⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⡀⠤⠖⠊⠉⢃⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⡗⠅⡉⠀⠀⠈⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢘⣛⠀⠀⠀⠀⠤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣇⠆⠠⠌⠋⠂⠉⠚⠋⠣⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢥⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠸⣽⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠉⡂⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠩⠉⠉⠉⠁

⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢼ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣟⡉⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠭⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⠁⠀⠀⣽⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⡠⠒⠖⡀⠀⠀⠀⠀⠀⠛⠛⢸ ⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢲⢿⣿⣿⠀⠀⠀⢀⣤⣿⣮⠍⢻⣿⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿⣿⣻⣿⣷⠈⢿⣿⠿⠁⠈⣿⣿⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠃⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⡉⠛⣱⣤⣴⣦⣀⠀⠀⢸⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣿⣿⣿⣷⡤⣻⣻⣯⣴⠿⣆⢀⣸⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣦⡻⠽⠇⠀⣡⠞⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡧⡄⠀⢀⣀⡀⢸⡀⣇⣀⣀⣸⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⠲⠖⠛⠁⠀⠀⣇⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢀⠀⠀⠀⠈⠀⡇⠀⠐⣀⣹⣿⣿⣿⣿⣿⣿⠻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠙⢦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣸⡀⠀⠀⠀⠀⠁⠀⣰⠛⠛⡷⢿⣿⣿⣿⣿⣷⣿⣿⣿⣄⣠⠤⡔⠒⣉⣽⠾⠉⠉⣉⣭⡙⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢰ ⣿⡷⣒⡆⠀⠀⠀⣄⡞⠁⠀⠀⠁⡾⣿⣟⣰⣿⣿⣿⣿⣿⡿⣫⠟⣻⠖⠋⠀⠀⠀⣘⢿⡕⢻⣿⡷⢮⣷⠒⣦⡀⠀⠀⠀⢸ ⣿⢏⣿⡇⠀⠀⢠⠏⠀⠀ ⠀⢰⣿⣿⣿⣿⣿⣿⣿⣽⣿⡿⠛⠉⠀⠀⠀⠀⢀⡞⠁⠉⠈⢉⣠⣯⠘⡯⢷⣻⣿⡄⠀⠀⢸ ⣿⣿⡗⡄⠀⣠⠏⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣱⣿⠿⠋⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢷⣽⣿⢛⣇⡴⢻⡉⣂⣿⠀⠀⢸ ⣿⣿⣇⡇⢸⡿⠀⠀⠀⠀⠀⣾⣿⣾⡿⣷⡿⠛⠛⠁⠀⠀⠀⠀⠀⡀⢀⡼⣶⡶⡷⠷⢷⣿⠿⡽⢫⠞⠀⠀⣇⠀⣿⡏⢳⣸ ⣿⡟⣿⢷⣿⣧⠀⠀⠀⠀⢰⣿⣿⣿⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⢼⡹⠋⠀⣽⡄⢠⣵⣼⠿⣆⡴⠃⠀⠀⠀⢸⣰⣇⣿⠂⢹ ⣿⣇⣽⣼⢷⣽⣧⡀⣠⠀⣸⣿⣿⠏⢀⡆⠀⠀⠀⠀⠀⠀⠀⢰⣾⢣⣴⣄⢾⣦⣩⣿⢯⡟⣼⠀⠀⠀⠀⢀⡄⣿⡿⣿⣷⢼ ⡇⠀⠈⡿⣀⣁⣯⣿⣞⣷⣿⣿⡟⣠⠞⠀⢠⠄⠀⠀⠀⢠⣓⡞⢿⣖⣺⣿⣿⣵⣿⣿⢯⢾⣿⡄⠀⠀⢀⡿⣡⣳⢹⣿⡇⢸ ⠁⠀⢸⣷⡾⠀⠀⠉⠻⣿⣟⣿⠊⡅⠀⢠⠃⠀⠀⠀⢀⣈⣯⣀⣹⣿⡟⠚⣻⢿⡿⣿⠋⢘⣿⣧⠀⠀⠀⠾⣿⡿⡎⣿⡇⢸ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠀⣷⡖⣧⣴⣃⣀⠂⠀⣠⣬⣿⣿⣷⣶⢿⣿⣿⡿⠽⠿⣟⠲⠾⠿⠿⠆⠀⠀⡄⢿⣶⣿⢹⠀⢸ ⠀⠀⠀⠳⢤⣀⠀⠀⠀⠀⠀⠈⠀⠸⠋⣸⠟⠷⢤⣷⣳⣻⣿⡿⢳⢾⠎⠀⠀⠀⠀⠘⡆⣄⠀⠀⠀⢀⢻⡄⠸⣟⣿⣿⣆⢸ ⠀⠀⠀⠀⠀⠈⠙⠲⠤⣄⡀⠀⠀⠀⠀⢹⠅⠀⠀⠀⠈⡻⢽⣶⣯⠏⡴⢣⡄⢠⣤⣾⣿⠀⠀⠀⠀⡈⡿⢳⠀⠹⣿⣿⠉⢻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠙⠓⠶⠤⣼⣦⣀⠀⡴⣔⠻⢿⣽⣛⣞⣡⢿⣵⡿⠛⠛⠛⠧⠤⣄⡀⠇⠀⠀⠀⣴⣿⣿⡄⣸ ⣇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⣾⠿⠳⣤⣭⣷⣾⣿⣯⣾⣿⡾⠋⠀⠀⠀⠀⠀⠀⠈⠹⡆⠀⠀⠀⠀⠹⣿⣷⣿

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