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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢖⡳⢞⣲⠳⣬⣁⠆⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢞⡱⢮⣝⡣⣗⠻⣴⢋⡿⣈⠭⣂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠮⣝⣣⠞⡵⣎⢟⡲⢏⡞⡥⠚⡄⠦⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡟⣬⢧⢻⡱⣎⣏⠾⣹⣜⢣⠓⢬⠱⡁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠱⣎⠷⣙⠶⣎⠯⡕⡌⠦⡙⢢⡑⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠰⠡⢎⡡⢃⠇⡜⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠗⣮⠵⣑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⢎⡰⠩⡜⠂⠁ ⠀⢀⢀⠰⣀⣆⡰⢂⠄⠀⠀⠀⢠⡺⣥⢻⠜⡣⢒⡄⢀⠠⣀⠰⣀⢤⣀⢀⣠⢞⡌⢦⠑⠃⠀⠀⠀ ⠠⢌⡼⣋⢷⢪⡝⣧⢝⠤⢋⡔⢃⠖⡤⠗⠀⠀⠡⡘⣌⠲⣁⠳⣈⡗⣮⢓⡮⠾⠋⠀⠀⠀⠀⠀⠀ ⡎⢼⢳⡹⢎⡷⣹⢬⣛⡎⠥⠚⣌⠲⠌⠀⠀⠠⣡⠓⠌⠢⡑⡎⠴⣘⠧⣻⢜⠁⠀⠀⠀⠀⠀⠀⠀ ⠨⠜⣧⢫⡝⢶⣙⠶⡭⡖⢩⡑⢢⠅⠀⠀⠀⡒⢤⠃⣶⡆⣤⣌⡑⢢⡑⢆⠎⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠑⢨⠳⣭⢳⢭⡞⡱⢌⠣⡼⠃⠀⡀⢄⠢⢍⡒⢬⢋⡅⡛⢇⡍⠦⣑⠪⠌⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠰⠏⢫⣾⡝⠷⠞⠃⠁⣀⣷⡹⣼⣷⣾⣿⣼⣞⡵⣻⡎⡽⢦⢻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢻⢦⣿⣿⣿⣿⣿⣿⣿⣿⣵⣛⢷⣫⣿⣷⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢬⡘⠦⣘⢛⣶⣿⣿⡭⣿⣿⠧⣉⢆⠣⢏⡟⣴⢛⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⢚⡰⠡⢎⡙⡛⢟⡱⠌⡆⡓⡌⠦⡙⠬⡙⡶⣋⡇⡀⢄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⢣⡙⠤⢃⡍⠲⡰⠩⡔⡱⢌⡱⢊⡗⡱⠢⠅⠰⣘⢢⠹⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠣⢜⡩⠲⢇⣜⡐⢎⡔⢻⣜⡳⢏⡗⡸⢄⢣⡙⢬⢒⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡻⢪⢅⡚⠴⣈⠣⠥⣉⡇⠴⡑⢪⠔⡸⢌⢎⠂ ⠀⠀⠀⢀⠠⣠⢂⠭⡰⢄⢀⠀⠀⠀⢀⢄⢢⠱⡌⡒⠥⡒⢬⡑⠬⣑⠊⠀⠀⠀⠱⢃⣜⠳⡬⠁⠁ ⠀⠀⠀⣆⢣⠣⠎⡜⣑⠪⡌⡅⠀⡀⡱⢊⢆⠣⡜⢡⢣⠑⠦⡌⡗⡰⣀⠀⠀⣀⡀⡠⡤⠀⠀⠀⠀ ⠀⠀⠀⠐⠢⡙⠼⣴⢨⡑⡌⣄⠣⡜⢡⠎⢢⠓⢬⡑⢢⡙⢆⣱⢋⠴⢡⠊⣵⣶⣦⣝⢻⣍⣂⠀⠀ ⠀⠀⠀⠀⠁⠬⣙⣎⢷⠨⡔⣎⠒⡥⢃⠎⡥⢋⠴⣈⠇⡜⣂⠂⠈⠘⠃⣙⣿⣿⣿⡷⣹⡛⣏⠆⠀ ⠀⠀⠀⠀⠀⠐⢡⡉⢆⠳⠐⠀⠀⠈⠣⡚⢤⠋⡴⣈⠖⠁⠀⠀⠀⠀⠀⠀⠒⠌⣫⣵⣽⣻⠐⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠀⠩⢥⡉⠖⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠴⡨⢍⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢬⡑⢣⠜⢢⠬⡑⢤⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠬⢅⠎⡥⡲⢩⡜⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠤⠶⠶⠶⠖⠚⠉⠀⠀⠀⣰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠛⠻⣿⣿⣷⣤⣤⣤⣀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⣧⣶⣿⣿⣿⣿⣿⣷⣦⣠⠋⠀⠀⢀⣿⣿⣿⣿⠟⠀⠈⠓⠶⠒⢿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀ ⠹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⡤⠊⠈⠉⣩⢲⠤⡀⠀⠀⢠⠴⠶⣍⠻⠿⠿⢿⠀⠀⠀⠀⠀ ⠀⠙⢿⣿⣿⣿⣿⡿⣣⣴⣾⡍⠀⠀⠀⠀⠻⢿⣷⠃⠀⢀⡏⠀⠀⢸⠀⠀⠀⠈⢧⡀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⣽⣿⣿⣿⣿⠃⢀⣀⣀⠀⠀⠀⠀⠀⣠⣾⠀⠀⠀⣸⠀⢀⣀⣀⣀⡙⢦⡀⠀ ⠀⠀⠀⠀⠀⣼⣿⣿⠿⠛⠁⢸⣿⣿⣿⣿⣶⡄⠀⠀⠹⣿⡄⠀⠀⡏⢸⣿⣿⣿⣿⣿⣷⡝⢦ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿⢻⣿⡗⠀⠀⠀⠙⣧⠀⠀⢧⠘⢿⣿⣿⣿⣿⣿⠇⢸ ⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⢧⣀⠉⠉⠉⠉⠁⣠⠏ ⠀⠀⠀⠀⠀⠀⠙⠲⣄⣀⢀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠈⠙⢓⣶⢾⣉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⣸⠉⣧⡀⠀⠀⠀⠀⠀⣀⠞⢳⣄⣀⠀⠀⣀⠔⠋⢀⡴⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣶⣃⡉⢓⡶⠒⠒⠋⠁⠀⠘⣿⣿⣿⡿⠋⢠⠞⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⣣⣾⣭⠉⠀⠀⣀⡀⠀⠀⠀⠀⠈⠁⠀⢀⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣽⣧⣿⡿⢟⡤⠴⢼⣿⣿⣷⣼⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣇⣿⡷⠋⠀⡔⢙⠿⠿⢿⠙⢯⣹⠃⠀⠀⡆⠀⢿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠳⣼⣄⣀⣼⣡⠞⠹⣄⣀⣴⣇⣠⠞⠁⠀⠀⠀⠀