⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⣹⠶⠶⠶⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⡾⠁⣠⣤⣀⠀⠙⣿⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣶⣄⠀⠀⠀⢸⣿⠇⢰⡏⢈⣿⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠻⢿⣿⣿⣷⣠⣤⣾⣿⠀⠘⡷⠞⢁⣴⢟⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣧⢀⡀⠀⠀⢸⣿⠃⠀⠀⠀⠙⣿⠷⠚⠋⠉⠁⠀⠀⠀⠰⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡠⠄⡀⠤⣀⠀⢻⣿⣿⡿⠛⠙⠻⢿⣦⣴⣿⣿⠀⠀⠀⢰⣶⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⣥⠟⠋⠉⠛⢿⣷⣾⣿⣿⠀⠀⠀⢠⣾⣿⠋⠁⠘⣧⠀⠀⠈⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣾⠃⢀⣴⢶⣄⠀⢻⣿⣿⣿⡄⠀⠀⠘⣿⣿⡀⠀⠀⠈⠛⠶⠶⠚⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣻⡀⠈⢷⣄⣘⣇⠀⠛⠉⠀⢙⣦⠖⠋⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠓⣶⠶⠒⠋⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠪⣽⣶⣤⣄⣉⠉⠀⠀⢀⣴⠟⣁⣠⡤⠶⠚⡿⠒⠒⠲⠶⣤⣀⠀⠀⣰⠟⠀⠀⠀⠀⠀⣠⡾⢏⠟⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀ ⠀⠀⠀⠉⠙⢿⣿⠀⢀⡴⠻⠛⠋⠁⠀⠀⠀⣼⠁⠀⠀⠀⠀⠈⠻⣷⠞⠁⠀⠀⠀⠀⣀⣴⣿⠗⠁⠀⠀⠀⠀⣠⡔⣺⣿⠿⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣾⡷⠋⠙⢦⣀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⢀⣀⡤⣿⡦⠤⠤⣤⣤⣾⣿⣿⣧⣀⣀⠀⠀⠀⣠⣭⡟⠉⠤⣀⣧⣀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡃⠀⠀⠀⠈⠙⠲⠤⣾⠁⠀⠀⠀⠀⠀⠒⠒⢲⡿⠦⣤⣄⣀⣀⠈⢻⡝⢟⠑⠤⠕⣀⣀⣿⡟⠀⠀⠀⠈⠙⢦⡑⢄ ⠀⠀⠀⠀⠀⠈⢿⢷⡀⣀⡤⢄⠀⠀⠀⣹⡶⠤⠤⠤⠤⠶⠶⠶⣿⣡⣾⠿⣅⡈⠉⠙⠓⠲⢬⣧⣀⣾⡿⠿⣿⣇⠀⠀⠀⠀⠀⠀⢻⡌ ⠀⠀⠀⠀⠀⣠⣾⡿⣿⣧⣖⠉⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠁⠉⠳⣽⢷⣄⠀⠀⠈⠻⣯⡟⠀⢰⡟⠹⣦⡀⠀⠀⠀⠀⠀⣧ ⠀⠀⠀⣠⡿⢿⣵⣿⡿⠛⠭⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡾⠀⠀⠀⠀⠀⠑⠿⡛⣦⡀⠀⠈⠃⠀⢸⣇⠀⠈⠻⣦⣀⠀⢀⣰⢯ ⠀⢀⡼⠋⠀⣼⣿⠏⠀⠀⠀⠀⠈⢻⣿⢦⣄⡀⠀⠀⣀⣴⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣄⠀⠀⠀⠀⣻⣄⠀⠀⠀⠉⠛⢿⣵⡃ ⠀⠋⠀⢠⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⠾⠋⣿⣟⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠙⠃⠀⠀⢰⣿⠙⢦⣄⠀⠀⠀⢸⣿⡇ ⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠸⣿⡀⠀⠙⠳⣤⣤⣾⡿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠙⣷⣄⠀⠀⢘⣿⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣷⡀⠀⠀⠈⠻⢷⣤⣾⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢦⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