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𝙉𝙤 𝙤𝙣𝙚 𝙣𝙤𝙩𝙞𝙘𝙚𝙨 𝙮𝙤𝙪𝙧
ˢᵃᵈⁿᵉˢˢ
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ᵖᵃⁱⁿ
𝘽𝙪𝙩 𝙩𝙝𝙚𝙮 𝙖𝙡𝙡 𝙣𝙤𝙩𝙞𝙘𝙚𝙨 𝙮𝙤𝙪𝙧
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⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣀⣴⣶⣷⣾⣿⣾⣿⣿⣿⣾⣿⣿⣷⣀⣈⢉⠿⣿⣿⣿⣿⣷⣍⢺⣿⣿⣿⣿⣿⣿⣿⣼⣽⣿⣛⣿⣿⣿⣿⣧⣏⠰⡈⢔⣧⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠀⠋⠐⠩⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⠀⠈⠻⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡗⣥⢚⣾⡿⣿⠿⡁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢚⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣿⡿⠏⠁⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣠⠐⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⢯⠹⡙⢬⢓⡁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡡⠙⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⠛⢩⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⣹⣿⣿⣿⣿⣿⣇⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡏⠆⠁⡘⣶⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠐⣀⣹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⣰⣿⣿⣿⡿⣿⣿⣿⣿⢋⡜⣲⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⢣⢿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠄⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢸⣿⣿⣿⣿⣿⣿⣿⠧⡁⢐⣾⣿⣿⣿⣿⣿⣿⠿⠿⠻⠟⠛⠁⠀⠀⢀⣽⣿⣿⠿⡟⡟⢻⢏⠧⠙⢾⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⡳⢌⣞⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣌⢤⣣⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⡀⠀⢀⠈⠀⢈⠸⣿⣿⣿⣿⣿⣿⣍⠒⣥⣾⣿⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠻⡟⠡⠈⠐⠈⠀⣾⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠜⠣⠛⡰⢾⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣻⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣷⡀⠂⠀⠐⠠⣘⣿⣿⣿⣿⣿⢋⠆⠑⣾⣿⣿⠟⠁⠀⠀⠀⠀⣠⣠⣄⡀⠀⠀⠀⠀⠌⠒⠀⠁⠀⠀⠀⣌⢿⢃⠐⣼⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠱⣿⣿⠿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⠎⡴⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣥⠈⠄⠂⢌⡿⣿⠻⠙⡀⠂⠈⢼⣿⣿⠃⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣆⠀⠀⠠⠌⠀⠀⠀⠀⢀⣾⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⢁⠀⠠⡑⢯⢏⡑⢮⣿⢏⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⠮⣵⢛⡿⡿⡟⣿⣿⠋⢽⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⣿⣿⣿⣿⡧⠀⠀⢂⡑⠢⢁⠂⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⡹⢲⡝⠢⢌⠢⢃⠎⢄⣹⣿⣿⠣⠉⢹⣿⣿⣿⣿⣿⣿⠿⣏⠳⢌⠣⠌⠱⣘⣷⣯⣏⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