1988 Emojis & Text

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠿⠿⠷⣶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⢀⣀⡀⠙⣷⡀⠀⠀⠀ ⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠘⠿⠃⠀⢸⣿⣿⣿⣿ ⠀⣠⡿⠛⢷⣦⡀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠟ ⢰⡿⠁⠀⠀⠙⢿⣦⣤⣤⣼⣿⣄⠀⠀⠀⠀⠀⢴⡟⠛⠋⠁⠀ ⣿⠇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀ ⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀ ⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀ ⠀⠹⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠉⠙⠛⠿⠶⣶⣶⣶⣶⣶⠶⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀

𓅸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇

⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⠛⠁⢰⣧⡈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣇⣼⡀⠻⠟⠁⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡞⣹⠙⣧⡀⠀⠀⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⡴⠋⠀⣀⣴⣿⡷⠴⠞⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢾⣁⣀⡤⠾⠛⠁⣸⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠁⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣿⠁⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⢿⣶⠶⠿⠟⠿⠿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠈⠙⠛⠿⠶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀⣠⣤⣤⣤⣤⣤⣀⠀⠉⠙⠳⢦⣄⡀⣀⣤⣀⣀⡄⠀ ⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠈⠉⠻⢶⣀⠀⠀⠈⠉⢁⠈⠏⣿⣁⠀ ⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⣀⡴⠁⠀⠀⢙⣿⡾ ⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⣀⣠⡾⠟⠃ ⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡔⢊⣵⠞⠋⠁⠀⠀⠀ ⠀⠀⠀⠙⠿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠳⠶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣴⠊⣁⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⡷⢶⡶⠶⠤⠔⢺⠃⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⢰⡇⠀⡇⠀⠀⠀⢸⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣤⣭⠿⠟⣃⣾⠋⠀⠀⢠⡟⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠙⠛⢋⣿⣙⣶⣾⡿⢷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠻⠧⠶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠘⠛⠚⠛⠻⠟⠛⠓⠟⠻⠓⠐⠚⠒⠛⠁⠀⠀⠸⠓⠇⠞⠛⠚⠙⠲⠀⠐⠞⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀

⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛🟨🟨🟨🟨⬛⬛⬜🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛🟨🟨🟨🟨⬛⬛⬛🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛⬛🟨🟨🟨⬛⬛⬛🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬛🟨🟨⬛🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬛⬛🟨🟨🟨🟨⬛🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬛🟨🟨🟨🟨🟧🟧⬛🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬛🟧🟧🟧🟧🟧⬛⬛🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛ ⬜⬜⬛⬛⬛⬛⬛🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛ ⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨⬛🟨⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬛🟨⬛ ⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬛⬛⬛🟨🟨⬛ ⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛ ⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛ ⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛ ⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜ ⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛🟨🟨🟨🟨🟨🟨⬛⬜ ⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛🟨🟨🟨🟨🟨🟨⬛⬜ ⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛🟨🟨🟨🟨🟨🟨🟨⬛⬜ ⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜ ⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬛🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜ ⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬛⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨🟨⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣩⣭⣶⣶⣮⣭⡙⠿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠿⣋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⡃⠄⠹⡿⣿⣿⣿⣿⠟⠛⣿⣿⣿⣿⣷⡌⢿⣿⣿ ⣿⣿⣿⣿⣿⠐⣠⡶⣶⣲⡎⢻⣿⣤⣴⣾⣿⣿⣿⣿⣿⠸⣿⣿ ⣿⠟⣋⡥⡶⣞⡯⣟⣾⣺⢽⡧⣥⣭⣉⢻⣿⣿⣿⣿⣿⣆⢻⣿ ⡃⣾⢯⢿⢽⣫⡯⣷⣳⢯⡯⠯⠷⠻⠞⣼⣿⣿⣿⣿⣿⣿⡌⣿ ⣦⣍⡙⠫⠛⠕⣋⡓⠭⣡⢶⠗⣡⣶⡝⣿⣿⣿⣿⣿⣿⣿⣧⢹ ⣿⣿⣿⣿⣿⣿⣘⣛⣋⣡⣵⣾⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⢸ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⢸ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⢸

⠀⢀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣠⣤⣤⣤⣤⣀⠲⢦⣄⡀⠀⠀ ⡶⢟⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠰⣷⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⡛⢷⣔ ⣾⡿⠟⠋⠉⠁⠀⡀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢻⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣛⣛⣉⢉⣉⡀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣝ ⠃⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛⢛⡛⠛⠛⠛⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣓⣀⠀⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⢀⣤⡾⠛⢻⣿⣿⣿⡿⣿⡟⢻⣿⠳⠆⠘⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠐⠛⣿⡟⢻⣿⣿⣿⣿⢿⣟⠛⠻⣦⣀⠀⠀⠀⠀ ⠀⠀⢴⠿⣧⣄⣀⣘⣿⣿⣿⣿⣿⡿⣀⡙⢷⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⡖⠀⣾⣋⣀⣺⣿⣿⣿⣿⣿⣏⣀⣤⣴⠿⢷⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠆⠀⠀⢀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠛⠋⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡼⠇⠀⠀⠀⠘⡆⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⢀⡼⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢠⠞⠀⢹⡄⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡿⣯⡷⡴⢦⣤⡠⣶⡶⠀⢷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⡾⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣼⣥⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⠀⠈⢧⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⠛⢦⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠳⠀⢳⡀⢹⡇⠀⠀⠀⠀⠀⡾⡇⠀ ⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠘⠀⠀⠹⣼⡇⠀⠀⠀⠀⢠⠇⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⢠⡏⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⡾⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡟⠀⠀⠀⠀ ⠀⣴⠓⣾⣳⣀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠃⠀⠀⠀⠀⠀⠀⢸⡇⢀⠇⠀⠀⠀⠀ ⣾⠃⠀⠀⠀⠑⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀ ⠹⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀ ⠀⠀⣷⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡏⠀⠀⠀⠀⠀ ⠀⢀⡇⢹⣄⠀⠀⠀⠀⣀⠉⠓⠶⢄⡀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠣⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣸⣧⠀⠀⠀⠀⠀ ⠀⣴⣿⠋⠘⣆⠀⢰⠶⠤⢍⣛⣶⠤⠿⣷⣦⡀⠒⠚⡟⠀⠀⠀⠀⠈⠛⠢⠤⡄⠀⠀⢀⡴⢯⠴⣳⠇⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠘⢦⡈⠻⣖⠤⣤⣉⣉⣹⣯⣭⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠛⣫⣼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⢦⡀⠀⠀⠈⠉⠁⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⣷⢚⡝⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢶⣷⠇⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠚⠉⠉⠉⠙⢯⣢⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢺⠊⠀⠀⣀⠀⠀⠀⠀⢱⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣮⠃⠀⠀⠘⠛⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⢀⣼⠒⣺⣻⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠛⠃⠀⠀⠀⠀⠀⠀⢞⠁⠈⠉⡿⡿⡄⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⡴⠊⠁⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⡀⣹⣖⠀⠀⠀⠀ ⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣧⠀⠀⠀ ⠀⠀⣎⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀ ⣠⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠈⠳⡅ ⢳⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠈⢞⣁⣀⣀⡀⢀⡀⣀⡀⠓⠉⠒⠦⡀⠀⢱ ⡾⠀⠀⠀⠀⠀⠀⠀⢰⠛⠉⠀⠀⠀⢰⠛⠛⠛⠁⠈⠙⠛⠛⡇⠀⠀⠀⠈⠛⡄ ⢻⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⣀⡀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⣀⣀⣠⠃ ⢸⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠁⢠ ⠸⡽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡼ ⠀⠙⠹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡞⠀ ⠀⠀⠀⠀⠙⢲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠘⢿⣿⣿⣶⡦⠶⠶⣾⠏⠉⠉⠉⠉⠉⠉⢉⢿⣿⣷⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠁⡸⠷⣶⣴⣶⣦⡀⠀⠀⢀⣤⣤⣴⣵⡿⢞⠿⡶⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⠤⠿⠧⠶⠶⠤⢧⠃⠀⠀⠙⠾⢟⣛⣁⣒⣻⣅⣙⡾⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⡶⠒⠒⠶⠦⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠚⠉⠁⠀⠀⠉⠻⣦⡀⠀⠠⠤⢬⣉⡛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⢁⡤⠀⠀⠀⠀⠀⠀⠀⠐⢬⣧⠀⠀⠀⠀⠈⠙⣶⡈⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢀⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⡄⠀⠀⠀⡀⢹⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠊⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⣿⠀⢿⢦⣄⠀⠀⠀⠀⠀⠈⣼⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢀⡼⢻⡇⢣⠀⠀⠀⠀⠀⣼⠀⠘⡇⠈⠛⠳⢦⡀⠀⠐⠘⣿⣻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡾⠁⢠⠃⠀⠀⠀⡀⢀⡴⠋⠀⠼⡇⠘⣆⠀⠀⠀⠀⣿⠄⢰⡇⠀⠀⠀⠈⢻⡄⠀⢲⣜⣷⢿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⠀⠀⠋⠀⠀⠀⣴⠛⠉⠀⠀⠀⠀⠹⣄⠀⠀⠀⣀⠀⣿⣼⣾⠃⠀⠀⠀⠀⠀⢻⡆⠘⣿⣾⣿⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠃⠀⠀⠀⡀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣿⣹⣿⠟⠁⠀⢀⣀⣀⣤⡤⠽⢿⣷⡈⢻⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⢠⠀⢀⢰⡇⢸⠃⢀⣀⣀⣴⡤⠦⠀⠀⠀⠀⠀⠀⠉⠁⠓⣆⠀⠀⠀⠀⣿⣿⡿⠀⣻⣿⣷⣆⠙⢿⣿⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⢸⠀⢸⣿⢳⣿⠀⠀⠀⣿⣿⡟⠀⠀⠀⢀⣤⠴⠒⠚⠛⠛⠛⠛⠦⣄⠀⠘⠙⠀⠀⠉⣠⣿⣿⡆⢸⣿⠀⠀⠀⠀ ⠀⠀⠀⢀⡾⣟⣧⡏⠿⠀⠋⠀⠀⠀⠈⠉⠀⠀⠀⠀⠿⣧⣀⣀⣀⣀⣀⣀⣤⡤⠞⠉⠒⠒⠓⠒⠒⠻⠋⠈⣇⣼⠇⠀⠀⠀⠀ ⠀⠀⢠⡟⠀⠈⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢿⢶⡀⠀⠀⠀ ⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⠀⢻⡄⠀⠀ ⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢻⡀⠀ ⣼⠁⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⣀⣤⠴⠚⠉⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢷⠀ ⣿⠀⠀⠀⠀⠀⠀⣰⠯⠤⣤⣤⡤⠴⠒⠛⠉⠀⠀⠀⢀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⡇ ⣿⡀⠀⠀⠀⠀⢰⠃⠀⡞⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿ ⠘⣧⠀⠀⠀⢠⠟⠀⠀⣧⣧⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿ ⠀⠘⣄⠀⠀⡼⠀⠀⠀⠈⠛⣳⡤⠤⠤⠤⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣄⠀⠀⣿ ⠀⠀⠸⠦⢾⡓⠒⠖⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠙⠦⠼⠏ ⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢤⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⠒⠓⠲⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣄⣤⠿⢧⣤⣤⠽⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠚⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠉⠙⠲⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡞⠁⣀⣀⣀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⡀⠘⡆⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣿⣿⠉⠉⠉⣹⡆⠀⠀⣿⣿⣿⣿⡇⠀⢀⣀⡿⠀⢹⠀⠀ ⠀⢀⣀⣠⡬⠿⠿⠟⠓⠚⠛⠉⠉⠉⠙⢲⡈⠉⠉⠉⠉⠉⠉⠀⠀⠀⢸⡆⠀ ⣞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀ ⠉⠓⠶⠶⣶⠶⠶⠶⠖⠒⠒⠒⠒⠒⢦⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⠈⠓⠒⠶⠶⠶⠶⠶⡶⠶⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠙⠛⠛⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠀ ⠀⠀⣀⣤⣴⣶⣶⣿⡟⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀ ⠀⢰⣿⡟⠋⠉⣹⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⠀ ⠀⢸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⣸⣿⡇⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⡇⠀⠀ ⠀⣿⣿⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀ ⠀⢿⣿⡆⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠸⣿⣧⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀ ⠀⠀⠛⢿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣰⣿⣿⣷⣶⣶⣶⣶⠶⠀⢠⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⣽⣿⡏⠁⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡇⠀⢹⣿⡆⠀⠀⠀⣸⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣄⣀⣠⣴⣿⣿⠁⠀⠈⠻⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

𓅷

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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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⠀⠀⠀⡴⠁⠀⠀⡜⢀⠎⠐⠀⠀⠀⠀⠀⠀⢠⣾⣷⠀⠈⢿⣆⠀⠀⢀⠀⠀⠙⣄⠀⠀⠈⠻⣿⣧⣀⠀⠙⢦⠙⢷⣝⠢⢄⣀⠀⠀⠀ ⠀⠀⠊⠀⠀⢀⡾⢠⠏⠀⠀⠀⠀⠀⠀⢠⣷⣿⡿⢽⡆⠀⠈⢿⣆⠀⠈⢣⠀⠀⢈⢦⡀⠀⠀⠈⢻⣟⡿⣦⡀⠱⡀⠙⢧⡀⠈⠉⠒⠢ ⠔⠁⠀⢀⡔⠡⢡⠃⠀⠀⠂⠀⠀⠀⢠⣷⡧⢴⠟⠃⠻⣄⢀⣀⠻⣧⠀⠀⢣⡀⠈⢎⣷⣄⠀⠀⠀⠹⣾⡈⠙⢆⠀⠀⠀⠱⡄⠀⣀⠀ ⠀⠀⢠⠊⢰⡷⠁⠀⠀⢠⢀⠀⠀⠀⣾⠏⠀⢠⣠⡒⠀⠼⢆⣿⠳⡈⠳⡀⠀⠑⡄⠈⢞⣏⠑⣄⠀⠀⠘⣷⠀⠀⠳⡀⠀⠀⠈⠢⡈⠙ ⠀⠀⠏⠐⠉⠀⠀⠀⢀⣾⣼⠀⠀⠀⣿⠶⠶⢿⡦⢽⣿⣿⣾⠿⢧⠈⢦⡈⠢⡀⠈⢦⠈⢿⣗⣚⣳⣄⠀⢸⡇⠀⠀⢹⣦⡀⠀⠀⠈⠂ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡇⡄⠀⢰⡇⠀⠀⠀⠀⠈⠻⣿⣿⡛⠀⠙⠦⣝⢦⡈⠀⠀⠑⢼⣏⠉⠙⠻⣷⣄⠳⣄⠀⠀⡏⠛⢄⠀⢳⠀ ⠀⠀⠀⠀⠀⠀⣰⡿⣹⣿⡇⢇⠀⢸⠀⠀⣠⡀⠀⠀⠀⢻⣿⣷⣾⣷⡞⠉⠀⣿⣦⡀⠢⡀⠙⡄⠀⠀⢻⣿⣷⣌⠣⡀⠸⡄⠀⠙⢆⣣ ⠀⠀⠀⠀⠀⢰⠛⡗⣿⡏⢁⠘⡄⠈⡄⠀⠈⠀⠀⠀⣠⣼⡿⣛⣯⡝⠋⠀⠀⠉⢛⡿⢦⠈⠢⡘⣆⣀⣘⣿⣿⡿⣿⠳⡀⠈⡶⠒⠉⣩ ⠀⠀⣴⢰⠀⣾⠀⢳⣹⣧⣈⣆⠙⡄⢣⣤⠴⢶⣾⣿⣟⡩⣭⣀⠀⢀⠀⠀⠀⠈⠉⠀⣼⣷⣷⣿⣼⡿⠻⠿⣿⡗⢻⣦⠷⡾⠁⠀⡴⠁ ⠀⡀⣇⠘⡀⡿⣧⠀⢻⡟⠺⠿⠦⡈⠈⢧⠈⠓⢈⠨⠇⠛⠉⠂⠈⠀⠀⠀⡠⠒⠁⢠⣿⠀⣿⡏⠙⠇⠀⠀⢿⡇⢸⡏⡼⠁⠀⡼⠁⠀ ⠀⣷⣿⡀⢳⡇⠹⣧⡀⠳⣤⠀⠀⠈⠢⡠⣷⣄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠐⠛⠀⠀⠀⠀⠀⣼⣧⡟⢰⣧⡴⠂⡗⠀⢀ ⠀⠘⣿⡱⡌⢇⠀⠘⢷⣄⡘⠢⡀⠀⠀⠈⢺⡟⠓⠒⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢀⣦⡀⠀⢿⣟⣠⣾⠻⠄⠀⡇⠀⣼ ⠣⡀⠈⢳⠈⠻⠦⠀⠀⠙⠮⣔⣌⡓⠦⣀⠀⠓⢀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡖⠛⠁⠀⠹⠃⠀⣿⡏⠀⣿⠀⠀⠀⡷⢺⡟ ⡄⢷⡄⠘⢦⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣖⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠉⡽⠉⢹⠛⢷⡄⠀⠀⠀⢀⣾⡟⡇⠀⢹⡖⠛⣷⢠⣿⠃ ⡷⣜⡳⡀⠀⠙⢗⠢⢄⣀⠀⠀⠀⠹⢦⡀⠑⣄⠀⠀⠀⠀⠀⠀⠒⡀⠒⠛⠒⠛⠒⠾⡲⡿⠇⠀⠀⣰⣿⣿⡇⣧⠴⢾⠀⢀⣿⣿⣿⠀ ⣧⠘⣧⢣⠀⢂⠐⡉⠲⠤⠌⠙⢷⡒⠤⢌⣳⣌⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⠀⢀⣾⣿⡿⢿⣃⡏⠀⢸⣶⣮⣾⣿⣿⣼ ⣿⡆⠈⢮⡆⢸⡆⢡⠀⢠⠀⠈⢖⠈⢲⣄⠈⠙⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠁⣼⠁⣧⠴⣃⣼⣿⣿⣿⣿⣿ ⡿⠸⡄⠘⣿⠀⠹⡀⡇⢺⣷⡀⠈⢣⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⢀⣼⣿⡔⣩⣿⣿⣿⣿⣿⣿⣿⣿ ⠇⢠⠷⡀⠘⢇⡄⡇⢠⢸⣿⡻⣦⡀⠳⣤⣄⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡀⡌⢠⣧⠀⠸⡇⢸⣿⣼⣿⣿⢾⣽⣦⣙⢿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣄⣀⣀⣀⣀⣀⣤⣶⣿⡏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡜⢀⣾⡟⢇⠀⡇⣧⣿⣿⡇⠀⠀⠙⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿ ⢡⣾⣿⡇⠘⣤⣷⡿⠷⠶⢿⡄⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡇⠀⠟⣻⣷⠀⠀⠀⠙⠢⣄⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⡯⠒⢹⣿⣿⣿⣿