⣿⣦⣤⣀⣀⣰⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⠟⠁⠀⠀⠈⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠛⠲⢾⣧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣇⠀⠀⠀⠀⠀⠹⣟⢆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠉⠻⣆⠀⠀⠀⠀⠀⢹⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠙⢧⣀⠀⠀⠀⠀⣿⡷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⡀⠀⠀⠉⠓⢦⡤⢴⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡞⣷⣄⠀⠀⠀⠀⢻⣽⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⠀⠙⠷⣦⣄⣀⣾⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣜⠷⣄⠀⠀⢹⣿⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢌⡻⠲⢺⡿⠃⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣿⣷⣦⣿⣿⣇⢀⣀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⢀⣠⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⣿⣿⣟⣿⣿⡹⣿⣿⠛⠛⠛⢻⡿⠿⣄⡼⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣿⣿⡉⢿⣝⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⣿⣿⣍⠈⠳⠷⢋⣴⡀⣠⣏⣄⠀⢸⢣⣿⣦⣤⠤⣀⡀⠀⠀⠀⠀⠀⠀⢀⡾⢉⡾⠛⢷⣾⣿⣯⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢿⣫⣽⠇⠀⠀⠀⠀⠀⠀ ⢠⣿⠋⣧⠀⠙⣧⡀⠀⣸⣿⣿⣿⡟⠿⠴⠚⣿⠃⠀⠉⠓⠦⣍⠀⠀⠀⠀⣠⣴⣟⣡⡟⠁⣴⠛⣧⡙⠻⣦⣀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠘⣹⡟⠀⠀⠀⠀⠀⠀⠀ ⠸⣿⡷⣬⡷⠀⠈⠻⢿⣽⢿⡏⠙⠳⣄⣠⡾⠋⠀⠀⠀⠀⠀⠀⣀⣤⠶⢟⣩⣴⣿⠋⢠⡞⢁⣧⠘⣿⣦⣄⡉⠛⢦⣄⣠⡤⢶⣏⡀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠷⠶⣭⣤⣄⣸⡿⣦⢿⣖⡒⠿⠷⠶⠶⠶⠶⠒⠒⠒⠛⢋⣡⡶⠛⣡⡟⠁⢠⡟⣹⡿⠙⣧⡈⢷⡈⠛⢶⣄⠈⠙⠳⠶⣄⡙⠷⣴⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠏⣰⠟⠀⢀⠈⢯⡉⠓⠶⣤⣴⠶⠶⠒⠚⠛⠛⠉⠁⢀⡼⠋⠀⢠⣿⣿⠋⠀⠀⠙⣷⡘⢷⣤⢞⣿⠟⢦⣄⠀⠈⢙⣶⣌⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠋⣰⠏⢀⣴⣿⡀⠀⠙⠳⣄⡀⠉⠙⠲⠶⠶⠶⠒⠲⣶⠟⠁⠀⢠⣿⡿⠁⠀⠀⠀⠀⠈⣷⠀⢻⣾⠁⠀⠀⠙⠳⠾⠋⠁⠉⠻⣮⡙⠶⣤⣀⣀⣀⣤⡀ ⠀⢀⣴⠟⢀⣼⣧⡾⠋⠁⠀⠙⠷⣦⣆⠀⠉⠓⠶⠤⣤⣤⣤⣤⡾⠋⠀⠀⢀⣾⠏⠀⠀⠀⠀⣀⣴⠞⣻⣧⠀⠹⣦⣀⣠⣤⣤⣤⣤⣀⡀⠀⠈⠙⠳⠶⢭⣭⣿⡿⠇ ⢠⡿⠁⢰⣿⠿⠋⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣼⣇⣀⣤⣤⠶⣟⣫⡶⠟⠁⠹⣧⠀⠈⠉⠉⠀⠀⠀⢬⣍⢿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀ ⠸⣷⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⣦⣤⣤⣤⣤⠶⠿⠷⠶⠶⠶⠒⠛⠉⠁⠀⠀⠀⠀⠹⢦⣤⣤⣤⣤⣤⣤⣤⡼⠷⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀

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