⠷⣀⢂⠤⣈⢅⠢⣐⣄⣦⣿⣿⣿⠟⠀⠀⠀⠀⠚⠿⡿⢿⠿⡿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠐⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢣⢋⠓⠬⠑⡀⢃⠂⢀⣾⣿⣿⣯⡄⠀⠀⠹⣿⣿⣏⠳⡈⢵⣈⠳⠌⠱⢈⢱⣻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⣿⣿⣿⣿⣷⣿⣾⣶⣯⣾⣷⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢂⠡⢘⠛⠟⠋⠌⠙⠛⠛⠻⠿⡿⠿⢛⠡⢂⠌⠈⠀⠁⠀⠀⠈⠈⠻⢿⣿⣿⣿⣦⡄⠁⠌⠻⣌⣳⣼⣶⣿⣜⣦⠐⣤⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⢀⠀⡄⢠⠐⠠⠌⡐⠠⢁⠂⠄⡀⠀⢀⠠⠈⠄⡈⠄⠂⠄⡈⠐⠠⢀⠀⠀⠀⠠⠱⣜⣷⣎⠦⠁⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠛⠻⣿⣿⣿⣄⠂⠁⠀⠁⠋⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠀⠀⠀⠀⡀⠄⠢⡐⡈⠤⢁⢊⠐⠠⢀⠑⠂⡌⠐⠠⠁⠀⠀⠌⠒⡠⠌⡐⠀⠀⠀⠁⠀⠂⠔⡀⠄⠡⢈⠢⢙⠀⠁⠀⠀⠠⣼⣷⣾⣾⣼⣷⣾⣶⣿⣿⣿⣿⣿⣶⣨⣶⣽⣿⣾⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢀⠀⢂⠔⡈⢡⠐⡐⡈⠄⠂⠌⡐⣀⠊⠡⠄⢃⠐⠀⠀⠌⣀⢃⡐⠰⢀⡁⢂⠀⠀⠀⠀⠐⠸⢨⠑⡠⠐⡀⢀⠀⡀⢤⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢏⡍⣹⣻⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠠⢈⠐⡈⠄⡡⠈⡄⢃⠡⠐⠀⠤⢡⣉⠒⠠⢂⠌⡀⠀⠀⢀⠩⣌⠁⠂⠌⡡⠌⡐⠠⠀⠀⠀⠂⠈⠐⡁⠂⠁⠌⠀⠳⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣌⠥⣫⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠹⣟⣿⣿⣿⠟⠀⠀⠀⠀⢌⠐⡀⢂⠐⡈⢄⠃⡐⠀⠀⠀⢈⠼⣡⠦⡑⠈⡄⠂⠄⠀⠀⠌⣓⢦⠡⢈⠐⢀⠓⢌⡁⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⣺⣿⣿⡏⠀⠀⠀⢰⡉⢆⢂⠐⡀⢢⠁⡆⡘⠀⠁⠀⠀⡌⢾⡱⣏⠴⡁⠄⠡⠀⠀⠀⠨⣽⣧⡃⠄⠀⠀⠈⠄⡐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠋⠀⣄⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢣⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢹⣿⡟⠀⠀⠀⡔⡣⠜⡌⠀⠠⠐⡡⢊⠔⠁⠀⠀⠀⠰⡌⢧⢿⣿⣦⡑⠈⠀⠀⠀⠀⣘⣿⣿⣧⠂⠀⠀⠀⠐⡈⣁⠂⠀⠀⠀⠀⠀⠄⡤⢀⠀⠀⠀⠀⢹⣿⣿⣧⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠧⡑⠈⠀⠀⠀⡐⢁⠂⠀⠀⠀⠀⠀⡰⡝⣎⣿⣿⣷⣇⠀⠀⠀⠀⠀⣼⣿⣿⣿⡅⠀⠀⠀⠀⠀⠄⢂⠁⠀⠀⠀⢠⢻⣼⣧⠆⠀⠀⠀⠀⠉⢿⠻⣜⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣿⡁⠀⠀⠀⠡⠐⠀⠀⠀⠠⠐⢂⠈⠀⠀⠀⠀⢠⢱⣻⣼⣿⣿⣿⣧⠀⠀⠀⠀⢰⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⢂⠐⠀⠀⠀⠀⠩⠻⢍⠣⢀⠀⠀⠀⠀⠀⠉⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠰⣿⣿⠀⠀⠀⠀⡁⠀⠀⠀⠀⢂⠁⠂⠀⠀⠀⠀⠰⣈⠶⣽⣿⣿⣿⣿⣿⠀⠀⠀⣠⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠃⠂⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠫⠅⠂⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⡆⠌⡀⠀⠀⠀⠀⠡⠈⡝⢻⣿⣿⣿⣿⣿⡇⡀⠠⣽⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡩⢂⠱⡌⠀⢁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣻⣿⣇⠀⠀⠀⠀⠀⠀⣀⢞⣼⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣄⢰⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⣧⠻⣔⠛⢿⣿⣿⣿⣿⣿⣿⣿⢏⡐⠀⠀⠀⠈⠀⣀⢻⡤⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⢀⣾⣿⣿⣿⣽⣦⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⢿⣿⣿⣯⣔⣩⣮⣱⠀⠉⠻⣿⣿⣿⡿⡟⢦⡐⡀⠀⠀⠀