Dragon Made of Dots Emojis & Text

Copy & Paste Dragon Made of Dots Emojis & Symbols ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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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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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⡶⠁⣠⣴⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣴⣿⣿⣴⣿⠿⠋⣁⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⣿⡿⠟⠋⠉⠀⣀⣀⣀⣨⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣤⣴⠂ ⠈⠉⠁⠀⠀⣀⣴⣾⣿⣿⡿⠟⠛⠉⠉⠉⠉⠉⠛⠻⠿⠿⠿⠿⠿⠿⠟⠋⠁⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⡿⠁⠀⢀⣀⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⡿⠁⢀⣴⣿⠋⠉⠉⠉⠉⠛⣿⣿⣶⣤⣤⣤⣤⣶⠖⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⡇⢀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⡇⠈⢿⣿⣿⠇⠀⠀⠀⠀⠀⢠⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣿⣷⡀⠀⠉⠉⠀⠀⠀⠀⠀⢀⣾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣷⣄⡀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣋⣠⡤⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠖⢛⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣋⣩⣤⠶⠾⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣠⣴⣾⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣷⣤⣀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀⣠⣴⣶⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⣠⣶⣿⣿⣿⣿⠃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠃⢠⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣫⣷⣾⣿⣿⣿⣿⣿⣿⣿⡏⠀⢠⣿⣿⣿⣿⣿⣿⣯⡻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣞⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⣿⣿⢟⣽⣿⣿⡿⣫⣽⣿⣿⣿⣿⣿⡟⠀⠀⢠⣿⣿⣿⣿⣿⣿⣯⡻⣿⣿⣷⣝⠿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣫⣶⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⣿⣿⡁⡀⢠⣀⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⣿⣿⣷⣮⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⡿⠟⢭⣾⡿⣻⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣯⣻⠿⠮⠙⠿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠿⠿⠿⢛⠋⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣀⣈⣙⣛⣛⣻⠿⠿⢿⣶⣤⣀⠀⠀⠀⠀ ⠀⠀⢀⣴⣿⠟⠉⠀⣰⣾⣿⣿⣿⣿⣿⡿⣷⣦⡀⠈⠿⣿⣿⣿⣿⣿⣿⣏⠁⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⠛⠀⣠⣶⡿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠹⣿⣷⣄⠀⠀ ⠀⣴⣿⡿⠋⠀⠀⠀⢿⣿⡿⣿⣿⣿⣿⣿⣮⣟⢿⣦⣴⣿⣿⣿⣿⣿⡏⠃⠀⠀⠀⠀⠘⢸⣿⣿⣿⣿⣿⣷⣾⠟⣫⣾⣿⣿⣿⣿⡿⣟⣿⡿⠀⠀⠀⠈⠻⣿⣧⡀ ⢊⢼⠟⠀⠀⠀⠀⠀⠘⢿⣿⣮⣻⣿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⢯⣾⣿⡿⠁⠀⠀⠀⠀⠀⠹⠗⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣮⡻⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣿⣿⣶⣽⡛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠉⠉⠛⣫⣵⣿⣿⣿⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣵⣿⣿⡿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⢹⡿⠿⣿⣿⣷⣻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⣛⣼⣿⣿⡟⠂⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠹⣿⣿⣷⣍⣙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠛⠛⠛⠋⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣇⠀⠀⠀⠀⠀⣀⣠⣤⠴⠗⠚⠛⠛⣯⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠖⠛⠋⠉⠁⣀⠀⢀⣀⣠⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⡍⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠇⡞⠀⠀⠀⠀⠀⠀⠀⡶⠃⠉⣅⡀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⣧⢤⣠⡤⣄⡀⢀⣭⣽⢖⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠉⠀⠀⠡⡤⠤⠤⣄⠀⠀⠀⠀⡇⠀⠘⠏⠀⠱⣄⠀⠛⠂⠉⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠞⠁⠀⠉⠑⠒⠲⠄⣀⠙⠢⡀⠀⠈⠳⣄⠀⠀⠀⠀⠇⢸⠥⠤⣄⣀⡀⠀⠹⡄⣀⢀⣀⠀⠀⠀⠀⠀⡠⠖⠉⠉⠉⠙⠛⠻⣝⡦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠑⡄⠀⠀⠀⠉⠳⡧⡀⠀⢸⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⡇⠀⠀⠓⠒⠚⠉⢠⠒⠋⠉⠉⠉⠉⠉⠉⠻⣼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡀⠡⠀⠀⠀⠀⢧⠁⠀⠀⢳⠀⠀⠀⠀⠀⣀⣀⣀⣀⡜⠀⠀⡤⠒⠋⠉⠁⠀⠀⠀⠀⢰⠁⠀⠈⠓⢆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣆⡀⠢⠎⠉⡟⡄⠀⠀⠀⡧⠔⠚⠁⣠⠄⠤⠤⠤⠖⠉⠀⠀⠀⠀⢠⠄⠊⠉⠉⠀⡤⡄⠀⠀⠀⠀ ⠉⠓⠒⠋⠉⠓⢆⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠤⡗⡇⠀⠀⠀⢣⡒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⢀⠤⠇⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢳⠀⠀⠀⡠⠊⠉⠀⠀⠈⠉⠣⡄⠀⠆⠀⢣⡀⣇⠀⠰⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠋⠉⠑⢆⡀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢇⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⡇⢸⡸⠀⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣇⡇⡤⠤⠤⠤⡄⠀⠀⠀⠀⠀⠀⡇⠀⢹⠓⡄⢢⠀⢰⢂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠒⠚⠀⡞⠉⡷⡄⠀⠀⠀⠀⠀⠀⢈⡆⠀⠀⠀⠀⠘⠦⠄⣀⡀⠀⠹⡄⢇⡖⡸⡼⠤⠃⠰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡯⠴⢲⡦⣸⡄⢸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⡖⠒⠦⠤⠤⡄⠀⠀⢳⠀⠓⡎⠀⡧⠜⠀⠀⠀⢰⠀⠀ ⠀⣰⠚⢫⠈⡖⢄⣀⡈⠐⣀⢂⣤⣄⡋⠀⠋⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⣈⡄⠀⠛⠙⢦⡏⠉⠉⠉⠉⠁⠀⠀⠀ ⠀⢻⣄⡀⠉⠓⠦⠖⠒⠛⠛⠛⠂⠒⣦⠔⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⣅⣀⣹⣤⡗⣄⡤⣼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠑⠒⠌⠙⠒⠒⠒⠤⠤⠖⠂⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠚⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀ ⢾⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣴⣶⣿⣿⣿⣿⡇ ⠈⢿⣿⣿⣿⡛⠛⠈⠳⣄⠂⠀⠀⠀⠀⠀⣠⠞⠉⠛⢻⣿⣿⣿⡟⠀ ⠀⠸⣿⣿⣿⠥⠀⠀⠀⠈⢢⠀⠀⠀⠀⡜⠁⠀⠀⠀⢸⣿⣿⣿⠁⠀ ⠀⠀⣿⣿⣯⠭⠤⠀⠀⠀⠀⠃⣰⡄⠌⠀⠀⠀⠀⠨⢭⣿⣿⣿⠀⠀ ⠀⠀⠹⢿⣿⣈⣀⣀⠀⠀⠠⢴⣿⣿⡦⠀⠀⠀⣀⣈⣱⣿⠿⠃⠀⠀ ⠀⠀⠀⢠⣾⣿⡟⠁⠀⠀⠀⠀⣿⣏⠀⠀⠀⠀⠘⣻⣿⣶⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⢂⠀⠀⠀⠀⠘⢸⡇⠆⠀⠀⠀⢀⠰⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣷⣿⣆⡀⠀⠀⠁⠈⠀⠠⠀⠀⢀⣶⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⣿⣷⣴⡜⠀⠀⠀⠀⣦⣤⣾⣿⣿⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡿⠛⠿⠿⠛⠁⠀⠀⠀⠀⠘⠿⠿⠿⠿⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⠒⠒⠒⠒⠒⠢⠤⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀(Ignore