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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣾⢿⡿⣷⣻⣟⣿⣻⣟⣿⣻⣿⣽⡶⣿⠿⣯⣿⣟⣿⢷⣦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⣞⣿⡽⣞⠯⣏⡽⢲⡱⣎⠶⣱⢎⠶⣭⢏⢭⢛⠿⢿⣷⣮⣝⡛⠿⣷⣿⣾⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠿⡻⣝⢦⣛⡜⣧⡹⣜⣣⠽⣌⡻⢴⣫⣞⡓⢎⡎⡝⣸⢎⡼⣙⢻⣿⣷⣬⣍⠻⢾⣿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⣫⢇⡻⡕⣞⢲⣣⡝⡶⣹⡜⣜⣣⠽⣘⣷⢏⢦⡙⠮⡜⣼⣻⢞⡱⣩⢞⡲⣝⡻⣿⣧⡳⢌⠿⣿⢯⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⣫⠞⣥⡛⡼⣱⢎⠷⣱⢞⣱⡓⣞⡥⢳⣭⢟⡱⢎⡲⢍⣳⢚⡵⢋⢦⡷⣏⡳⣝⡲⡝⢮⣻⣿⣾⡘⣬⢻⣷⣟⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⢏⣞⣥⣿⣶⣿⣷⡱⣎⣛⠶⣙⢶⣙⠶⣩⢿⣿⢾⣿⣶⣧⣋⢶⢫⠜⣩⣞⢳⡜⢧⣣⢳⣙⠷⣘⡞⣿⣷⣦⠳⡜⣿⣯⣿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⣳⣿⣿⡻⢏⢧⣋⠷⣱⣚⢬⢏⡵⣣⠞⣭⡗⢎⡜⢣⡜⣫⣿⣿⣞⡬⡽⣣⢭⡓⣞⢣⢧⣛⡬⢏⡳⣜⢖⣻⣿⡷⡜⣜⣻⣷⣻⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢳⢹⣿⢳⠙⣮⢳⣬⠓⣧⡎⣧⢻⣴⢫⣾⢫⡜⡎⣼⢡⡞⣥⠛⡟⡏⣾⢱⡝⢲⣽⣬⢳⠓⣮⣵⠋⡗⠚⣮⢲⣽⣿⡝⣦⠓⣿⣷⢻⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣏⢮⠳⣍⡞⣹⣜⣦⢫⣛⡴⣙⡞⢦⣳⢾⢩⠎⡖⣩⢦⣹⣶⢩⢎⣱⣟⢣⣳⣙⠶⡱⡞⣎⣳⢣⡗⣫⣝⣣⢏⢶⢣⢿⣿⣜⢣⡝⣿⣟⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣿⡿⡜⢮⣛⢼⡸⣥⣿⣿⣗⠮⡵⢫⣜⣿⢋⠶⣩⠞⣡⢧⣾⣿⣿⣗⢮⠵⣎⠷⣱⢮⡹⡱⣝⠲⣇⢷⣩⢗⡼⣒⢏⢮⡣⢟⣿⣏⡞⡼⣹⣿⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⢷⣙⡳⢎⡶⣍⣿⣿⣿⣿⣛⡜⣧⠟⣆⠏⡶⣡⢋⡶⢧⣻⣿⣿⣿⡏⢾⢥⠻⣜⡲⣍⠗⣎⡻⡜⣖⣣⢏⡶⣹⢎⠧⣝⠮⣿⣿⢼⣱⢣⣿⡿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⢎⡼⣱⢫⢶⡱⢿⣿⣿⡿⣜⠾⣍⠳⣌⢧⡱⣦⢿⡙⢦⢛⣿⣿⡯⡝⢮⢇⡟⡲⣝⢬⠻⣬⢳⣙⢦⡳⢎⡳⡵⣪⢛⣬⢳⣹⣿⡞⣼⢣⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣿⣿⢎⡵⢣⣏⢶⡹⢎⡽⢯⡷⢫⡑⡎⢵⢊⢦⢳⡙⠮⡜⣣⢞⡹⢏⡵⡹⢭⠞⣼⢱⠮⣍⡻⢴⢫⡜⡶⣍⡏⢷⡱⣭⢓⢮⠧⣽⣿⡟⣼⢣⢾⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣚⢼⠳⣜⣎⢳⠽⣘⠧⣜⣱⣼⡿⠾⠿⠿⠻⠿⠷⣾⣷⣎⣝⡺⣜⡹⢮⡹⢎⢧⣛⡬⡝⢮⣓⢮⣓⢮⡝⣣⡝⣖⠯⣎⡗⢾⣿⡟⣬⠧⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⡞⡼⣙⢦⡝⣮⠽⣱⣾⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⢻⣷⣮⢝⢮⡝⣮⠳⡜⢶⡙⣧⡹⢦⢏⡞⣭⡓⢾⡸⡝⡦⣝⣻⣿⣙⠶⣹⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣯⣕⢫⠞⣼⢣⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣲⡝⣲⡝⣹⢎⡵⢎⡵⣫⢞⡹⣆⠿⣡⠟⡼⣱⢎⣿⡿⣽⣾⣿⣿⣿⣇⠀⠀⠀⠀ ⠀⠀⢀⣴⡿⠛⢿⢿⣿⣎⢧⢟⡱⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⡱⢞⡱⡞⣼⡙⢶⡱⣫⠵⣎⠽⣥⢻⡱⣣⣾⣿⢯⣙⢶⣿⢻⡿⠙⠿⣦⡀⠀ ⠀⣴⡿⠃⠀⠀⠈⢿⣿⣿⡎⢦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⢮⣳⣙⢦⣝⣣⢽⣡⠟⣬⣛⢴⣣⢛⣴⣿⡟⣮⣹⣾⢿⣿⠃⠀⠀⠙⣿⣦ ⣼⣿⠁⠀⠀⠀⠀⠘⢾⣿⣿⣦⠙⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢧⠶⣩⢖⡺⡴⣣⢧⣛⠶⣩⢖⡣⣿⣿⢯⡝⣶⣿⣯⡿⠃⠀⠀⠀⠀⢸⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⠈⢻⣯⣿⣏⡞⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡻⣽⢻⡿⣿⣿⢮⣹⢣⡞⣱⡓⣧⠞⣥⢻⢥⣛⣼⣿⣏⢷⣽⣿⣷⡟⠁⠀⠀⠀⠀⠀⢸⣿ ⣿⣿⣆⣀⣀⠀⠀⠀⠀⠀⠹⣿⣻⣿⣌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣺⣭⡷⣫⢷⣹⣻⣿⠲⣥⢳⣚⣥⢛⡴⣛⣜⣣⣾⣿⣟⣳⣾⡿⣫⡾⠋⠀⠀⠀⠀⣠⣤⣤⣾⣿ ⢸⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠈⠻⢿⣻⣯⣟⣿⣿⢻⢏⣛⠶⣭⠮⡵⢎⡽⢭⢻⡻⢷⣿⣧⣟⣿⣧⠻⣜⢣⡞⣴⢫⢞⣱⣾⣿⡟⣧⣿⣿⣽⡾⠋⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿ ⠘⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣻⣷⣏⣮⢣⣛⡴⣛⡼⡹⣜⢣⠷⣩⣛⠼⣻⡿⣿⣖⠻⣜⢳⡚⣦⣿⣾⣿⣻⡵⣿⣿⣿⠗⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠏ ⠀⠘⠻⠿⡿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣟⢿⣿⣿⣤⣧⣇⢧⢻⣘⠿⡜⣇⡻⡼⢣⢼⢣⣜⣿⣸⣧⣿⣿⢿⡼⣧⣿⢿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠛⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠫⢿⣽⡿⣿⣻⣿⣾⣷⣿⣶⣷⡿⣿⢿⣿⣻⣟⣿⣽⢿⣾⡿⠿⠛⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠋⢹⣿⠙⠻⠛⠋⠙⠻⠛⠟⢻⣏⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠄⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⡂⠀⠀⣀⣤⣤⣤⣄⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠔⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠂⠁⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠂⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⡧⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠄⠀⡀⠰⣀⠀⠄⣀⡀⡀⡀⢀⢀⠀⣀⣀⣤⣀⡀⠀⠀⠀⠀⠰⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠀⠐⠁⠀⠀⠈⠹⠊⠀⠱⠖⠁⠉⠒⠉⠀⠀⢀⠎⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⡢⣁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠘⠊⢄⡈⣑⢒⣊⠠⠜⠉⠉⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠑⡀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⢀⡼⣅⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⡆⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡔⠈⠀⠀⠀⠀⠀⠀⡞⠉⠉⠀⠀⠀⢹⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⡨⠀⠀⠀⠀⠀⠀⠇⠀⠀⠉⢹⠉⠈⠉⠉⠉⠉⡃⠀⠈⢄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠒⠄⠖⠁⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢆⠀⠀⠀⠀⠀⠈⠉⠒⠂⠒⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠁⠀⠀⠀⠀⠀⡌⠀⠀⡠⠎⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠊⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠙⣄⠀⣀⣀⣀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠒⠒⠂⠊⠊⠂⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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