⠀⠄⣿⢾⡥⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣘⣮⣷⣿⣷⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢉⢏⡐⢌⢦⡱⢄⠀⠀⠀⠠⢘⡼⢯⣟⣥⠂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⠂⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⠿⢿⣿⣿⣿⣧⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡄⡀⠀⢄⡲⡸⡜⣦⢳⡎⡔⡠⢂⢡⢊⡼⢯⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠅⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣎⢿⣿⣿⣿⣧⠌⢸⣿⣿⣿⡿⣿⣿⣿⣿⠇⠰⣁⢮⣷⡱⡹⢌⢷⣛⣶⣽⣿⣶⣯⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢻⠏⠁⠀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣌⡁⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠠⣿⣿⠻⢿⣿⣿⡾⣹⣿⣿⣿⡆⢨⣿⣿⣿⠷⡙⢿⢋⠁⠈⢠⣽⣿⣿⡷⣑⠎⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠡⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⢀⡰⡿⠁⠀⠢⣽⣿⠓⠈⠿⣿⣿⡗⠰⢿⣿⣿⠇⡈⠆⡌⢌⢣⣞⣿⣿⣿⣿⣱⢞⡼⣳⢎⣿⣿⣿⣿⡿⣿⡬⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⢏⡒⡀⠀⠀⠀⠀⠀⡍⢛⠻⢟⠟⡏⠁⠀⠀⠀⢀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣾⣿⠁⠀⠀⠐⡡⢇⠀⠀⠀⠈⠉⠀⠀⢌⣿⣿⡇⠰⠡⢌⢢⣿⣿⣿⣿⣿⣿⣿⣾⣷⣽⣎⡾⣿⡽⣧⣟⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣫⠖⡱⢢⠄⠀⠀⠀⠀⠐⣦⣳⣬⣖⠠⠀⠀⡀⠰⣈⢞⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⢍⡀⡀⠀⠀⠀⢀⢠⣾⣿⣿⢍⠢⡑⢮⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢯⡱⠃⠌⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⢆⠐⣈⠱⣘⣮⣷⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣄⠀⠀⠀⠀⠀⠐⢩⢳⡽⣮⣿⣿⠟⣏⠣⢊⠔⡡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣾⢯⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⡹⢀⠀⠠⠀⠀⠀⠀⠹⣿⣿⣟⢀⠂⢀⢄⡣⣝⣾⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡙⢢⠉⡄⠣⢌⢢⡱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⢣⢅⡀⠀⠀⠀⠀⠠⢡⡜⣿⣭⣲⣬⣞⣾⣿⣿⣿⣿⣿⣿⣿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣷⣆⠀⠀⠀⠀⠀⠀⠤⡘⢄⠣⢌⡑⢎⢶⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡎⣮⣗⡠⠀⠀⠀⠡⠃⠽⣿⣿⢿⣿⣿⣿⣿⣿⣿⠿⡛⠍⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣀⠀⠀⠀⠀⠢⡑⢌⠒⡬⡘⢬⣚⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⡜⣱⣿⣷⡄⠀⠀⠁⡐⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡓⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣴⣤⣰⣾⣿⣿⡀⠀⠀⠀⠀⠈⠢⡉⠔⡩⢆⡍⢫⠹⣉⠗⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⠛⠻⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡙⠶⢹⢿⣿⡷⠀⠀⠀⠠⢻⣿⣿⣿⣿⣿⣿⠿⠿⠃⠱⠌⠧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⠏⠔⠀⠀⠀⠀⠀⠀⠀⠁⠂⠇⠞⣧⠗⠬⢞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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