for z00phile rights, Like for YIPPEE) ⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠦⠀ ⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧ ⠀⡇⠀⠀⠀⢀⡶⠛⣿⣷⡄⠀⠀⠀⣰⣿⠛⢿⣷⡄⠀⠀⠘⣿⠀ ⠀⡇⠀⠀⠀⢸⣷⣶⣿⣿⡇⠀⠀⠀⢻⣿⣶⣿⣿⣿⠀⠀⠀⢸⠀ ⠀⡇⠀⠀⠀⠈⠛⠻⠿⠟⠁⠀⠀⠀⠈⠛⠻⠿⠛⠁⠀⠀⠀⢸⠀ ⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠁ ⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣚⡁⠀⠀ ⠀⠀⠀⠀⠈⠙⠒⢢⡤⠤⠤⠤⠤⠤⠖⠒⠒⠋⠉⠉⠈⢙⢨⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹ ⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣤⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢠⣿⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⢸⠘⡆⠀⠀⢸⣀⡰⠋⣆⠀⣠⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠼⠀⠘⠤⠴⠃⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣴⣿⣿⣿⣿⣯⣤⣶⣶⣾⣿⣶⣶⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⠶⠶⠦⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣟⣡⣤⣾⣿⣿⣿⣿⣿⣿⢏⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠈⠻⡄⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠙⠻⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⠛⠉⠉⠉⠛⠛⠛⠛⠋⠁⠀⠀⠀⠁⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠈⠙⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠈⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⢋⣩⡿⠿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⡀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⡄⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⠀⠀⠀⠠⣄⣀⣀⡉⢻⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣦⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀ ⠀⢻⡟⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠋⠉⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀ ⠀⠀⠃⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠈⠉⠻⢿⣿⣿⣿⣷⡄⠀ ⠀⠀⠀⠀⢸⣿⣿⡟⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⣿⣿⣿⣿⣿⣧⣀⣀⡄⠀⠀⠀⠀⠀⠀⠈⣿⡿⣿⣿⣷⠀ ⠀⠀⠀⠀⢸⣿⡿⠁⠀⠀⠀⠙⠻⠿⣟⠻⢿⣿⣿⣿⣷⣦⡀⠀⠈⠻⢿⣿⣿⣭⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠸⣿⣿⡄ ⠀⠀⠀⠀⣸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣦⡀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁ ⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡴⡖⡴⡖⡴⡄⢰⣀⣶⣰⡂⣶⢰⡆⣶⢰⣆⣰⣀⣆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⠀⠀ ⠀⠀⣠⣤⣤⣄⣀⣾⣿⠟⠛⠻⢿⣷⠀ ⢰⣿⡿⠛⠙⠻⣿⣿⠁⠀⠀⠀⣶⢿⡇ ⢿⣿⣇⠀⠀⠀⠈⠏⠀⠀⠀ text here ⠀⠻⣿⣷⣦⣤⣀⠀⠀⠀⠀⣾⡿⠃⠀ ⠀⠀⠀⠀⠉⠉⠻⣿⣄⣴⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠁⠀⠀⠀⠀
