CODM Emojis & Text

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