟⣠⢎⡞⠀⠀⠀⠀⠀⠀⠘⣿⣇⠉⡆⢸⠀⠀⠀⠀⠀⠈⢦⠘⢆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⢠⣿⠋⡞⣼⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⡆⠁⢸⡄⠀⠀⠀⠀⠀⠈⢣⡈⠳⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⡿⠆⡴⡗⢸⢸⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⡇⣹⣷⠀⡀⣇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠱⡄⠀⠀ ⠀⠀⠀⠀⣰⣿⠟⠁⠉⠛⠚⠀⠘⢾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⢹⠀⠇⠘⡆⠀⠀⠀⠀⠀⠀⠀⢳⡀⠹⡄⠀ ⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣏⣿⠀⠀⠀⠀⠀⠀⠀⢸⢇⡟⣸⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⢧⠀⢳⠀ ⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⣼⣸⢣⡏⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⢸⡆⠘⡇ ⠀⠀⠀⠘⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢠⢿⣏⡾⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛⠛⠛⠻⢿⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡾⠡⢀⠀⣀⡀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀ ⠀⠀⠀⣾⣑⣥⣄⠀⠀⣰⣖⡀⠈⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀ ⠀⠀⢸⡷⠋⣀⡀⠀⢀⠀⠉⠛⢦⣄⠀⢀⢰⢲⣆⢀⣄⣼⣿⣦⡀⠀ ⠀⠀⢨⠧⢞⡠⣹⠀⣟⡟⠓⢕⡀⠈⠁⢣⣟⢿⡿⣿⣿⣿⣿⣿⣷⠀ ⠀⢠⣿⠐⡼⣧⠂⠀⠹⡽⠟⠠⣙⠦⠄⠈⢿⣗⣿⡿⣛⢿⣿⣿⣿⣇ ⠀⣼⣿⠀⣠⠃⢀⠈⠢⡀⠢⡊⠀⠀⠀⠀⠀⣿⡟⣼⡛⠅⣿⣿⣿⣟ ⠀⢸⣿⡆⢠⣗⡄⣹⣦⡙⢦⠈⠆⠀⠀⢀⡼⢹⡇⣻⠇⢤⣿⣿⣿⣿ ⠉⢛⣿⡀⣾⣿⢿⣿⣿⣿⣷⡃⠘⠀⠀⠚⠅⠟⠀⠐⣪⣿⣿⣿⣽⠏ ⠀⠀⠈⡇⣿⢧⡠⠍⠩⢏⣿⢿⢰⠃⢸⠀⠀⠀⡶⠾⠿⣿⠟⠋⠀⠀ ⠀⠀⠀⢱⡘⠈⡟⣻⠋⢛⡓⢻⠂⠀⡌⠀⠀⡸⠁⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⢱⡈⢍⣉⣀⡉⠔⠘⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⣰⣤⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠛⠶⠶⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠴⠒⠛⠛⠋⠉⠉⠉⠉⠉⠛⠛⠛⠒⠦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠠⠴⠶⠶⠤⣀⢀⡠⠴⠶⠶⠒⠒⠒⠶⠶⠤⣄⣀⠤⠶⠶⠦⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡏⠁⢀⣀⡠⠤⢤⣀⡀⠀⠈⠻⣦⠶⠖⠒⠒⠒⠒⠲⢦⡴⠋⠁⠀⢀⣀⡤⠤⣄⣀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⠖⠛⠉⠉⠙⠳⢶⢋⡞⠁⠀⠋⠀⠀⠀⠀⠀⢀⣤⠴⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⢦⣤⠀⠀⠀⠀⠀⠀⠳⣄⡀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⢀⡟⠀⣠⡶⠟⠋⠉⠀⣠⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠈⠉⠛⠦⡀⠙⢦⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣻⣡⠞⠉⠀⠀⠀⣠⠞⠁⠀⢀⡴⠖⠒⠶⢄⡀⠀⠀⠀⠀⢀⡠⠖⠒⠲⢤⡀⠀⠙⢷⡀⠀⣀⠈⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣦⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⢠⠞⠉⣠⠟⠀⠀⣰⠋⠀⠀⠀⠀⠈⢳⡄⠀⠀⣠⠎⠀⠀⠀⠀⠀⠻⡄⠀⠀⢱⡀⠈⠲⡄⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⡿⠀⢠⡇⠀⢀⡟⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢷⠀⠀⢻⣆⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠳⠦⠤⠤⠤⠟⢷⢰⠇⠀⠀⠸⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠸⠀⠀⠈⠹⣇⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠿⠏⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⣠⣶⣤⣤⠇⢸⠀⣾⣧⡄⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠸⠶⠬⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡄⠀⠀⠀⠀⠙⠿⣿⣽⡆⠸⣄⣻⠿⠃⠀⠀⠀⠀⢸⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⢙⣣⡄⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⢀⡴⠛⠋⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⣤⣔⠛⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⡠⠎⠀⠀⠀⠀⠀⠀⠀⠈⠋⠈⠁⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⢀⣀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⢀⣤⣀⣀⣀⢀⡀⠀⠀⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢯⡿⠓⠒⠦⠤⠾⠃⠀⠉⠑⠚⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠒⠲⠤⠴⠋⠀⠈⠉⠉⠙⢯⡽⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠙⢦⣄⡀⠀⠀⢀⣤⡔⢃⣀⣀⡀⠀⠀⠙⢢⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠈⢉⣛⣿⠽⠛⠛⠉⠁⠀⠉⠻⣄⠀⠀⢻⡀⠀⠀⠀⠀⢨⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⣠⣴⠞⡋⠉⢀⣀⣀⣀⣀⣀⣠⣤⣤⣼⣧⠀⠈⡇⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡴⠋⠀⠀⠀⠀⣼⠃⠀⠀⢀⣴⣿⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢰⠇⠀⣠⠖⢦⡀⠈⢧⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠋⠉⢻⡄⠀⠀⠀⠀⢰⡟⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⡄⠀⠈⠛⠋⠀⠉⠛⠦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⢸⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙⢧⣀⠀⠀⠀ ⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠈⢱⡄⠉⠻⣿⣿⣿⣿⠁⠀⠀⠀⢻⡀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⠀⠀ ⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇⢀⣀⣀⣠⣤⣤⣀⣀⢘⣿⣿⡇⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀ ⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠃⠀⠀⠀⢀⣤⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃ ⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⠀⢻⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⢘⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣤⡖⠲⢤⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠤⠤⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠤⠀⠤⠄⠀⢀⠀⢰⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡀⠀⠀⢰⠁⠨⡦⠐⠀⠉⠉⠁⠀⠒⠩⡀⠀⠈⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⡆⢈⡴⠂⠁⢆⠀⣑⣤⡠⢠⢔⣈⠀⠁⠲⡌⣦⡀⠈⢄⠀⠀⠀⠀⠀ ⠀⠀⣠⡞⠀⠒⢄⠈⠢⢃⠀⡆⢸⠀⠀⠈⢂⠀⢸⡴⠈⢂⠈⠆⠀⠀⠀⠀ ⠀⠔⡝⡤⢊⠧⣄⡁⢀⠈⠂⠘⢅⠈⠑⡄⠀⢁⡸⠃⣇⠈⠀⠘⡀⠀⠀⠀ ⠊⢹⢳⠃⡌⢀⢤⢀⣿⣷⡢⠄⠈⠶⣦⠶⠒⠻⢤⣤⣸⠀⠀⠀⢡⠀⠀⠀ ⠀⢸⠸⡄⡇⢢⡼⠾⠞⠋⠀⠀⠀⠀⠈⠀⠀⠀⣀⠉⠉⡆⠀⠀⠀⡄⠀⠀ ⠀⢸⡆⡻⠗⡿⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⠀⠀⠀⠃⠀⠀ ⠀⢸⢯⠌⠀⠀⠀⠐⠀⢀⠤⠤⣄⡀⠀⠀⠀⠐⠂⢄⠀⢰⠀⠀⠀⢠⠀⠀ ⠀⢸⠈⠆⡄⠀⠀⠀⠰⠿⠛⠒⠚⠛⠓⠂⠀⠀⠀⠀⣰⢿⠀⠀⠀⢸⠀⠀ ⠀⠘⠀⠈⢣⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣤⠾⢃⡼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡶⢤⡤⣀⣀⣀⣀⡀⢀⠎⣠⠾⠇⢚⡉⠏⡄⠀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⢰⠈⠉⠁⠒⠚⢐⠿⢛⠉⠡⠤⠰⢙⣾⡼⠥⡇⠀⠀⠀⠃⠀ ⠀⢀⠀⠀⠀⠈⡀⠀⠠⣔⠈⡄⡤⢃⡡⠕⠂⠉⠀⠀⡏⠆⠃⠀⠀⠀⢠⠀ ⠀⠀⠀⠀⠀⠀⢁⢠⠊⠏⠁⢣⠞⠁⠀⠀⠀⠀⠀⠀⣿⢴⢸⠀⠀⠀⠀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠂⢈⣁⣦⣀⡠⠒⣒⣦⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠁⠀⠀⠀⠈⠙⡄⠀⠀⠀⠙⢄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⡤⠀⠀⠀⠀⠀⣤⣦⣽⠀⠀⠀⠀⠘⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡔⣄⠀⢣⡀⠀⢢⡀⠐⣏⢹⣿⡀⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠙⠿⣿⣶⠿⠶⠾⠿⠒⠛⢏⠀⠈⢢⠀⠀⣸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⣰⡿⠛⠉⢣⠀⡴⠛⠳⣌⡆⠀⠈⡇⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⢠⡏⠀⢀⣄⡀⣷⢁⣄⠀⠘⣿⠀⢀⡇⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⠤⡏⢳⣀⠘⢛⡽⠋⢿⡛⠀⣠⢿⣠⣿⠃⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣦⡉⠛⠛⠉⠁⠀⢀⠙⠛⠃⡾⢶⠏⠀⠈⢆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡞⢠⠋⣽⣀⠀⠈⠷⠶⠟⠀⢰⠻⡇⢸⢧⠀⠀⠀⠑⢒⠎ ⠀⠀⠀⠀⠀⠀⠀⡼⢁⠎⣰⠋⣽⠀⠀⠀⠀⠀⢰⢿⡀⢳⠸⢼⠀⠀⠀⢠⠎⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⡘⢰⠃⢠⠇⠀⢠⣾⣷⠀⢸⡀⣇⠸⡄⢺⣧⠴⠒⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣇⠀⠁⠀⡟⠀⠀⢸⣿⣿⠀⠀⡇⠹⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠊⢳⣄⠘⢧⡀⠀⠈⠙⠛⠀⠀⡇⠀⠀⢠⢧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠊⢀⠴⠋⠉⠃⠀⣹⢷⣤⣤⣤⣤⠾⡇⠀⠀⠾⡄⠙⣄⠀⠀⠀⠀ ⠀⠀⢠⣾⣶⠖⠁⠀⠀⠀⢀⣼⣯⠾⣧⢀⣼⠵⣦⣻⡄⠀⠀⠹⣤⣘⡄⠀⠀⠀ ⠀⢀⠞⠋⠀⠀⠀⠀⠀⢀⡞⠉⠁⠀⠘⠿⠃⠀⠈⠛⣿⡄⠀⠀⠙⣿⣏⠀⠀⠀ ⢠⠏⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠈⢻⣄⠀⠀ ⢸⠀⠀⠀⠀⠀⣀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠙⣇⠀ ⠈⠳⠤⠤⠶⠞⠋⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⢦⡀⠀⠀⡸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠉⠛⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣤⣀⣀⣀⣀⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠄⠀⠀⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠐⠈⠤⢄⡀⠤⠤⠤⠤⣀⠤⠄⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⡠⠒⠒⠠⡚⢀⣊⠉⢀⠤⠚⠁⠀⠀⠙⠢⢄⠈⢁⡢⡐⡄⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⢰⡔⠉⢀⠜⢁⠄⠂⢄⠀⢀⠄⠒⢄⠑⢄⢀⠀⠱⡀⠀⠀⠀⠀⠀ ⠈⠢⣀⣀⣸⡠⠁⠎⢀⠃⠀⠀⠀⡆⡆⠀⠀⠀⢆⠈⠀⠱⡀⢡⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⠚⠃⠀⠀⠘⡀⠀⠰⣶⡆⡷⡶⠀⠀⡸⠀⠀⠀⠑⠣⡀⠀⠀⠀⠀ ⠀⠀⠀⢣⠈⠢⠀⠀⠀⠡⣀⠔⠁⠀⠀⠁⡆⡠⠁⠀⠀⠐⠊⢠⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⢰⠦⠤⠴⠒⠨⢆⠀⠀⠀⢀⠦⠤⢔⠒⠒⢦⠐⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣀⠀⠀⢀⠜⠀⠀⢑⡲⠖⠓⠂⠒⡄⢡⠀⠀⢵⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡠⡌⠃⠀⡜⠀⣠⣾⣷⣶⣶⣾⣿⣿⣿⠘⠀⡆⢄⡦⢀⠀⠀⠀⠀ ⠀⡰⠈⠀⠀⠑⢄⠀⠇⢸⣿⣿⣿⡿⠛⠿⢿⣿⣿⠀⠀⠡⠀⠀⠀⠈⠢⡀⠀ ⡜⠀⠀⠀⠀⠀⡠⠃⠀⢸⣿⣿⠿⠤⠀⠒⠀⠽⠇⠀⢀⡇⠀⠀⠀⠀⠀⠈⠄ ⠀⠀⠀⠀⠀⠀⠘⢄⠀⠈⡟⠁⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⢂⠀⠀⠀⠀⠀⠀⠀⠀⢡⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⢀⠀⠀⠀⠀⠀⡔⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠔⢂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⣀⣀ ⠀⢻⡿⣁⠀⢿⡄⠀⢻⣿⠰⠀⠀⠇⣾⢸⡇⠀⠸⠘⠇⠀⠀⠀⢘⣺⡙⠁⠀⡛⢡⠏⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹ ⠀⠈⠿⠋⠀⠸⣧⠀⠸⠋⠂⣀⡴⠖⠋⠉⠉⢉⣙⣻⣝⢯⡉⠙⠲⢥⣀⡀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠉⠀⢀⡴⠊⢁⠔⠀⢀⣴⡾⠋⠀⠀⢹⠀⢱⢄⡀⠀⠙⢯⠲⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠇⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⢀⡔⠉⢀⠔⠁⢀⡴⢫⠋⠀⢠⠀⣠⡞⠀⡼⠀⠙⢦⠀⠀⠣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⢠⠎⠀⡴⠃⠀⡰⠋⠀⠀⣠⣔⠥⡾⡱⠁⢠⠃⠈⣦⡀⠳⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⢀⠏⠀⡞⠀⠀⠀⠀⣠⠴⠛⡋⢁⠞⡰⠁⢠⠋⠀⢠⢧⢸⢆⠱⡀⡇⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⣼⠀⡜⠀⠀⠀⠔⠉⠀⢀⡜⢠⠋⠐⠀⡴⠁⠀⡠⠋⠘⡼⢸⢧⢹⣱⠀⠀⠀⠀⠀⠀⣀⣩⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⢠⡇⢰⡁⠀⡰⠀⢠⠃⢀⠎⡴⠁⠀⣠⠞⠀⣠⠞⢁⡇⢠⡇⢸⠈⣆⢿⣇⠀⠀⠀⠀⠴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⢀⣾⡇⣎⠇⡸⠁⢀⠏⢀⠞⠈⠀⣠⠞⣡⠔⠋⡞⠀⢸⠁⡸⠀⡎⢀⡿⣼⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⢀⣾⣾⣧⢸⢠⡇⠀⡸⢀⡞⢀⣴⠮⠒⣩⠇⠀⣰⠇⠀⡎⢰⠃⢀⡇⣼⡄⢣⡇⠈⡗⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺ ⠀⠞⠁⣿⠀⡎⡞⡄⠀⠁⣾⠖⠉⠀⣠⡾⢿⠀⢠⢿⠀⢰⡷⠃⢀⣞⣼⠫⢿⠘⡇⢠⢸⠀⢹⣷⡦⠤⢄⣀⡀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⢸⢹⡀⡇⠇⡇⠀⣻⡟⠀⢀⡴⣩⣤⣸⠀⡎⠀⢀⡞⠀⡠⣯⣿⡧⣤⣈⣇⡇⢸⢸⡆⢸⣿⢧⠈⠁⠈⡇⢠⠇⠀⠀⠀⠀⢸ ⠀⠀⠘⣼⡇⢹⠀⡇⠀⡿⠁⢠⠟⠀⣰⣤⢹⡜⠀⢀⣜⠴⣺⠟⡿⠁⣴⡧⢹⣿⡇⡸⣸⡇⢸⡿⠀⠳⠀⣸⡵⠃⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⢸⠀⠸⠀⠸⢀⡇⢠⠏⠻⢤⣈⣀⡸⠸⢀⡞⢡⠞⠁⠀⠳⠤⠦⠶⠚⢹⢃⡇⡇⡧⡏⣇⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⢸⡄⠀⡇⠀⠸⣧⢿⠀⠀⠀⠀⠀⠀⠀⠎⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⡿⢸⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⡇⢠⣷⠀⠀⡏⣌⡆⠀⠀⠀⠀⠀⠀⠀⠹⠿⠖⠀⠀⠀⠀⠀⠀⠀⢸⡟⠣⡇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⢷⡼⡟⡆⢠⡇⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣼⣇⣧⠟⠛⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠀⠀⠀⠀⠈⣧⡇⠘⣼⣇⢸⢻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⠞⡿⣿⠻⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣇⠀⠈⠘⣎⢧⠇⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠃⢸⡀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠐⣿⡄⠀⠀⠈⠈⢧⠀⠀⠈⠻⣶⣤⣀⠀⠀⣀⣴⣾⡿⠁⠀⠀⠀⠀⣧⣀⣀⡀⠀⠀⠙⣿⣧⡀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠿⢳⠀⠀⠀⠀⠀⢳⡀⠀⠀⠈⠛⢿⣿⣿⣿⣿⡿⢡⢶⣒⠒⠒⠚⠋⠂⠀⠈⠑⢤⡀⢩⣿⡵⡄⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣙⣄⠀⠀⠀⢠⡿⠟⠉⣸⡳⠋⠀⠃⢩⠓⡄⠀⠀⠀⠀⠀⠀⠉⠲⣯⣻⡌⢦⠀⠀⠀⠀⠰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡏⠈⢢⡀⠈⠉⠀⠀⢰⡗⡧⡠⠀⠀⠌⠀⣼⡄⠀⠀⠀⠀⠀⠀⠀⠸⡭⠻⣌⠳⡀⠀⠀⢨ ⢠⠀⠀⠀⠀⣀⠀⠀⠀⠰⠶⣾⠋⢠⣇⠀⠀⠹⡅⠀⠀⣠⡿⠛⣟⣵⣤⣎⢆⣼⣏⣽⡀⠀⠀⠀⠀⠀⠀⠀⢇⢠⠈⢳⣳⠀⠀⠀ ⠀⠱⡀⠀⠀⠈⢦⠀⠀⠀⠀⢹⠀⠀⠻⡷⣄⠀⠙⣦⣰⠏⠀⠀⠉⠁⠈⠛⠁⠘⠛⠛⢳⡀⠀⠀⠀⠀⠀⠀⢸⠀⢣⠀⠻⣇⠀⢀ ⠘⣄⠱⡄⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⣘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⡇⠈⣆⠀⢹⡄⠈ ⠀⠘⢆⠹⡄⠀⠀⡀⠈⠢⡀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠤⢤⣤⣤⣴⠇⠀⡼⠀⢸⠘⣄ ⠀⠀⠈⢳⡙⡄⠀⢣⠀⡄⠈⠂⠀⠀⠀⢦⠀⠀⠻⣿⡙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡝⣿⣀⣰⠃⠀⠸⠀⠸ ⠀⠀⠀⠀⠹⣽⡄⢸⠀⢹⠀⠀⠀⠀⠀⠀⠣⠀⠀⠘⡇⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⢿⠏⠀⠀⠀⠀⢼ ⠀⠀⠀⠀⠀⢺⢷⣾⡇⠸⡜⣄⠀⠀⠀⠀⠀⠀⠀⠀⡿⡀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⠀⠀⠈⢲⢄⠀ ⠀⠀⠀⠀⠀⠀⢯⣿⣧⠀⣧⡈⠂⠂⠠⠄⠀⠀⣀⣀⣇⢳⡀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⡟⡄⠀⠀⡠⣀⠰ ⠠⠤⠤⠤⠤⠤⢬⣿⣿⠤⢿⠿⠧⠤⠤⠤⠤⠤⠤⠤⠬⠧⡭⠷⡼⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠮⠷⠤⠤⠥⠤⠤⠤⠬⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠈⠳⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠊⠉⠙⠛⠉⠉⠙⠓⠒⠒⠢⠤⠤⣤⣀⠀⠀⠀⣾⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⠞⢁⠄⠀⢀⣠⠤⠴⠶⠒⠶⠶⠶⠤⣀⣈⣉⠑⠲⠿⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⣀⠞⢻⡇⠀⠀⠸⣤⣣⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⣀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠈⠳⣄⡀⢀⡔⢁⡴⠟⣧⠀⠀⠀⠘⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠢⠤⣄⡀⡀⠈⣳⣄⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡏⠀⠀⠈⣩⣿⠞⠉⠀⠀⠸⣇⠀⠀⠀⠀⠙⠦⣄⠀⢀⡴⢦⣤⠚⠉⠀⠀⠀⠀⠀⠀⠉⢮⣦⡀⢹⢷⢤⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠃⠀⢀⣞⡵⠋⠀⠀⠀⠀⠀⠸⣆⠀⠙⡶⠒⠒⠒⢛⡎⠀⠘⡇⠶⠖⠒⠲⢤⡀⠀⠀⠀⠀⠹⣵⡈⣎⢣⠳⣄⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⣠⢯⠏⠀⠀⡖⠲⢄⡀⠀⠀⠘⢧⠀⢳⠀⠀⠀⢸⠁⠀⢠⡇⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⢻⣽⠘⡆⢣⠈⣦⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡴⣳⠇⠀⠀⠀⣇⠀⠀⠙⣄⠀⠀⠀⠳⣌⢧⠀⠀⢸⡄⢀⣼⠀⢀⣀⡀⠀⠀⠀⠀⠸⡄⠀⠀⢸⡇⡇⢹⠈⠆⠘⡆⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡞⢡⡏⢠⢂⠖⠙⠺⣆⠀⠀⠈⢆⠀⠀⠀⠈⠛⢧⡀⠀⠳⠛⡇⠀⠏⠀⠙⢷⡄⠀⠀⠀⢻⠀⠀⣼⣿⠁⠈⣇⠀⠀⠁⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠋⢠⡿⢠⣮⠟⠀⢠⠎⠉⢳⡶⣤⡼⠀⢀⣀⠀⠀⠀⠈⠀⠀⠀⢧⠀⡄⠀⠀⠀⢿⡄⠀⠀⠀⡇⣰⡿⠃⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀ ⢀⡼⠗⠚⣿⡇⣜⡞⠀⢀⠏⠀⠀⠀⢧⠀⠀⢀⣿⡇⢹⣦⣀⠀⠀⠀⠀⠘⣷⣄⣀⡀⠀⣸⣇⣀⣤⣴⣿⣋⣀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⣿⡇⠀⢸⠀⠀⣴⠖⢿⠀⠀⡾⡞⡿⡜⣏⣨⠴⠚⠁⠀⠀⠈⠳⠿⣿⠟⠛⠛⠋⠉⠉⠚⠟⣚⣺⠿⣟⣛⣿⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⣿⡅⠀⣾⠀⢠⡇⠀⣼⠀⡸⣽⣵⣷⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠒⠩⠗⠦⢿⡀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⢟⣇⠀⢧⠀⠘⣧⣰⣿⡴⠿⠽⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⣜⢿⣦⣸⣄⣀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⢤⣀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠈⠳⣿⡿⠟⢋⡷⠓⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢾⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣇⣠⠞⣵⠀⠤⠜⠁⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀ ⠀⠀⠀⠀⡿⣿⠁⢰⠃⠀⠀⠀⠀⠀⠀⠈⠓⢤⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⢤⣀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⢸⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡶⢋⣉⣀⣀⣩⣵⡒⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⢰⠇⠀⢻⡆⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⣼⣼⣿⣋⣭⠤⠴⠶⠶⠿⠷⠿⠿⠷⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠈⠻⡄⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠹⣇⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⡀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢷⣄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⣢⣾⣿⠿⠋⢀⣴⡯⢾⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⣿⣷⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⢀⣾⣿⠟⠁⢠⣴⣯⡼⣤⠌⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢻⣿⡛⠿⠿⣷⣶⣦⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢸⣽⡿⠿⠞⠋⠉⠁⠀⠀⢿⢠⣇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠙⠳⢤⣶⠭⣒⣂⠈⠉⠉⣍⣉⠛⠿⠿⣿⣷⣶⣿⣥⠶⠞⠋⠉⠀⣀⡠⢤⡀⢸⡏⢻⣄⣼⡖⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠀⠉⣉⣽⠿⠟⠋⠁⠀⢀⣀⡤⢤⣀⣹⠀⠈⢛⣻⣧⣤⣧⣼⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀ ⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠉⠁⣠⡤⠲⡄⢀⣸⡇⠀⠈⣉⣥⡤⠖⠚⠛⢿⡿⣍⠁⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⢀⣠⣄⠀⣹⠄⠀⢙⢩⣵⡶⠟⠋⠉⠀⠀⠀⠀⠀⢘⣧⠘⣆⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠛⢉⣹⣦⣀⠀⢯⠀⠙⠊⢁⣠⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⢹⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⣠⠞⠉⣰⠋⠈⠙⢾⡁⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣧⡀⡇⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢠⣿⡀⢾⡃⠀⠀⠀⠋⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⢻⠙⣷⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⣦⣄⣀⣀⣀⣀⡤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠉⠀⠀⠀⠀⠀⢨⠏⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⢀⣠⠤⠚⠋⠁⠀⣿⣠⠴⠂⢀⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⣭⠵⢒⢾⣿⠀⠀⢸⡅⣠⠶⠋⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⢀⣤⣶⣫⣽⡦⣄⠀⠀⣷⣧⢶⣿⣂⡀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡾⠀⠀⠀⠀⠘⠟⣋⡥⠶⠛⠉⠉⣀⣴⢿⣿⣿⣿⡲⠾⠆⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠚⠛⠉⠀⠀⠁⠈⠉⠙⠛⠳⢦⣄⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀ ⠀⠀⢀⡏⠀⠀⠀⠀⠀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠘⣇⠀⠀⠀ ⠀⠀⣸⠁⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⢹⡆⠀⠀ ⠀⠀⣿⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⣇⠀⠀ ⠀⠀⣿⡀⠀⢠⡟⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡿⠀⠀ ⠀⠀⠘⣇⠀⡟⠶⠋⠉⠙⠛⠻⠶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡶⠶⠿⠓⠦⣾⠀⠀⢰⡇⠀⠀ ⠀⠀⢸⢹⠀⡇⠀⠀⠀⣠⣤⢤⣤⣤⠈⠁⢀⠀⠀⠀⠀⠀⠐⠫⣝⣷⣷⣶⣀⠀⠀⢸⠀⠀⣼⠁⠀⠀ ⠀⠀⣿⡏⢸⠁⠀⠀⠈⢿⣍⣽⣿⡍⢣⣀⠀⢳⠀⠀⠀⡾⢩⡽⢿⣽⣭⣉⢿⠀⠀⢸⠀⠀⣿⡆⠀⠀ ⠀⢸⣿⡇⢸⡇⠀⠀⠀⢈⠙⠿⠟⠁⠛⢱⠆⢸⣦⠀⠀⠀⢾⠙⠺⠿⠿⠟⠋⠀⠀⢸⡇⢸⢹⡇⠀⠀ ⠀⠈⣿⠇⢸⣇⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠁⠀⠀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⣸⡇⠀⠀ ⠀⢰⣿⢀⠈⢿⠞⣷⡦⣀⢸⣹⡍⠳⢄⡀⠀⡀⠀⠀⣾⢻⣳⣤⡤⣄⡀⠀⠀⠀⠀⣸⠀⠀⣿⡇⠀⠀ ⠀⠈⡟⢸⠀⢸⣷⡞⠁⠘⠳⢿⣄⠀⠀⠙⠶⠧⢤⣤⣿⣄⡈⠉⠀⠈⠋⠳⣄⡀⢸⡏⢲⠂⠘⣧⠀⠀ ⠀⢰⡇⢸⠀⠈⢷⡟⢦⣀⠀⠀⠈⢷⣄⢰⡶⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⠤⣬⡙⢾⡇⠈⠀⠀⢸⡄⠀ ⠀⡾⠁⡜⢸⠀⠸⡟⢄⠈⠳⣄⢠⣄⠉⠻⠶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢳⠀⠀⣤⠀⣿⠀ ⢀⡇⠀⠇⣸⢠⠀⢻⡈⠳⣄⠈⣿⠣⢄⡀⠀⠀⠈⠙⠓⠒⠶⠒⠂⠳⣄⠀⠀⠀⠀⠸⡆⠀⢹⠀⢸⡆ ⠀⣧⠀⠀⡇⢸⠀⠀⢳⡀⠙⢷⣇⡴⠀⠉⠳⢤⡀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣇⠀⢸⠀⢸⡇ ⠀⠹⣧⠀⠇⢸⠀⠀⠈⣿⣦⠀⠙⢿⡢⣄⠀⠀⠉⠓⠀⠈⠳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡿⠀⢸⡇ ⠀⠀⠘⢷⣄⢸⡇⠀⠀⣿⠈⠳⣄⠀⠙⢎⡙⠂⠰⣄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⡿⠀ ⠀⠀⠀⠀⠙⠻⢿⣤⠀⣿⡄⠀⠈⠳⢦⣀⠙⢦⣄⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠓⠟⠀⠀⠀⠀⠀⠀⠉⠙⠛⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠠⣤⠤⢤⠤⣤⡤⠤⣤⢤⠤⠤⡤⠤⠤⣤⡤⢤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤ ⠀⠻⠂⠸⡄⠙⢁⠤⠚⠚⣑⣒⣗⢖⠒⠭⣀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠂⡡⠊⡠⠞⢁⠀⡜⢸⠐⢄⠀⢽⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⢸ ⠀⠀⠀⡰⢁⠎⠀⠊⣀⡴⢒⠪⠁⠆⢰⢌⢂⢸⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⢸ ⠀⠀⢠⠁⠂⠀⠄⠊⠠⡠⠃⢁⠊⡠⠂⡌⣧⢻⡀⠀⠀⢀⣸⠁⠀⠀⠀⠀⠘ ⠀⠀⣼⢸⢀⠂⡘⠠⠑⢁⢔⡡⡚⢁⢀⢃⠃⣟⡷⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀ ⠀⡼⡿⠸⡎⠠⢱⡡⠞⢋⡏⢠⡇⢘⠌⠠⣴⡜⡇⢹⠢⣀⠀⠀⠀⠀⠀⠀⠘ ⠀⢀⢃⢠⠃⢠⡟⢀⠴⠭⡇⠎⢀⠋⣰⡿⢭⣱⡇⢨⡄⡿⡍⠉⡇⡄⠀⠀⠠ ⠀⠀⠟⢸⠸⢸⢡⠮⡐⠃⣿⢀⢞⠝⠹⣐⣻⠟⣇⡹⣧⡇⠈⡰⠋⠀⠀⠀⠘ ⠀⠀⢠⢈⡀⢸⢾⠀⠀⠀⠀⠢⣆⠀⠀⠀⠀⠀⣿⢣⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣼⢇⢸⢸⡀⠀⠀⠀⠀⢁⡀⠀⠀⠀⢠⣧⡷⠣⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢻⠀⠺⡼⡗⢤⡀⠀⠀⠀⠀⠀⢀⡔⠙⢙⠁⠀⠈⢷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣇⠀⠈⠱⡀⠙⠲⣤⣀⣠⣶⡟⠀⢀⣈⣤⠄⡀⠈⢿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠀⠀⠀⢑⡄⠀⠈⡿⠟⣟⠈⠛⠲⠄⠀⠀⠀⠑⢼⣻⢢⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⡴⢻⠈⢢⠀⠀⣰⢿⣆⣀⣀⡜⡄⠀⠀⠀⠀⡏⠳⣵⠀⠀ ⢈⢆⠀⠐⢄⠀⠈⠃⠘⢦⣄⠱⡴⠁⠈⠉⠙⠁⠛⠓⡀⠀⠀⠀⢰⠠⠈⢇⠀ ⠈⢆⢂⠀⠀⠡⡀⠀⠀⠈⢻⣷⡃⠀⠀⠀⠀⠀⠀⠀⠰⣀⣀⣀⣨⠀⡇⢸⢂ ⠀⠀⠻⣆⠘⠠⠈⠀⠀⠡⠀⠙⡏⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢻⡴⠀⠈⢈ ⠀⠀⠀⢸⣾⡆⡧⡀⠀⠀⠀⠀⡗⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠢⠄ ⠀⠀⠀⠀⣻⡇⢰⠦⠀⠀⠀⠐⠳⢑⢔⠄⠀⠀⠀⠀⠀⠀⠀⠢⠀⠠⠀⠈⠢

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣷⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⣠⣴⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⢰⣿⣿⣷⣦⣤⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠟⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠴⠚⠛⠛⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⣠⠴⠋⠉⠁⠉⠉⠓⢦⡀⠀⠀⠀⠀ ⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀ ⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⡰⢺⣦⡀⠀⠀⢸⡇⠀⠖⣷⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⣿⢾⣿⡇⠀⠀⢸⡇⠸⣗⣿⡟⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠸⡄⠀⠀⠀⠀⠀⠙⠿⠟⠀⠀⠀⣸⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀ ⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢧⡀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀ ⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠈⠙⢦⣀⡀⢀⣀⡠⠖⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠓⠲⠶⠖⠚⠋⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⢻⠉⠁⠀⡇⠀⠉⠉⡟⠛⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠾⣉⣀⠀⢸⠀⠀⠀⡇⠀⠀⠀⡇⣀⣀⠠⠼⠛⣶⣄⡀⠀⠀⠀ ⠀⠀⠀⢀⡼⠋⠀⠀⠀⠉⠉⠉⠉⠓⠛⠉⠉⠉⠉⠀⠀⠀⠀⢸⡇⠈⠓⠀⠀⠀ ⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀ ⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀ ⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀ ⣼⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠙⠲⢴⠚⠉⠉⠲⡄⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⢀⣠⣼⠥⠴⠒⠒⠒⢻⠛⠛⠒⢲⠒⠻⠤⣄⠀⠀⠀⠹⣆⠀⠀⠀ ⣿⠀⠀⠀⢠⡏⠀⠀⣀⣆⣀⣀⣀⣸⣄⣀⣀⣀⣇⣀⣀⣸⣦⣀⣀⣀⣹⣦⡀⠀ ⠿⠶⠶⠞⠛⠛⠛⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣙⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄

⠀⠀⠀⠀⠀⣀⡤⠖⠚⠛⠒⠲⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠊⠁⡇⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀ ⠀⠀⢰⠇⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠠⠉⠢⣘⡦⡰⡄⠀⢸⠀⠀⠀ ⠀⠀⢸⠇⢀⠔⣁⠀⠀⠀⠀⣈⠉⠢⡸⡄⠀⠀ ⠀⠀⢸⣼⠀⠘⠛⠁⢠⠀⠀⠛⠃⠀⡤⡇⠀⠀ ⠀⠀⠀⣿⡀⠀⠀⠀⣴⣧⡀⠀⠀⠀⣾⡁⠀⠀ ⠀⠀⡞⠁⠳⣄⠀⠀⠿⠻⠃⠀⣠⠞⠀⢳⡀⠀ ⠀⠘⡇⠀⠀⠸⡿⡖⠒⠒⢲⣿⡇⠀⠀⢠⡇⠀ ⠀⠀⣹⣆⠀⠀⠋⠁⡀⠀⡸⠹⠀⠀⠠⣏⠀⠀ ⠀⢰⠃⠀⠆⠀⠘⠀⠈⠁⠀⡆⠀⢠⠁⠈⣇⠀ ⠀⣾⠀⠀⢸⠀⢠⠀⠀⠀⠀⠇⠀⠀⠀⠀⢹⠀ ⠀⡇⠀⢠⠂⠔⠁⠀⠀⠀⠀⠈⠂⠌⢄⠀⢸⡄ ⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡾⠟⠛⠉⠁⠀⠀⠀⠉⠙⠻⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠛⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⠉⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠈⣳⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⡏⠙⢦⡀⠀⠘⣷⡄⠀⠀⢠⡀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠉⠳⢤⣘⣟⠶⣄⠸⡷⡄⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠛⠿⠜⢦⡀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⡿⢧⠀⢀⡤⠞⠁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠙⢦⡾⢿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⡇⢸⠚⠁⠀⠀⣾⣯⣿⡧⠀⠀⠀⠀⠀⠀⠀⢸⣯⣽⣿⠀⠀⠀⠀⡇⢸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡷⠚⣧⠀⠀⠀⠈⠛⠛⠁⠀⠀⣰⠚⠅⠀⠀⠈⠙⠛⠋⠀⠀⠀⢰⠟⢾⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢿⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣾⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⠟⢿⣇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⡿⠙⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⠋⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⢿⣿⡿⠟⣻⠇⠀⠀⠀⠀⢀⣴⡿⠁⠀⠈⢿⣦⠀⠀⠀⠀ ⠀⠀⠀⣿⠇⠀⠀⠀⠀⠙⢿⡶⣄⡀⠀⠀⠀⠙⠒⠚⠉⠀⠀⠀⣀⣴⣾⠟⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀ ⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⣿⣾⣭⣶⡶⠤⢤⣤⣤⠤⠴⣶⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀ ⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⢹⣷⣉⣿⡇⠀⠀⠀⠀⠀⠀⣿⣏⣸⡿⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀ ⠀⠀⠀⠘⢿⣆⡀⠀⠀⠀⠀⠀⣿⠛⢻⡇⠀⠀⠀⠀⠀⠀⡏⠛⢻⠃⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⣨⣿⣧⡀⠀⠀⠀⠀⠸⡆⠘⠧⣀⠀⠀⠀⢀⡤⠗⢀⡞⠀⠀⠀⠀⠀⣴⣿⣧⡀⠀⠀⠀⠀ ⠀⠀⢀⣾⠟⠁⠈⢳⡀⠀⠀⠀⠀⢳⠀⠀⠈⠙⠶⠚⠉⠀⠀⣸⠃⠀⠀⠀⠀⣰⠁⠈⠙⣿⣆⠀⠀⠀ ⠀⠀⣾⡏⠀⠀⠀⠀⢧⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⠃⠀⠀⠀⠘⣿⡀⠀⠀ ⠀⢀⣿⠃⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⣿⡇⠀⠀ ⠀⢸⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢹⣧⠀⠀ ⠀⣸⡟⠀⠀⠀⠀⠀⢰⠃⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⣧⠀⠀⠀⠀⠀⢸⣿⠀⠀ ⠀⣿⡇⠀⠀⠀⠀⣠⠋⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠘⢧⠀⠀⠀⠀⠀⣿⡄⠀ ⠀⣿⠃⠀⠀⠀⠾⠓⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠚⠳⠂⠀⠀⠀⢻⣇⠀ ⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀ ⣾⡇⠀⡀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⢀⢸⣿⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠉⡄⠀⠀⠀⠀⣀⣀⣉⣀⣉⠀⠒⠤⢄⣼⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡴⣿⠀⠀⢸⣰⡡⠖⠋⠉⠀⠀⠀⠀⠀⠈⠉⠒⠢⢄⡀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡏⠙⢦⣀⣰⣫⠴⠻⡄⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⣠⠄⠒⠒⠢⢄⣄⠈⢧⡀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠁⠀⢠⣾⠏⠀⠀⠀⠱⡀⠀⣀⣈⣑⣦⣤⠊⢳⢋⢀⣀⡀⠀⠀⠀⠙⢷⡄⠻⡷⣄⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⣰⡟⠁⢠⠠⣀⠀⠀⠑⡄⠸⡀⠀⠀⡆⠀⢸⠀⠀⠀⠈⠑⢄⠀⠀⠈⣿⡼⡌⡌⢢⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⢞⡟⠀⠀⣰⡀⠈⠳⡀⠀⠈⠢⣣⠀⠀⣇⣠⡟⢀⣄⣀⠀⠀⠀⢣⠀⠀⣿⡇⢹⠐⠀⠇⠀⠀⢣⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠋⡼⢡⣿⠋⢉⠷⣄⡀⢱⠀⠀⠀⠈⠓⠄⠈⢩⡇⠉⠀⠈⢷⠀⠀⠀⡆⢀⣿⠃⠈⡇⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀ ⢀⣴⠥⣾⠃⣾⠃⢠⠇⠀⠈⡏⠉⢀⣾⢲⣄⡀⠀⠀⠀⢳⣅⡀⠀⢈⡇⢀⣀⣽⠟⠁⠀⠀⢹⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀ ⠀⠀⠀⣿⢀⡏⠀⡘⠀⢠⠒⡇⠀⣼⣿⣟⣯⠭⠖⠂⠀⠀⠙⠻⣿⠛⠛⠉⠉⠙⠿⠷⣶⡶⢼⡇⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀ ⠀⠀⠀⣿⢸⣇⠀⡇⠀⣇⢀⡇⣸⣿⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠉⠉⠛⢣⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀ ⠀⠀⠀⣿⠀⢻⣆⣡⠀⣸⣾⡟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠤⢀⠀⠸⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀ ⠀⠀⠀⣿⠀⠑⣿⡿⠛⡿⠛⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡇⠀⠀⠀⠀⠀⢹⠀⠀⠀ ⠀⠀⠀⣿⡦⠊⡱⠀⠘⠁⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⠀⠀⠀ ⠀⠀⠀⡟⢷⡴⠁⠀⠀⠀⠀⠀⠀⠙⠀⠀⣠⠔⠒⠒⢒⡤⢄⡀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⠀⢀⣇⠀⠀⠀⠀⠀⠀⡆⠀⠀ ⠀⠀⠀⡇⠈⣧⠀⢰⠀⠀⠀⠀⠀⠀⠀⣿⣷⡯⠭⠭⠭⠽⠿⠿⠷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠑⣾⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⡇⠀⠈⢧⡌⠀⠀⢀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⢹⠀⠀⠀⠀⠀⠀⠇⠀⠀ ⠀⠀⠀⠃⠀⠀⠈⠳⡄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣾⠟⠁⣠⣼⡆⠀⠀⠀⠀⠀⢠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⣼⣿⠟⣁⣴⡯⢯⡬⡇⠀⠀⠀⠀⠀⠸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢟⡛⠻⢷⣶⠦⠤⣤⣤⣀⣀⣀⣀⢀⣠⠞⣁⣀⠿⠟⠛⠋⠉⡀⡀⠘⣧⡇⠀⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠉⠙⠋⠓⠢⠤⠤⠗⠢⠽⣽⣿⠿⠛⠉⠁⢀⡀⢰⡊⠳⠤⣇⡹⣚⡇⣧⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⡠⠤⡀⢀⡏⠉⢉⣩⡤⠖⠛⢿⣿⡉⠃⢸⠀⠀⠀⠀⠀⠀⢁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⣠⣴⡚⠉⢀⡤⢄⡠⠇⢀⣩⡤⠗⠛⠁⠀⠀⠀⠀⢸⡇⢱⠀⢸⠀⠀⠀⠀⠀⠀⠸⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠸⡀⠀⢀⡤⠜⡷⠢⢌⡆⠈⣠⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡀⠇⢸⡄⠀⠀⠀⠀⠀⠀⡆ ⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢃⠀⣿⠀⡞⠀⠀⠘⢳⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣟⡟⣷⠀⡇⠀⠀⠀⠀⠀⠀⢳

⠀⠀⠀⠀⠀⠀⠳⡒⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⡀⠀⠈⢆⠀⠙⢖⠈⡙⡇⠐⠒⢦⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠚⠋⠤⢄⡀⠈⠉⠛⠀⠀⠈⢆⠇⢰⠀⠀⠀⠱⡀⠉⠒⢄⠀⠀⠀⠀⠀ ⠀⠀⣀⠤⠐⠚⠀⠀⠀⠀⠀⠀⠈⠀⢸⠀⠀⠀⠀⠹⡀⠀⠀⢣⠀⠀⠀⠀ ⢠⠮⠒⡖⢀⠶⠆⠀⠀⠀⠀⠀⠀⠀⣘⣤⠀⠀⠀⠀⢡⠀⠀⠀⢃⠀⠀⠀ ⠀⠀⢰⠼⠤⠤⣤⡀⠀⠀⠀⢀⣀⠀⢠⠂⠀⠀⠀⠀⠈⡄⠀⠀⠘⡄⠀⠀ ⠀⠀⠘⠀⠀⠈⠍⠹⠓⠂⠉⢽⠀⢩⠉⢢⣀⣀⡀⠀⠀⢣⠀⠀⠀⢃⠀⠀ ⠀⠀⢠⠀⣀⣤⠄⠒⢓⡷⠈⢉⣽⠿⣟⠛⠛⢳⡂⠈⠉⠙⡦⡀⠀⢸⠀⠀ ⠀⠀⢨⠃⡔⡹⠀⡠⣊⢸⠀⠛⡇⢊⠔⣋⢢⠤⣻⣦⡀⠀⠰⡸⡢⡸⠀⠀ ⠀⣠⠧⣮⣾⣥⠾⠩⢶⡁⢣⠀⡇⡷⡩⠀⢤⠙⠆⠱⡈⡖⢤⣈⡷⠘⡇⠀ ⠀⠀⠀⠏⣿⠘⡜⠉⠙⣧⠸⠵⠅⠇⡇⠆⠀⡇⢸⡑⡇⡇⠸⠀⡷⡀⢹⠀ ⠀⠀⠀⡀⢸⣤⢇⠀⠁⡸⠀⠀⠀⠘⢝⠤⠔⢁⡦⠃⢀⡣⠃⡠⠁⠑⡀⡇ ⠀⠀⠀⣇⠆⡟⠿⠵⠖⠃⠈⠀⠀⠀⠀⠈⠉⠀⠀⠀⣜⡓⠉⠀⢋⠒⠚⠀ ⠀⠀⠀⠁⠈⠣⡀⢠⠂⡄⠀⠀⢠⠂⡄⠀⢀⠤⠐⢉⢅⣨⠒⠠⢜⡄⠀⠀ ⠀⠀⠀⠀⡄⠀⠈⢙⠒⢗⣒⢒⢢⡤⢤⣊⠡⠒⠊⣁⡼⠉⢫⣦⡀⠱⡀⠀ ⠀⠀⠀⠀⣇⡠⠔⠙⢀⣼⡟⠻⢿⠮⣩⢎⠀⠗⠉⠀⢠⠀⠀⠱⣹⢢⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⣾⠋⠀⠠⢡⣹⡟⠙⠀⠀⠀⠀⢸⠀⠀⠀⢫⡆⢹⠀ ⠀⠀⠀⠀⠀⢀⣼⣮⠃⠀⢠⢃⢇⣿⠃⢀⠀⠀⠀⠀⠸⠀⠀⠀⠸⡏⢺⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠈⠑⢦⡀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠙⢿⡉⠁⠀⡟⣇⠈⠉⠛⠲⢶⡤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣤⣴⣒⠚⠉⠉⠉⠉⠉⠙⠒⠦⢼⣧⠀⠀⠀⠀⢳⡀⣸⠀⢸⡄⠀⠀⠀⠀⠳⣄⠈⠉⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠙⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡏⠀⠀⡇⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⡤⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀ ⠀⢀⡤⠖⢉⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀ ⠠⠿⠛⠉⢉⡏⢀⣠⠬⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣡⢴⠆⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣴⣋⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⡞⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀ ⠀⠀⠀⢀⡏⠉⠀⠀⢠⣤⣿⣿⣆⡀⠀⠀⢀⣀⣠⡶⠶⢤⣀⣴⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⢻⠀⠀⠀ ⠀⠀⠀⢸⠃⠀⠀⠀⠀⠡⠄⠒⢻⠟⠉⠉⡉⠁⠼⡇⠀⠀⢧⠀⠉⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠘⡇⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣈⣧⣤⣤⠤⠤⠶⠿⢒⣶⢿⣒⣲⣿⣿⣿⣯⣍⡛⠒⠒⠲⠦⢼⣄⠀⠀⠀⠀⠀⣷⠀⠀ ⠀⠀⠀⠈⡇⢀⡤⠴⢶⣾⠉⠉⠀⠀⣠⢿⠀⠀⢀⣴⣿⠞⢛⣷⣄⡀⠀⠀⠘⣯⡉⠀⠀⠀⠀⠀⢻⡳⢄⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⣹⠋⢀⡴⢋⡇⠀⠀⣠⡞⠁⢸⡀⠠⠿⠋⡇⠰⢋⡤⠖⠛⠲⢤⣀⡘⢿⣦⣄⠀⠀⠀⠀⢳⡘⣷⢦⡀⢸⠀⠀ ⠀⠀⠀⣰⠃⣠⠎⣴⡞⠀⣠⡾⣯⣙⠢⠀⢧⠀⠀⠀⡇⢠⣟⣠⠖⠋⠉⠓⢮⡉⠛⠻⡝⠶⣄⠀⠀⠀⠱⣜⣆⠹⣼⡆⠀ ⠀⢀⣴⡷⠚⣷⣼⣟⣤⣾⠟⠒⠒⢿⣷⡀⠈⣧⡀⠀⡇⢸⡟⣡⠖⠛⠒⢦⡀⠙⣆⠀⢻⡀⢸⡙⠲⢤⣄⣸⣟⠓⠸⣷⠀ ⠀⠈⠁⠀⠀⡿⣿⣿⢠⠇⣰⠛⠉⠓⢿⣧⠀⢿⢳⡄⡇⢸⡇⡇⠀⡄⠀⠀⢧⠀⢹⠘⡼⣷⠘⡇⠀⣸⠀⠈⣿⡀⠀⠹⡆ ⠀⠀⠀⠀⠀⡇⠸⣿⢸⠀⡇⠀⠀⡄⠈⢿⠀⠈⠉⠙⠛⠈⣇⢷⡀⠁⠀⠀⡼⠀⢸⢠⡇⠇⢀⡇⢠⠏⠀⢀⡟⢳⡀⠀⢳ ⠀⠀⠀⠀⠀⡇⠀⢻⣸⡄⣇⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠸⣎⠳⣄⣠⠴⠃⢀⣿⠟⠀⠀⢸⢁⠞⠀⢀⡞⠁⠀⢳⡀⢸ ⠀⠀⠀⠀⠀⡇⠀⠸⡿⣷⣜⢦⣀⣀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠒⠒⠉⠁⠀⠀⢠⣿⣋⣠⠔⠋⠀⡶⢤⣀⢹⣾ ⠀⠀⠀⠀⢸⣧⠿⣆⡇⠘⠿⠗⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣉⣁⠀⠀⠀⠀⢳⠀⠈⠉⠁ ⠀⠀⠀⠀⠘⠋⠀⡏⢧⡀⠀⠀⢀⣤⣀⡀⠀⠀⠀⠀⣠⡤⢤⡀⠀⠀⠀⠀⢀⣀⡤⠖⠋⢁⠀⠈⡧⠤⢤⣀⡘⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⠲⢤⣼⠀⠀⡇⠀⠀⠀⠀⠙⠂⠀⠃⠀⢀⡤⠖⠉⠀⣀⡤⠖⠙⣦⢾⡧⣄⠀⠀⠙⢻⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠈⠙⠚⣿⣉⡉⠉⡙⢳⣶⣶⠶⣾⣁⠀⠰⡞⠉⠁⠀⣀⣴⠋⠀⠙⢮⡳⣄⠀⠀⢹⡀⠀ ⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣠⠞⡿⠀⠀⣨⣿⣿⣏⣿⣿⢡⡖⠒⢲⡌⡇⠀⣧⠤⠖⠋⠁⠉⡀⠀⠀⠀⠹⡜⢿⣄⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠿⠤⠖⠋⠁⢀⡇⢀⣼⣿⡟⠁⠀⠙⣻⣌⣓⢲⣺⣡⡇⠀⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠹⣼⡌⠳⣾⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⡿⣿⠋⠀⠀⠀⡴⢁⡎⣽⣿⠏⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢻⣷⠀⠙⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡿⡽⠁⠀⠀⢀⡞⢀⡞⣸⣿⡟⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⣿⡷⡀⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⣿⡿⠁⠀⠀⠀⣼⠁⣼⢀⣿⣿⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣿⡇⠹⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠉⠈⠉⠉⡶⠋⠉⠉⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠞⠁⣀⠤⠒⣉⠀⠰⡧⠐⢀⡀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡞⠁⠀⠀⠒⣋⣿⣟⠀⠀⣧⡔⣩⡄⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀ ⠀⠀⢀⡞⠀⠀⠀⠴⢛⡫⠿⠟⠃⣀⡿⣿⣿⡿⠶⡄⠀⠀⠀⠀⢣⠀⠀⠀⠀ ⠀⠀⣼⠁⠀⠀⠀⢀⣠⠴⠒⠒⠊⠁⠀⠉⠉⠉⠑⠲⢦⣀⠀⠀⠈⢧⠀⠀⠀ ⠀⢠⠇⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡄⠀⠈⢇⠀⠀ ⠀⢸⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢸⡀⠀ ⠀⢸⡄⠀⡞⣁⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠇⠀ ⠀⢀⣧⢸⠛⠁⠀⠈⠉⠓⠲⠆⠀⠀⠀⠀⠀⣰⢶⣾⣛⠋⠉⠛⡇⠀⣸⠀⠀ ⠀⣸⡟⡸⠀⠀⠰⣿⣻⣿⠧⡀⠐⡄⠀⠀⡴⣠⣿⣿⣟⢷⠀⠀⡇⠀⣧⠀⠀ ⠀⣿⡗⣿⠀⠀⠀⠙⠛⠛⠑⠻⠆⢿⠀⠀⠰⡟⠚⠻⠿⠛⠀⠀⡇⢸⢹⠀⠀ ⠀⣸⠃⢻⣄⣀⠀⢀⣤⡤⡀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⡇⠸⣾⠀⠀ ⠀⠿⢰⠈⣧⡽⠉⠶⣿⡁⠈⠢⣤⣀⣀⣹⠙⠛⠋⠱⠦⡀⠀⢰⢧⠀⢻⡀⠀ ⠀⡇⢸⠀⢻⡗⢤⡀⠀⠑⢤⣠⡦⠀⠀⠈⠉⠑⠒⠢⠤⢬⣓⣾⠈⠀⠀⢧⠀ ⢸⠃⡌⡀⠀⣏⢢⡈⠢⣰⠄⠉⠓⠢⢄⣀⣀⣀⠀⣀⠀⠀⠈⠉⡆⠀⡆⠘⡆ ⢸⠀⠁⡇⡄⠘⣄⠙⣤⡟⡉⠢⢄⡀⠀⠀⠈⠁⠀⠈⠂⠀⠀⠀⢡⠀⠀⠀⡇ ⠈⢧⠀⠃⡇⠀⠘⣦⡈⠻⣷⢄⡀⠈⠓⠀⠘⠦⠀⠀⠀⠀⠀⠀⠘⣄⡇⠀⡇ ⠀⠈⠳⣄⣧⠀⠀⡇⠙⢦⡈⠳⢝⠀⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡼⠁ ⠀⠀⠀⠀⠉⠳⢤⡇⠀⠀⠉⠓⠢⠿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⢶⠖⣰⣤⣾⣿⣿⣿⣷⣦⣼⡒⠨⡑⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⡡⢊⣴⣿⣿⣿⣿⣿⣿⣿⡿⠦⣠⠐⣡⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠞⠔⡠⠚⣩⡽⡍⠛⢿⣿⣿⡿⣿⣷⡦⠀⠈⢂⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠆⠀⠀⢠⣾⡟⢀⢘⣷⡪⡹⢜⣷⣧⣿⡗⢅⠀⠀⠢⠀⠀⠀⠀ ⠀⠀⡠⠊⠀⠀⢠⢻⣿⡇⠀⠈⠩⢥⠀⢡⠉⠀⣿⠀⠈⠄⠀⠀⠑⢄⠀⠀ ⠰⡆⠀⠀⢀⠔⠁⠀⢖⠃⠀⠀⠀⡓⠂⠚⠇⠀⡏⠀⠀⠀⠑⡀⠀⠀⠀⡀ ⠀⠇⣀⣀⠂⠀⠀⠀⠘⣻⠀⠀⠀⠐⠟⠗⠀⡐⠣⡀⢀⡀⠀⢩⠉⠉⠁⠀ ⠀⠀⠀⠇⠀⠂⠆⠀⠁⠁⠑⢤⣀⡀⠈⢁⠔⣅⠀⡘⠁⠀⠉⠈⡀⠀⠀⠀ ⠀⠀⠀⡆⠀⠀⠀⠀⠀⠑⢄⠀⡆⠤⠭⠅⢪⠁⠑⠂⠀⠀⠇⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠃⠀⠀⠘⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠾⠟⠛⠛⠛⠿⠶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣴⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠰⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⡟⠁⠀⠀⠀⢀⣴⡾⠛⠛⠛⢷⣦⡀⠀⠀⠀⢀⣴⠿⠛⠛⠻⢷⣦⡀⠀ ⠀⣼⡏⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠘⣿⡀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠹⣷⠀ ⢰⡟⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠘⠛⠀⠀⣿⠇⠀⢸⣿⠀⠀⠀⠘⠛⠀⢀⣿⣇ ⣾⠇⠀⠀⠀⠀⠀⠀⠹⣧⣀⠀⠀⠀⣀⣼⠟⠀⠀⠀⢻⣦⡀⠀⠀⠀⣠⣾⠟⣿ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠉⠛⠿⠿⠟⠋⠁⠀⣿ ⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿ ⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⣸⡏ ⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠉⠁⠀⠀⠀⠀⠀⠈⠉⢿⡆⠀⠀⣰⡿⠀ ⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⣀⣀⣀⣀⣀⣀⣀⣠⣾⠃⠀⣰⡿⠁⠀ ⠀⠀⠀⠙⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⣠⡾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠶⣶⣤⣤⣤⣤⣴⡶⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡾⠿⠛⠛⠛⠛⠛⠛⠻⢷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀ ⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠙⣿⡄⠀⠀ ⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠋⠙⢿⣦⡀⠀⠀⠸⣷⠀⠀ ⢀⣴⠿⠷⠶⣶⣶⣶⣶⣶⣶⡶⠶⠿⠛⠛⠉⠀⠀⠀⠀⠀⠙⠻⠷⢶⠶⠿⣷⡄ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠘⣿ ⠹⣧⣄⠀⠀⠀⠀⠀⠀⠀⠿⠿⠃⠀⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⠀⠀⠀⣀⣼⡟ ⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀ ⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠉⢻⣆⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀ ⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠈⠛⠿⠶⠿⠋⠀⠀⠀⢀⣴⡾⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣤⣤⣀⣀⣀⣀⣠⣤⣶⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⣠⠤⠶⠦⢤⡀⢀⣀⣀⡴⠒⠉⠉⠉⠒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠈⢯⢀⠏⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⢸⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠦⡀⠀⠀⠀⠀ ⠀⠀⡼⠀⠀⠀⠀⢰⣲⠆⠀⢸⠻⡄⠀⠀⢾⡷⠀⠀⠀⠀⠀⣻⠀⠈⢦⡀⠀⠀ ⠀⠀⣣⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠱⡄⠀ ⠀⣰⠻⡄⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠹⡀ ⢀⠇⠀⠑⢤⣀⣀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠙⠒⠶⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⢇ ⢸⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⢇⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⡎ ⢸⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡰⠁ ⠀⢧⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀ ⠀⠈⢣⡀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣠⠞⠁⠀⠀ ⠀⠀⠀⠙⢦⡀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀ ⠀⢠⠔⠂⠀⠉⠓⠦⢄⣈⡉⠉⠛⠛⠛⠛⠉⠉⣀⣠⠤⠖⠋⠀⠉⠁⠒⢠⠀⠀ ⠀⠀⠁⠒⠀⠤⠤⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠠⠤⠄⠐⠂⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠦⠭⠍⣀⣠⣇⣠⣈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⣠⡼⠁⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣜⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⣶⠶⠲⣄⠈⣷⡄⠀⠀⠀⠀ ⠀⠀⢀⡴⠋⠉⠉⠀⠀⠀⠀⠀⠀⣼⠇⠀⡰⠊⠀⠀⠀⠈⢧⡸⣽⠀⠀⠀⠀ ⠀⢠⠊⠀⠀⣀⠤⠤⠤⣤⡀⠀⠀⠀⠀⢸⠁⠀⠀⠀⣤⠀⠀⠱⡈⢧⠀⠀⠀ ⢰⡏⠀⠀⡞⠁⠀⠀⠀⠀⠉⢲⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⡇⠘⣇⠀⠀ ⢠⠃⠀⠠⡁⠀⠀⠶⠀⠀⢀⡌⠀⠀⠀⠀⠈⠳⢤⣀⣀⣀⣀⡤⠃⠀⢡⢣⠀ ⢸⠀⠀⠀⢇⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀ ⠸⠀⠀⠀⠈⠲⠤⠤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀ ⡟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⢡⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅ ⠈⢮⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃ ⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀ ⠀⠀⢰⠘⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀ ⠀⠀⠀⠣⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⢛⠛⠛⠛⠛⠓⠲⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡴⢛⠩⡐⠌⣐⠈⠀⠀⠀⠀⠀⢀⡀⠀⠉⠻⢦⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡾⠋⡀⠔⠁⠰⠋⠉⠉⠀⠀⠀⠀⠈⠁⠉⠳⠀⠀⠀⠙⢷⡄⠀⠀⠀ ⠀⠀⣰⠏⣰⠋⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀ ⠀⣸⠏⡼⠁⠀⠀⠀⠀⣴⠟⠉⠉⠙⢷⣠⡾⠋⠉⠛⢷⡄⠀⠀⠀⠀⠀⠹⣧⠀ ⢰⡏⠸⠁⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⢻⡆ ⣼⠃⠃⠀⠀⠀⠀⠀⢾⠀⠀⢴⣶⠀⠀⠀⠀⠀⢴⡆⠀⢸⡇⠀⠀⠀⠀⠀⠘⣧ ⣿⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⣿ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⣤⣴⠞⠙⣷⣤⣀⣤⡾⠃⠀⠀⠀⠀⠀⠀⢠⣿ ⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢀⣀⡿⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⡇ ⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢱⡿⠀ ⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⡐⣱⡿⠁⠀ ⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠃⠀⠀⠀⠀⠀⡠⢊⣾⠟⠁⠀⠀ ⠀⠀⠀⠀⠈⠻⣷⣦⡠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢂⣡⣾⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣶⣤⣭⣉⣁⣀⣈⣥⣤⣶⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣉⡉⣙⣛⣛⣋⣉⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠊⠉⠉⠉⠉⠉⠑⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⡠⠤⠐⠒⠒⠒⠢⠤⣀⡈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣿⠀⠀⠀⢀⡔⠉⠀⠀⣀⡤⠤⣬⣀⠀⠀⠉⠲⣄⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⡮⠍⢉⡑⠿⠡⠀⢠⠎⠀⠀⠐⠊⠉⠉⠉⠉⠒⠤⡀⠀⠀⠈⠳⡀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢣⠮⠊⣀⠤⠤⠬⠭⠥⣁⣸⠀⠀⢀⣠⣤⢤⠶⢖⢒⡤⠀⠀⠀⠀⠀⠀⠙⡄⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⡰⠊⠀⠀⠀⣀⣤⠤⢄⣙⣤⣴⣵⣿⣾⣿⣿⣷⣶⣌⠹⢶⡀⠀⠀⠀⠀⢹⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡞⣰⠄⢀⡴⢋⣴⣾⣿⠟⠋⠉⠉⠛⠛⠛⠛⠛⠿⣿⣿⣿⡢⣙⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠟⠀⢸⢣⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠈⡆⡀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢸⠀⠀⠀⣞⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠉⠀⣧⢷⠁⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⡄⠀⠀⠀⡇⣿⡴⠟⠛⠛⠿⣦⠀⠀⠀⠀⠀⢰⠾⠟⠛⡏⠀⠀⡿⠏⠀⠀⢰⠃⢀⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢳⠀⠀⠀⢸⡟⠀⣀⣴⣖⣲⡄⠠⡀⠀⠀⣀⣠⣔⣲⣶⡇⠀⠀⠀⠀⠀⠀⡎⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⡆⢠⠀⢸⡇⠈⠻⣍⣿⣇⣹⠆⢃⠀⢸⠑⣞⣹⣿⣟⡇⠀⠀⠀⠀⠀⡼⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⣀⠀⢿⢸⣰⡿⠀⠀⠀⠀⠀⠁⠀⠀⢸⠀⠈⠀⠀⠀⠀⠀⢣⡆⢀⠀⠀⣰⠃⢀⣦⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡤⢕⣾⣼⡿⢻⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠈⣾⡀⢣⡄⣯⣖⡭⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⡈⢫⣿⡿⣼⡀⠀⠀⠀⠀⠀⢠⣦⣀⠀⢸⣢⡄⠀⠀⠀⠀⠈⢧⡀⣿⣿⠊⡸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠒⢷⣷⡼⡄⠀⠀⠀⠀⠀⠀⠁⠀⡉⠉⠈⠀⠀⠀⠀⠀⠀⢀⡿⣳⡷⢲⢇⢱⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢰⡇⠳⡀⢻⣽⣷⢄⠀⠀⠀⠀⢀⡖⣩⣤⣬⡱⡄⠀⠀⠀⢀⣤⣾⣿⠋⣠⠃⠀⢆⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡼⠡⢯⢃⠄⠑⡄⠙⢽⣿⣧⡀⠀⠀⢸⢿⠛⠛⠛⡻⡿⠀⠀⣠⣿⣿⠟⠁⣴⠁⠀⠢⡈⠊⢇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠫⠤⠴⡇⠎⠀⡄⡞⣦⠀⠀⠈⢿⢦⡀⠈⣇⠣⠤⠔⢡⠃⢠⢼⠟⠁⠀⢀⡞⡄⠳⠤⣄⣈⠀⠈⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣥⢴⡾⠉⠂⠹⡳⡀⠀⠐⠱⡝⢦⠈⢳⡶⠖⢡⠞⡱⠛⠀⠀⡰⣻⠁⠈⠀⠀⠙⢦⡈⠉⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠳⡃⠀⠀⠀⠈⠢⣳⠤⣤⢤⡫⠊⠀⠀⠀⠀⡳⠋⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⢀⡠⣿⠀⠀⢸⡣⣀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⣧⠀⠀⠉⠴⢹⠀⠀⢸⠙⠀⠁⠀⢰⡗⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣾⡍⠁⠀⢀⠇⠀⠀⠀⠀⡜⠀⠀⠈⡄⠀⠀⠀⠀⢇⠀⠀⠉⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠀⣿⣿⣿⣇⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠸⡀⠀⢠⣿⣿⣿⡇⠈⠙⠲⢄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⢀⡇⠀⠀⠀⠀⢰⠃⠀⠀⠀⢱⠀⠀⠀⠀⠀⢇⢀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀ ⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡾⠀⠀⠀⠀⠀⢸⣀⣀⣀⣀⣸⠀⠀⠀⠀⠀⠸⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀ ⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀ ⠀⢠⠁⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣿⣿⣿⣹⣿⣿⡇⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢃⠀ ⠀⡎⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⡄ ⢸⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠸ ⣇⣀⣀⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣤⣤⣤⣬⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⣀⣀⣀ ⣿⣿⡟⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣟⣿⣟⣟⣿⣿ ⣿⣿⣷⣶⣶⣷⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣶⣶⣶⣶⣿⣿

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠤⣀⡀⠀⣀⡤⠤⠤⠤⠤⠄⣀⢀⣀⠤⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡀⠀⠀⣠⡔⠉⣀⡠⠤⠤⣀⠀⠈⢻⡴⠒⠒⠒⠒⠒⢠⡞⠉⠀⢀⠤⠤⢄⣀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠞⠉⠁⠀⠉⠛⡵⠁⢀⣀⡀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⠀⠀⢄⡈⠳⣄⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠃⠀⠀⠀⠀⠀⢰⣇⠴⠋⠁⠀⣠⠞⠁⢀⡀⠤⣀⠀⠀⠀⠀⠀⣀⠤⢄⡀⠈⠳⣄⠀⠈⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡄⠀⠀⠀⠀⠀⢸⠏⠀⡔⠂⡼⠁⠀⡴⠁⠀⠀⠀⠳⡀⠀⢀⠞⠁⠀⠀⠈⢦⠀⠈⢧⠀⠢⡀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣆⡀⠀⠀⢀⣼⢀⡞⠀⢰⠁⠀⢸⠁⠀⠀⠀⠀⠀⢳⠀⡞⠀⠀⠀⠀⠀⠀⣇⠀⠀⡆⠀⢻⡄⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠉⣉⣽⡟⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⣀⣀⣘⠀⡇⣀⣀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠹⣄⣘⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⢽⠀⠀⠀⠀⠻⣿⣿⠀⢇⣿⠟⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢇⠀⠩⢶⡀⠀⠀⠀⠀⠈⢇⠀⠀⣠⠞⠉⠀⠀⠀⠈⠑⢦⠀⠀⡸⠁⠀⠀⠀⠀⢠⡶⠍⠀⣸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢶⠃⠀⠀⠀⠀⠀⠀⠀⠘⡦⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠓⠲⣶⠶⠤⢄⡤⠏⠉⠒⠼⣇⠀⠀⠀⠀⠀⠀⠀⣸⠡⠤⡀⠴⠉⠑⠒⠲⣶⡶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢴⠒⠉⠀⠀⠀⠀⠀⢠⠆⠀⠈⠳⢄⣀⠀⣀⣤⣞⣁⣀⣀⠀⠘⢢⡀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⣀⡤⠼⠛⠉⠁⠀⠀⠀⠙⣆⠀⢱⠀⠀⠀⠐⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⠂⠀⠀⢠⠇⠀⠀⣠⣴⣿⣧⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⡄⢸⠀⢀⣄⡀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⠴⠒⠚⢿⠀⠀⠀⠀⣿⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠸⡀⠉⠒⠋⠉⠒⠦⣀⠀⠀⠀⠀ ⠀⢀⡴⠋⠀⠀⠀⠀⠀⠣⡀⠀⠀⠟⠀⣸⣿⣿⣿⣿⣿⣿⡿⠿⠿⡿⠿⣿⣿⣿⣿⡇⠀⠀⢀⠱⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀ ⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⠀⠀⠀⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠘⠀⠈⢻⣿⣿⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀ ⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠉⠀⠀⠀⢿⣿⣿⣿⣿⠿⠓⠚⠉⠉⠉⠉⠁⠘⠛⠃⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠈⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣤⡀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⣀⡤⣄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠤⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⠴⠂⢉⠁⠖⠀⠀⠂⢄⠀⠀⠀⠀ ⠀⠀⡔⠁⠰⣸⡶⠀⣏⢔⠀⠀⠈⢢⠀⠀⠀ ⠀⡜⠀⠀⠫⣙⡋⠤⠻⠿⠟⣀⠀⠀⢣⠀⠀ ⢠⠁⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⢃⠀ ⢸⠀⡔⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢸⠀ ⢨⣦⠉⢀⣭⣍⠂⡀⠀⢀⣒⣯⣍⠉⡀⡘⠀ ⢺⢺⠀⠈⠛⠃⠳⠸⠀⠱⠛⠛⠚⠀⡇⣿⠀ ⠾⡜⣖⠦⣼⠑⢄⣀⢀⡲⠆⠤⡀⢠⠃⢻⠀ ⡆⢧⢹⡂⢄⢑⠴⡂⠀⠈⠁⠐⠊⠼⠀⡈⡆ ⡄⠈⠌⢌⠢⣣⠂⢄⠈⢉⠁⠑⠀⠀⠇⠀⢀ ⠑⢄⡇⢸⠑⠈⠗⡄⢄⡀⠀⠀⠀⠀⠘⢇⠌ ⠀⠀⠉⠚⠀⠀⠁⠚⠢⢄⡀⠀⠀⠀⠀⠀⠣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠈⠁⣀⣉⣁⠐⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡏⠀⢀⠀⠁⡀⠀⡄⠈⠑⠢⠑⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⡎⠉⣀⣊⣑⠀⠁⠀⢀⣀⣀⢀⠑⠀⠀⠘⡄⠣⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⠁⠔⠁⢀⠤⣀⣬⠦⣶⣿⣿⣷⣮⣕⢆⠀⠀⠸⠀⢁⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡇⡘⠞⢰⣡⣿⠋⠁⠀⠀⠀⠀⠈⠻⣿⡑⣄⠀⠀⡇⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠁⢁⠀⠘⣿⣇⣤⣤⡀⠀⠀⠀⣠⣤⡏⠀⣿⠀⠀⠃⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡆⠘⡀⠀⢹⢁⣴⣶⣄⢀⠀⣠⣤⣶⡇⠀⠁⠀⡘⢠⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢃⠀⢃⣦⡞⠀⠑⠛⠈⢰⠀⠈⠙⠛⢣⠀⠀⢠⠁⣼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡞⣿⣿⠃⠀⠀⠀⠀⠈⠀⡀⠀⠀⠘⢇⢳⣶⢟⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⢸⡺⣷⣉⠀⠀⠀⠈⢉⠀⠉⠀⠀⠀⢈⣾⠟⡎⢳⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡈⡼⡐⡈⢿⣦⡀⠀⢰⡵⠶⢧⡄⠀⣰⡾⠋⠌⢀⠊⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠋⠐⠗⣀⡸⣆⠀⠹⡄⠘⢔⣄⡱⡠⡞⠉⢠⠾⠑⢤⠁⠈⠢⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠃⠀⠸⡇⠀⠈⢰⡌⡉⡬⠊⠀⠀⠟⠒⠒⠒⠓⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠠⢜⡇⠀⣗⠄⠀⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⢤⣴⡆⠁⢠⠁⠀⠀⠃⠀⡅⠀⠀⠃⠈⢰⣦⡤⣀⠀⠀⠀⠀⠀ ⠀⠀⡠⠂⠁⠀⢸⣿⣿⡀⡈⠀⠀⢰⠀⠀⠂⠀⠀⠸⠀⣼⣿⡇⠀⠉⠀⢄⠀⠀ ⠀⢠⠀⠀⠀⠀⢸⣿⣿⣷⠁⠀⠀⢠⣤⣤⣼⠀⠀⠀⢻⣿⣿⣇⠀⠀⠀⠀⠄⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⣿⠇⠀⠀⠀⣼⣿⣻⣿⠀⠀⠀⠈⣿⣿⣿⡄⠀⠀⠀⠀⠀ ⠘⠀⠀⠀⠀⣾⣿⣿⡟⠀⠀⠀⠀⣿⣿⣿⣿⡆⠀⠀⠀⠸⣿⣿⣿⠀⠀⠀⠀⢠ ⣧⣤⣤⣤⣤⣿⣿⣿⣥⣤⣤⣤⣴⣿⣿⣿⣿⣧⣤⣤⣤⣤⣿⣿⣿⣧⣤⣤⣤⣤ ⣿⣧⣤⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