⠀⣠⣶⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡏⢀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⣠⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣟⣋⣼⣽⣾⣽⣦⡀⠀⠀⠀ ⢀⣼⣿⣷⣾⡽⡄⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣿⣿⣿⡿⢿⣟⣽⣾⣿⣿⣦⠀⠀ ⣸⣿⣿⣾⣿⣿⣮⣤⣤⣤⣤⡀⠀⠀⠻⣿⡯⠽⠿⠛⠛⠉⠉⢿⣿⣿⣿⣿⣷⡀ ⣿⣿⢻⣿⣿⣿⣛⡿⠿⠟⠛⠁⣀⣠⣤⣤⣶⣶⣶⣶⣷⣶⠀⠀⠻⣿⣿⣿⣿⣇ ⢻⣿⡆⢿⣿⣿⣿⣿⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠀⣠⣶⣿⣿⣿⣿⡟ ⠈⠛⠃⠈⢿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠋⠁⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⣆⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣼⣿⡗⠀⠀⠀⠀ ⠀⠀⠀⣠⠟⠀⠘⠷⠶⠶⠶⠾⠉⢳⡄⠀⠀⠀⠀⠀⣧⣿⠀⠀⠀⠀⠀ ⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣤⣤⣤⣤⣿⢿⣄⠀⠀⠀⠀ ⠀⠀⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠙⣷⡴⠶⣦ ⠀⠀⢱⡀⠀⠉⠉⠀⠀⠀⠀⠛⠃⠀⢠⡟⠂⠀⠀⢀⣀⣠⣤⠿⠞⠛⠋ ⣠⠾⠋⠙⣶⣤⣤⣤⣤⣤⣀⣠⣤⣾⣿⠴⠶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀ ⠛⠒⠛⠉⠉⠀⠀⠀⣴⠟⣣⡴⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣠⠤⣶⣶⣤⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠟⢦⣤⡄⠒⠋⠁⠀⠀⢻⡝⢧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢿⡏⠀⢀⡀⠀⠀⠀⠀⠀⢷⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠃⠀⠀⠀⠀⠀⣸⣸⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠁⠉⢳⣴⢻⣽⣟⢦⠘⠃⠀⠀⠀⠀⠀⠀⠀⢀⡿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠋⠐⠉⠙⣿⢿⡇⠀⠀⣀⡀⠀⠀⢀⡴⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⣄⠀⠀⠀⠀⠀⣰⠟⣽⠁⠀⣀⠓⠃⠀⢠⡞⣱⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣿⣧⣦⣤⣤⡔⢋⠈⠁⠀⠀⠀⠀⠀⠀⠏⡼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⢸⣻⣿⣿⣯⠟⠋⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣞⣳⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⢠⡀⢠⡄⠀⢀⡾⡯⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣡⡾⢋⡼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠉⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣸⢸⢠⡆⠀⠀⠀⠀⠀⠰⠞⠁⠰⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡽⠛⠘⢿⣥⣤⣤⣤⣀⠀⠤⠠⢤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠶⣿⡛⠁⠀⠉⠉⠉⠙⣿⣦⢠⣰⠚⣋⣉⣁⣀⣤⠤⣶⣫⡤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠓⠚⠿⠯⠭⠭⠭⠤⠼⠏⢹⢾⠿⠿⠟⠓⠒⠚⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢸⣼⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡄⢠⡏⠀⠘⣿⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⣤⠏⠀⠀⠀⡿⠀⠀⠀⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡾⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⡶⡦⢤⣀⡴⠋⣥⣍⡻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⢿⠀⠠⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣥⣾⣷⣷⣶⡝⠂⠈⠀⠘⠓⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠘⣆⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⣸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⣔⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣆⠹⣆⠀⢠⡆⠀⢀⡀⠈⠁⠀⢸⠐⣿⣿⡀⠀⠀⠀⠀⢀⢠⣶⣟⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠫⢘⢧⣼⣷⣂⡈⠉⠀⢀⣀⡌⢧⠻⣿⣷⡀⠀⠀⠀⠨⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⢉⣿⡟⠿⠥⣶⣟⣉⣁⣠⡤⠴⠖⠙⠟⣴⣀⠀⣽⡿⣳⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠃⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⢤⣈⣨⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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