The amazing world of Gumball 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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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣵⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣦⡀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠁⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣦⡀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢙⡧⠠⣄⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣠⠏⠀⢠⠏⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⢷⢦⠀⠀⣠⣾⣿⡆⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⢰⠃⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⡽⠲⡀⠀⠀⢀⣼⣾⣀⠔⢭⣿⡿⢳⣼⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣷⣄⡀⠀⢷⣄⠀⠀⠀⢀⡞⠁⠀⡼⣀⠴⣫⠶⠛⢧⡀⣸⣿⡔⢺⡇⢀⠇⠀⠀⠀⠀⠀⣰⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠓⠾⠏⠳⣄⣀⡜⠀⠀⠚⠋⢡⠞⢁⡤⣶⣾⡟⣿⣟⠀⢸⠄⢸⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⡗⠒⠢⣄⡀⠀⠉⠀⠀⠀⠀⣠⡿⠚⠙⣷⡿⠟⢸⣿⠙⠀⣸⠀⡇⠀⠀⠀⢀⣾⠟⡠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⡿⣋⣹⣟⣷⣄⠀⠀⠀⠀⠀⠛⠒⠒⠉⠁⠀⠀⡾⣿⣇⡴⠁⠀⡇⠀⠀⢀⣾⡟⡔⠁⠀⠀⠓ ⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⡄⣀⣼⠁⠀⣿⠁⠉⠁⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡿⠁⠀⠀⢸⠀⠀⠀⣼⡿⡰⠁⠀⠀⠀⠀ ⡟⠀⠂⠀⠀⠀⠀⢿⣿⣿⣿⣿⠃⠀⠀⡟⢦⠀⠀⠀⠀⠺⠄⠀⠀⠀⣠⡞⠀⠀⠀⠀⢠⡇⡇⠀⠀⠀⢸⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⣠ ⣿⣇⡀⠀⠀⠀⠀⠈⠉⢸⣿⠏⠀⠀⣸⠀⡏⠑⢦⡀⠀⠀⠐⣾⣿⣿⡿⠁⠀⠀⣀⠴⠉⡇⢹⠀⠀⠀⢸⠀⠀⣸⣿⠘⠀⠀⠀⠀⠀⡀ ⠿⠿⠇⠀⠀⠀⠀⠀⠀⢀⣯⡤⠄⢴⠇⣸⣀⡀⠀⠉⠓⠦⣀⡉⠉⠉⠀⢀⡤⡾⠁⠀⣰⡇⢸⣷⣦⠤⠞⠒⠒⠺⣧⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⡎⢠⠃⠀⠉⠙⠒⠂⠤⠤⣽⠓⠒⠊⠉⠀⣧⣀⣼⣿⡇⠀⣿⣿⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⢀⡞⢠⠇⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⡇⠀⡿⠃⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⡼⠀⠀⠀⡞⢠⠏⠀⠀⠈⠑⠦⡀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠟⠁⢠⠇⠀⠀⡸⣰⣯⠏⠀⠀⠀⢀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀ ⠀⢀⡼⠧⠶⠦⠾⠦⠤⠤⠷⠿⠥⠤⠤⠶⠿⠋⣸⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⡇⡜⠀⠀⠀⠀⠀⠀⣸⣄⠀⠀⠀⠀⠀ ⠀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⣤⣤⣤⣴⣾⣿⣦⣈⠙⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠤⠼⣟⠁⠀⠀⠀⠀⠀⢠⠟⢏⠻⠷⣦⣀⣀ ⠞⡏⠳⣄⡀⠀⠀⠀⠀⠘⡆⢹⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠀⠀⠀⢀⡞⠀⠈⢆⠀⠀⠀⠀ ⠀⡇⠀⠀⠈⡏⠹⡟⣆⠀⢃⢸⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢁⡴⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢸⠆⠀⠀⠀⡼⠁⠀⠀⠈⢆⠀⠀⠀ ⠀⠀⠀⠀⠀⢧⠀⠹⢶⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠋⡰⠋⢁⣠⢤⣤⣤⡴⠚⠁⠀⡼⠀⠀⠀⢰⠃⠀⠀⠀⠀⠈⡆⠀⠀ ⠀⠀⠀⠀⠀⢸⡀⠀⠈⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⣉⣴⣾⣿⡟⠀⠀⠀⠀⡇⠀⠀⢀⠟⡇⠀⠀⠀⠀⠀⠸⠀⠀ ⠀⠀⠀⠀⠀⠀⢧⠀⠀⡇⢸⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢠⠇⠀⠀⡼⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠀⠀⠀⠀⠀⠘⡆⠀⣣⢸⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢸⠀⠀⣰⠁⠀⠈⣇⠀⠀⠀⠀⠀⠈⡄

Warning: This item may contain sensitive themes such as nudity.

⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠀⠀⠉⠛⠿⣦⡀⠀⠑⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⢞⠀⡠⠊⠀⠀⠀⠀⠀⢠⡀⠀⠈⢹⠠⡀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢐⢡⠃⠀⡁⠀⠀⠀⢲⢄⠀⠀⣫⢆⢔⣿⢇⡇⡆⠀⠀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⠈⠚⣷⣄⣱⢄⠀⠰⠁⡰⠕⠞⢊⣱⣼⡗⢸⢀⠁⠀⠀⣠⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣖⣢⣄⠉⠁⠀⢀⠎⢊⡿⠟⣾⠁⡸⠘⠀⠀⣴⢯⠀⠀ ⠀⠀⠀⠀⣠⣤⡀⣰⠈⡗⠚⠚⠃⡀⠀⠀⠀⠀⠀⢰⢹⠊⠀⡆⠀⣸⢏⠃⠀⠀ ⣅⠁⠀⠀⠹⢿⣿⠃⢀⢓⢄⠀⠈⢃⣀⢤⡎⠀⢀⣼⢰⠀⠀⡇⠀⡿⡀⠀⠀⠐ ⠿⠇⠀⠀⠀⢀⡧⠄⡜⡬⢀⡉⠢⠄⡉⠉⡀⢴⠁⣸⠘⣶⠤⠓⠚⢇⠀⠀⠀⠐ ⠀⠀⠀⠀⣠⠋⠀⡐⡐⢀⠀⠀⠉⠁⠁⠀⠀⢘⣶⣿⠀⡿⠀⠀⠀⠀⠡⠀⠀⠀ ⠀⠀⢠⠊⡌⠀⡰⣐⠄⠀⠁⠂⢀⣀⣤⣶⣾⣿⣿⣿⠀⡇⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⡴⠁⠀⠃⠤⠿⠧⠤⠶⢊⡏⢿⣿⣿⣿⣿⣿⣿⣿⠀⣣⠁⠀⠀⠀⣆⣀⠀⠀ ⢼⢣⡀⠀⠀⠀⡐⠘⣿⣿⣿⣿⣦⣬⣍⠉⠉⠉⠉⠉⠉⠣⠀⠀⠀⡜⠘⡌⠑⠒ ⠘⠀⠈⡍⢏⣀⣧⣤⣿⣿⣿⣿⣿⣟⡡⢂⠄⠀⠀⣀⠴⢀⠃⠀⢰⠁⠀⠘⡀⠀ ⠀⠀⠀⢧⠀⠃⢻⣿⣿⣿⣿⣿⣿⣿⣷⣧⣮⣽⡿⠁⠀⢸⠀⢀⠳⠀⠀⠀⠰⠀ ⠀⠀⠀⠈⡄⢸⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠈⠀⡌⠀⡆⠀⠀⠀⠀

Warning: This item may contain sensitive themes such as nudity.

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