Toon Link Emojis & Text

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