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