⣿⡿⢸⣿⣿⡏⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡇⠀⢺⣿⣿⡄⠀⠀⠀⠀⠀⠉⠉⠒⣢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠃⠀⠀⢸⣿⣿⣿⣿⡟⢲⣿⣿⣿⢱⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠏⣿⣽⣿⣧⡟⣳⡇⢘⠛⡀⠀⠀⣸⣿⣿⣿⣿⠅⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢅⠊⢀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠐⣄⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢏⣀⣸⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢡⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿ ⢀⠄⠊⢈⢝⠝⠂⠀⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠈⠄⠖⣀⠀⡈⢿⣿⣿⣿⣿⣿ ⣾⣦⣤⡜⠁⠀⠀⠀⠀⠔⠁⠀⠀⠌⢁⠢⡀⠀⡠⠚⠁⠀⠀⡀⡎⢻⣿⣿⣿⣿ ⣿⡿⠋⢇⣀⠀⠀⠀⠸⠀⠀⠀⢉⠑⢄⠑⢌⠫⠀⠀⠀⢰⠋⢩⡇⠘⣿⣿⣿⣿ ⣿⠁⠀⠀⠈⠉⠙⠲⢾⣀⠀⠀⠀⢢⣀⠑⢄⠄⢃⠀⠀⠈⣧⣀⣻⣀⣼⣿⣽⡟ ⣿⡄⠀⠀⠀⠀⠀⠀⢀⠉⠻⣶⣄⠀⠹⡦⣀⢹⣀⣾⣯⠙⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣧⠀⢀⡠⣤⢤⡖⢯⣓⣖⠈⠿⣿⡦⣈⣿⢧⠒⠘⢽⣷⡘⠻⣛⢿⠋⠙⣿⣿ ⣿⣿⣧⢻⡁⠈⢦⣳⡊⢻⣞⢪⠭⠿⣿⣿⡭⣼⠳⡀⠀⠉⠀⠀⠈⠠⡔⠀⠻⢿ ⣿⣿⣿⣧⠳⡀⠀⠻⣷⣀⣻⣷⠃⠀⠹⣟⡿⣭⠆⠜⠀⠀⠀⠀⠀⠀⠀⠉⠑⡀ ⣿⣿⣿⣿⣷⡝⠋⠉⠉⠉⠉⠀⠀⠀⣠⣤⠀⠀⠰⠃⠀⠀⢀⠴⠛⠿⠿⣶⠖⠀ ⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠰⣾⡇⠉⣫⡄⣾⣷⠀⠀⠠⠁⠀⠄⠀⠀⢱⣶⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡑⢄⠀⠀⠘⠿⠃⠀⠀⢀⡔⠁⠀⠀⠁⠀⠀⠘⣿⣿

⠇⠀⠀⠀⢻⡆⢀⣀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣠⡞⠨⣭⠒⣺⣧⡿⡏⠉⡯⠛⠻⠟⠃ ⠀⠀⠀⠀⠉⠁⠈⠉⠉⠉⢣⣤⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢵⣴⣷⣶⣻⠽⠛⠃⠘⠓⠒⠢⢄⠀ ⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⣶⡆⠀⠀⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⣸⡇⠀⢰⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠬⣥⠀⢨⣼⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⡀⠀⠀⠀⡜⠀⠀⠀⠀⢸⢹⠦⣄⡀⢀⣠⡇⠀⠀⠀⠀⠀⠀⣶⡄⠀⢠⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⢰⠁⠀⠀⠀⢀⠇⠀⣧⠔⠛⠉⢲⠃⠀⠀⠀⠀⠀⢠⣿⣇⠀⢈⡧⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠀⠀⡀⠈⠀⠰⢸⠀⠀⠀⡇⠀⠀⠀⠀⣜⠀⠀⠸⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣉⡀⠀⢈⣗⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⡇⡄⠀⠀⡈⠀⢸⢸⠀⠀⠀⠀⡼⠁⠀⠀⠀⢣⠀⠀⣾⠀⠀⠀⠀⠀⠀⢀⣿⣥⠀⠚⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣷⢸⠀⣿⡦⡇⠀⣿⡅⠀⠇⠏⠀⠀⠀⣼⣷⣦⣄⠀⠀⠈⢶⢰⣿⡇⠀⠀⠀⠀⠀⢈⣻⡧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣧⠀⢸⠀⣿⡌⡆⠹⣿⡇⠀⣿⠃⢀⢹⠀⠀⠀⡜⠁⣾⣿⣿⣷⣦⠀⣼⠀⠀⣧⠀⠀⠀⠀⠀⠀⣹⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡆⠸⣧⢩⣧⠹⠀⠻⠷⠀⣿⡇⢸⣼⠀⢀⠎⠀⠀⢇⠙⣃⠿⠜⢠⠋⢠⡾⣿⢆⠀⠀⠀⠀⠸⣿⡋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢧⠘⣄⢿⣾⣿⡄⠀⠀⠀⠀⠈⠁⠈⠋⠀⠋⠀⠀⠀⠉⠉⠁⠀⣠⢃⣴⠟⣠⠃⠀⢳⡀⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡵⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠡⣾⣶⡟⠁⣀⡴⠯⠚⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⡀⡠⠖⠲⡀⠀⠀⠀⠉⠻⢿⣷⣄⡀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣏⡤⠾⠃⠀⠀⠀⠀⠈⠒⠆⠠⠤⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢧⡀⠀⢱⠀⠀⠀⠀⠀⠀⠰⣿⢿⣶⣤⡀⠀⠀⠀⢀⣀⣤⣴⣾⡿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⡄⠈⡇⠀⡀⠀⠀⣀⡠⣇⠈⠛⢌⠻⢶⣶⣿⠿⢿⠟⢻⡏⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