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