⢉⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡶⡏⠛⢽⠂⠉⠀⠀⠘⣄⠀⠀⡆⢀⡝⠁⠀⢠⢠⣿⡀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⡀⠀⠀⠀⠀⠀⢻⠓⠂⢾⠀⠀⠀⠀⠀⠈⠣⡀⢸⡎⠀⠀⠠⠾⠊⠁⠈⠑⢠⡤⢴⡞⠁⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢳⣤⡀⠀⠀⠀⠀⣷⣤⠜⢣⡀⠀⠀⢀⡤⠤⢤⣤⡧⠭⣄⡀⠀⠀⠀⣠⡴⠋⠉⡏⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠁⠀⠀⣰⡟⠹⣄⠀⠹⣦⣀⠈⠳⠖⣻⠋⢻⠲⣄⣹⣧⡴⠾⢏⣀⣠⣾⡇⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠑⢎⡀⠉⣻⠷⣶⠧⠄⠼⡖⠚⢫⣁⣀⣠⡾⠛⢹⣿⠃⠀⠀⠈⠉⠁⢻⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢡⡀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠈⠉⠙⢤⣇⡀⠼⣀⣧⠴⠚⠉⠉⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⡎⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⠃⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⣠⠞⠁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⣶⣤⣀⣴⣾⣯⠤⠶⠶⠶⠶⠶⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠒⠚⠛⠛⠁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⡉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣟⢦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⣀⠀⣷⠀⣿⣾⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡾⠃⣰⡇⠀⣀⠀⠀⠀⠀⢠⣄⣾⠃⠀⠀⢰⣶⢰⣿⡇⠀⠀⠀⠀⠀⣿⡀⢸⣆⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣀⠀⣿⣇⠀⣿⣇⠀⠀⠀⣸⣿⣿⣧⠀⠀⢸⣿⣾⣿⣷⣤⣄⠀⢀⣼⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡰⢻⣿⠸⠀⣿⠻⢿⡿⠟⢷⣶⢿⡿⠛⠛⠿⠷⠶⠿⠛⠛⠋⠛⠟⠛⢛⡿⢻⣯⡍⠻⣿⠙⣿⡆⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⣰⡧⣿⣿⡆⣼⣿⠀⡎⠀⠀⣿⣿⠏⢳⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⣞⠀⠙⠿⠃⠀⣸⣧⡟⠳⢄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡠⠞⡟⠀⣿⣿⣷⣿⣿⡆⢣⡀⠀⠈⠁⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⢀⠤⠔⢻⡟⠛⠛⠉⠉⠉⠉⢙⡦ ⠀⢀⣠⠴⠿⠖⠚⣿⡉⠛⠉⢩⣿⠋⠁⠀⠈⠑⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢀⡾⠁ ⠸⣿⣷⠄⠀⠀⠀⣿⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣀⡴⠋⠀⠀ ⠂⠈⠻⢷⣆⠀⠀⠉⠀⠀⠀⠘⣷⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⢀⣠⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⢲⣤⣄⣀⠀⠀⠈⠳⡈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠿⠋⠀⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⢸⡆⠀⠉⠙⢦⡀⠀⠘⠲⣄⠈⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⢉⣤⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⡿⠈⢷⡀⠀⠀⠈⠙⠲⠤⣄⣀⣉⠉⠓⠒⠒⠒⠒⠒⠋⣉⣁⣠⣴⡚⠋⠁⠀⣽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠈⢷⡀⣀⡤⠤⠶⠶⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠙⢳⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⠀⠀⠻⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣤⣀⣠⣤⣽⣷⡦⢤⣀⣀⣀⣀⣀⣀⣀⣀⡤⣤⣶⣏⣉⣡⣠⡤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡄⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣄⣀⠀⠀⢀⣀⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