Happy Dot Art

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣤⣤⡀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿⢻⠛⢿⣿⣦⣠⣀⣠⣾⡿⠿⣿⠛⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣿⣿⠁⣾⣿⣿⡌⣿⣿⠿⢿⣿⡏⠁⣾⣿⣷⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⢾⣿⠿⠛⠋⠁⠸⣿⣧⡘⠛⠉⢠⣿⡟⠀⠀⢿⣷⣄⠈⠉⢁⣼⣿⢧⣤⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣶⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠉⠿⢭⣽⣾⣽⠟⠁⠀⠀⠀⠹⣯⣽⣲⣯⡷⠋⠻⣿⣿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠻⣿⢷⡄⠀⠀⠀⠀ ⠀⠀⢠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣻⣆⠀⠀⠀ ⠀⢰⣟⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⢻⡄⠀⠀ ⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀ ⢸⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡝⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠕⢸⠃⠀⠀⠀⠀⠀⠀⢽⣿⠀⠀ ⢸⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⣼⠇⣠⡎⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀ ⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠈⠛⠲⢤⣤⣤⣤⠞⠃⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⡄ ⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢤⣀⣀⣀⣀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⡇⠀⠀ ⠀⢹⡿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⡟⠀⠀⠀ ⠀⠀⠻⣎⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣿⠟⠀⠀⠀⠀ ⠀⠀⠀⠈⠣⣿⣧⣼⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡷⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣹⣿⣿⣿⣶⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡀⢀⣀⣀⣠⣤⢴⣞⡿⠿⣷⣽⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣯⣿⠃⠀⠉⠛⠒⠒⣾⣽⣭⣿⠷⠶⠶⠶⣾⣿⣿⡿⠽⠯⠗⠒⠛⠉⠁⠀⠀⣻⡿⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⣴⣶⡶⠻⣿⣿⠃⠀⠀⢀⣤⣴⠶⣿⣿⠓⠀⠀⠀⠀⠀⠀⣹⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⣴⡟⢻⠙⠿⣦⡄⠀⠀⠀⠀ ⠀⠬⢳⡤⣾⠋⢹⣿⠒⠂⠚⢥⠀⣼⠏⢹⡏⠉⠉⠉⠁⢠⣾⠋⢿⡀⠙⢿⠯⠉⠉⠉⠉⠚⠋⠀⠸⠇⠠⠬⠥⢤⣀⡀⠀ ⠀⠀⠉⠉⠛⠒⠾⠿⠤⠄⣀⣈⣐⣿⣀⣈⣿⣀⣈⣀⣀⣞⣁⣤⣹⣗⣶⣄⣁⣀⣀⣀⣀⣀⣀⠠⠀⠴⠶⠶⠒⠒⠛⠉⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠶⠾⠿⠟⠛⠉⠉⠉⠁⠀⠈⠉⠙⠛⠿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀ ⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀ ⠀⣸⠏⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⢿⡄⠀⠀ ⢠⡏⠀⠀⣀⣘⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣧⠀⠘⣧⠀⠀ ⠈⡇⠀⠀⣰⠛⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠃⠀⠀⢻⡄⠀ ⠀⡇⠀⠰⡇⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⡀⠀⠈⣷⠀ ⠀⣷⠀⢸⣟⣚⣫⣾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⣴⣾⠟⠀⠀⣿⡆ ⠀⢻⡆⠈⠙⢿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠇⠀⠀⠀⣿⠃ ⠀⠀⢳⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⡿⠀ ⠀⠀⠀⣷⠀⠀⠀⠹⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁⠀⠀⠀⣼⠃⠀ ⠀⠀⠀⠘⣷⡀⠀⠀⠈⠙⠻⠷⣶⣤⣤⣀⣀⣀⠀⠀⠀⠀⢀⣀⣠⣴⡾⠟⠋⠁⠀⠀⠀⠀⡴⠃⠀⠀ ⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠻⠿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠈⡁⡇⢸⡇⠀⠀⠀⠀⠀⠐⠸⠀⠀⠀⡇⣿⠋⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⠀⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⢸⣧⣤⠤⠤⢤⣤⣿⠦⣄⣀⡀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢾⣶⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣾⠀⣿⣤⣤⣤⣤⣤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢫⠀⣿⠉⠉⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢈⡴⠃⠀⠀⠀⠀⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠤⠀⠠⠄⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡞⠁⠀⠀⠀⠀⢆⣧⠀⠀⢀⠀⠘⢣⠀⠀⠀⠀⠀⠀⠀⢦⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⠒⠒⠲⡏⡰⠁⠀⠀⢰⢸⡾⢹⠀⠀⠈⡇⢠⠠⢷⡻⣖⠒⠤⣀⠀⠈⡆⠀⢷⣤⣤⣴⣶⣦⣤⣤⣼⠀⢿⣤⣤⣤⣤⣤ ⣀⣀⣠⣤⣄⣠⣤⣤⡼⢠⠃⡀⠀⠀⣼⣾⠛⠚⢇⠀⠀⠸⡼⠀⠀⠑⣿⢦⡀⠈⡗⠄⠸⡀⠘⡇⠀⠀⠀⠀⠀⠀⢹⠀⣿⠉⠉⠉⠉⠉ ⠿⣉⠉⠉⠉⠉⠛⢻⣇⡿⢰⠁⢀⡞⡟⣿⠀⠀⠈⢦⠀⠀⢣⠀⢠⣶⣾⣷⣿⣄⡇⠀⠀⡇⠀⢹⡄⠀⠀⠀⠀⠀⢠⠀⣿⠀⠀⠀⠀⠀ ⡀⠙⢦⡀⠀⠀⠀⣼⡺⠁⢸⠀⠈⣇⡇⣿⣶⣿⣿⡜⣷⡀⠈⣆⠘⢹⣿⣿⡎⢻⡇⡄⠀⢸⠀⠀⢳⡀⠀⠀⠀⠀⢀⡆⡇⠀⠀⠀⠀⠀ ⠙⣦⠀⠹⣦⠀⠀⣿⡄⢸⠘⡄⠀⢿⣿⡟⣿⣿⣿⡀⡟⠑⢄⢸⡄⠘⢿⣯⠇⠀⣷⡇⠀⢸⠀⠰⡈⢿⠿⠿⠿⠿⢿⡇⣿⣷⣶⣶⣶⣶ ⠀⠀⠱⣄⠈⠳⣄⣼⡇⢸⡄⣷⣄⢾⡟⠃⠘⠿⠿⠃⠀⠀⠀⠙⠻⠄⠀⠀⠀⢀⣿⠀⠀⢸⢀⠀⣹⣌⢧⠀⠀⠀⢸⠇⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⣄⠈⠻⡇⠀⣷⣻⣿⣎⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡼⢻⠀⠀⢸⠘⡆⢳⡟⢪⣷⣄⠀⢸⡀⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣷⠄⠘⠀⡟⢻⣿⣿⠻⣿⠁⠀⠀⠀⣴⡾⠋⠉⠛⢿⠂⠀⠀⢀⡎⠀⠀⣸⠀⢳⠈⣿⣶⣿⣿⣶⣾⠁⣿⣤⣤⣤⣤⣤ ⠀⠀⠀⠀⣠⠞⢁⣴⡆⣸⣡⡟⢹⠸⡄⡏⢣⡀⠀⠀⠘⠦⣀⡠⠴⠋⠀⢀⣠⠞⡇⠀⠀⡿⡇⠈⡆⠸⡏⠉⠉⠉⢹⠀⣿⠉⠉⠉⠉⠉ ⠀⢀⡴⠛⢁⣴⡿⢻⡷⠛⠁⡇⢸⠀⢸⣷⠀⢹⡦⣤⣀⣀⡀⠀⢀⣠⠴⡏⠀⢶⢁⠀⢠⠃⢷⠀⠸⡀⢻⡀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀ ⠔⠉⣠⡶⠟⠉⠀⢸⡇⠀⣿⠀⢸⡧⣴⣼⡀⢸⡇⡇⠀⠘⣯⠉⠉⠀⢠⣧⡀⡞⡘⠀⣸⠧⣼⣇⡀⢣⠀⢳⡀⠀⢸⡀⣿⠀⠀⠀⠀⠀ ⢀⡴⠋⠀⠀⠀⠀⢸⡇⠐⡏⢀⢎⡴⢋⡹⣷⠚⢶⣷⠴⠚⠡⠤⠤⠚⠁⠀⣹⣧⠇⢀⣇⡴⡉⠣⡘⡌⢆⠈⢷⣶⣾⡇⣿⣤⣤⣤⣤⣀ ⡋⠀⠀⠀⠀⠀⠀⢸⡇⡸⠀⣎⠈⠀⠉⡠⢿⡄⣼⡏⠐⠲⠤⡄⠀⠤⠒⠉⢸⡟⠀⢸⡟⠢⡘⠂⠈⣡⠈⢆⠈⢯⢹⡇⣿⠉⠉⠉⠙⠛ ⠓⢤⡀⠀⠀⠀⠀⠸⣧⠃⠀⣿⡄⠀⠈⠀⣜⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣿⡷⠀⠁⠀⡠⠙⡄⠈⢢⠈⢻⡇⢹⠀⠀⠀⠀⠀ ⡀⠀⠙⢦⡀⠀⠀⢰⠇⠀⣸⢯⡘⣆⠀⠀⢸⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣿⠁⠀⠀⢰⡃⣠⠟⣷⠀⢣⡀⠹⣾⡀⠀⠀⠀⠀ ⠉⠲⣄⠀⠈⠳⣤⠏⠀⣰⠏⠀⣿⣏⠣⢄⣸⠀⢹⡈⠓⠦⣤⣤⣤⣤⣴⣾⠃⠀⢸⣿⣄⣀⣤⣾⢿⣇⠀⢈⣧⠀⠑⣄⠘⢿⡿⠿⠿⠿ ⠀⠀⠈⠑⢄⢀⠎⠀⣰⣿⣀⣴⡏⢹⣦⣤⡞⠀⠈⣧⣀⡔⣢⣴⣾⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⠁⣸⠛⢾⡟⢻⠀⠀⠈⣢⡈⠳⡄⠀⠀ ⠀⠀⠀⠀⢠⠏⠀⢰⣾⡾⠋⠀⢻⣴⣿⣿⠁⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣼⠋⠀⠀⢻⡿⢧⡀⠀⠱⡑⣄⠙⢦⠀ ⠀⠀⢀⡠⠁⠀⣸⡟⢻⠃⠀⠀⠀⢹⡟⠱⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⡁⠀⠀⠀⢸⡇⠈⢻⡄⠀⠱⡈⢷⣌⠳

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⠀⠀⣄⡀⢀⡩⠞⠋⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣠⠇⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠸⡆⠀⢹⡄⠀⠀⢠⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀ ⠀⠀⠉⠛⠀⠲⠶⠶⠤⠶⠶⣶⠖⠀⣸⡏⠀⠀⠀⠀⠀⡼⠃⣴⠿⠶⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣧⠀⡄⣿⡄⠀⠈⣇⠀⠀⠀⠀⠀⠸⡄⠀⠀ ⠀⠀⠐⠨⠀⠀⠀⠀⠀⣠⠞⠁⠀⢠⣿⠃⠀⠀⠀⢠⠞⢡⡞⠁⠀⠀⠀⠨⣝⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢻⠀⠀⢹⣷⡀⢰⣿⡀⠀⠀⠀⠀⠀⠃⠀⠀ ⠀⠀⠀⠀⠆⠀⢀⣠⠞⠁⠀⠀⢠⣾⡞⠀⠀⠀⢠⠏⣠⡏⠀⠀⠀⠀⠀⠀⠀⠙⢭⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠸⣿⣧⢸⣿⡇⠀⢰⡄⠀⠀⡀⠀⠀ ⠀⠀⠀⢰⣧⠴⠋⠁⠀⣀⡤⢞⣿⢿⠃⠀⠀⣠⠋⣰⠋⢷⠀⠀⠀⠀⠀⠀⠀⣤⡀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡇⠀⠀⣿⣿⣿⣿⣿⠀⣸⡇⠀⠀⣧⣤⣤ ⣀⣤⠶⢋⣁⣤⠴⠖⠋⠁⢠⣞⡿⠘⠀⠀⣰⠃⣼⣣⠀⠈⢧⠀⠀⠀⠀⠀⠸⡿⠁⠀⠈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣰⣿⠀⠀⣿⣿⡇⢻⣿⡇⢿⣿⠀⠀⣿⣿⣿ ⠉⠻⠦⣤⣠⣀⣀⣀⠀⣰⠏⢸⠇⠀⠀⣼⢋⣼⡵⠃⠀⠀⠀⠑⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠭⠍⠉⠉⠹⢿⠀⠀⢻⣿⠃⢸⣿⣷⠈⣿⠀⢸⠹⣿⣿ ⠀⠀⠀⠀⢹⡍⠉⠉⠉⡏⠀⡟⠀⠀⣼⢡⣾⡽⠁⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⢀⣤⡄⠀⠀⠀⢸⡄⠀⣸⡿⠀⠀⣿⡿⠀⣿⠀⠈⠀⢻⣿ ⠀⠀⠀⠀⠘⡇⠀⢀⣴⢧⢠⡇⠀⠰⣻⣯⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠼⠿⠁⠀⠀⠀⠀⡇⢀⣿⡇⠀⠀⢿⡇⠀⢿⢀⡇⠀⠀⠛ ⠀⠀⠀⠀⠀⣇⣠⠞⠁⢸⣿⠁⠀⣰⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⡇⠸⡌⠀⠀⠀⠘⣧⠀⠈⢸⠇⠀⠀⠀ ⠀⠀⠀⣀⣴⣟⣡⡤⠴⠚⡿⠀⣰⡷⠴⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⣀⣀⣀⣤⡗⠀⠃⠀⠀⠀⣴⣿⠀⠀⡟⠀⠀⠀⠀ ⠀⠀⠈⠉⠉⢹⣀⡤⠖⢻⡇⣼⠻⣦⣀⣼⡆⠀⠀⠀⠀⠀⠀⢺⣿⣯⡉⠙⠛⠓⠲⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⢠⡏⠸⠀⢠⡿⢿⣛⣻⡶ ⠀⠀⠀⣠⡴⠋⠁⣠⠴⢻⣿⠃⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⡿⣿⠀⠀⣸⡶⠞⠋⠁⠀ ⢀⠴⠛⠁⢀⡴⠋⠁⢀⣾⠃⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⠀⣸⣹⢿⠀⢀⡿⠀⠀⠀⢀⡤ ⠀⠀⣠⠶⠋⠀⠀⣴⠟⠃⢀⣠⣤⠄⠀⠀⠀⣸⣆⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⡏⢠⣿⣿⣼⡄⢸⡇⠀⠀⠀⠀⠀ ⣴⠞⠁⠀⢀⣴⣿⣵⣶⣚⣩⣾⣡⣤⡶⣾⣿⠃⠘⢦⠀⠀⠀⠀⠈⢿⢻⡉⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢀⡴⠛⣿⠀⠀⠈⣿⡋⢹⣧⡏⣿⠒⠀⠀⠀⠀ ⠁⠀⢠⡴⠟⠉⠉⠉⠉⠉⠉⣡⡾⠋⠉⢻⠏⠀⠀⠈⣷⡀⠀⠀⠀⠈⢧⠙⠲⢤⣄⣀⡀⢉⣻⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⣠⡞⣡⡾⡏⠀⠀⣰⠃⠙⢮⡿⠙⣾⡄⠀⠀⠀⠀ ⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠐⢿⣀⣀⣠⡞⠀⠀⠀⠀⢿⡙⢦⠀⠀⠀⠈⠳⣄⣀⠀⠈⣉⣉⡥⠽⠋⠁⠀⠀⠀⠀⠀⢀⣠⣶⠛⠹⡇⢀⡇⠀⣴⠿⣄⠀⠀⠳⣄⠈⠃⠀⠀⠀⠀ ⠀⢿⡀⣀⣀⣀⣀⣀⣀⣀⣤⡤⠽⠿⢿⠁⠀⢆⠀⠀⠀⣧⠈⢷⣄⡀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠋⠁⢸⠀⠀⠙⣾⠁⢰⡏⠀⠘⢷⡀⠀⠘⢦⠀⠀⠀⠀⠀ ⠀⢸⠋⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⡏⠀⠀⠈⢦⠀⠀⠸⡆⠈⢿⣿⣶⣤⣀⡀⠀⢀⣀⣀⣀⣠⡤⠶⠚⢉⣿⣄⡀⠀⠀⢸⠀⠀⠀⢸⢀⣾⢷⠀⠀⠀⠹⣄⠀⠈⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠳⣄⠀⠹⡄⠀⠙⠿⠿⠛⠋⠉⠉⢉⣡⠞⠁⠀⠀⠀⣼⣣⡬⣷⣦⠀⢸⠀⠀⠀⢸⡜⠉⠻⣧⡀⠀⠀⢸⡄⠀⢻⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠈⠁⠀⢻⡀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⢠⡏⣿⠀⠈⢿⠷⣾⣇⠀⠀⠸⠁⠀⠀⠀⠁⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢀⣀⡤⠤⠖⣶⢦⣀⠙⠦⢤⣤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⡞⣧⡘⣦⡀⣸⡇⠀⠉⠛⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⡆⠀⠀⢳⠀⠀⠀⠀⠀⠀⠘⠒⠚⠉⠉⠀⠀⠀⠀⡇⠀⠈⠙⠓⠒⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠈⠙⢮⣍⠁⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢱⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡾⠳⡀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠉⠳⢤⣄⡀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠒⠿⣷⣤⣀⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣶⠟⠀⠀⠹⣄⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠙⠿⣿⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢠⡾⠁⠀⠀⠀⠀⠘⣆⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⢿⣿⣶⣤⣄⡀⠀⣀⣰⢟⠁⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⣆⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡞⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠠⠁⢀⠀⠀⡴⠁⢀⠔⡹⡁⠀⢠⢀⠀⠀⢆⠀⠤⡀⢄⠈⠄⠀⠀⠀ ⠀⠀⢀⠂⢠⡟⢀⠊⣆⠔⢁⣎⠀⢃⠀⡎⡜⠪⡐⢌⠗⢄⠩⣆⢄⣘⡄⠀⠀ ⠀⠀⡌⠰⠱⠣⠁⢠⠅⢺⡏⠹⢩⠈⢄⠀⣸⠈⠩⠫⠙⣄⠑⠃⠃⢀⡃⠀⠀ ⠀⢀⢸⠀⡄⠀⠀⠸⢠⣽⣷⡿⣿⣦⠀⠀⠷⣶⣿⡿⣷⣧⠀⠀⠀⠀⢀⠠⠂ ⠀⠀⠀⠀⡇⠀⠀⣸⢿⢱⠿⡿⠀⢑⠳⣄⡸⠉⡾⡿⡏⢻⣝⣔⠆⠉⡇⠀⠀ ⠀⠀⢰⠀⢀⠀⠀⢻⡀⠨⠤⠤⢀⡼⠉⠉⢧⡁⠣⠤⠇⣰⠏⢨⡏⠑⠇⠀⠀ ⠀⠀⠀⡄⢠⠀⠀⠘⡍⠉⠉⠉⠉⠀⠈⠀⠀⠈⠉⠉⠉⢡⢔⠝⣇⡀⠀⠀⠀ ⠀⢀⠀⡏⠲⡄⠀⠀⡿⣄⠀⠀⠀⡴⣶⣶⢶⡄⠀⠀⢀⠎⡟⢰⠁⡇⠀⠀⠀ ⠀⠘⡆⢿⠀⣷⡀⠀⢠⠈⠳⣄⡀⠫⠄⠠⠝⠁⣠⣴⢹⠀⣧⢸⠀⡇⠀⠀⠀ ⠀⠠⠹⣸⠀⣏⣷⡀⠀⣇⣰⠰⡏⢶⣤⣠⡾⢫⠃⢁⣊⡄⣸⠠⣤⠡⢀⠀⠀ ⠀⠀⠱⡡⠇⣏⠎⣹⢄⠱⡘⠀⠈⢂⡝⢋⠔⣱⡇⠆⠀⠡⠀⠰⠋⡐⠀⠃⣄ ⠀⢊⢉⠕⣊⣄⠙⢤⣣⠷⢵⣇⠀⣈⠰⡈⢠⠛⡽⠀⠀⠀⡱⡟⠍⠘⢒⠅⡀ ⢨⡀⠉⣣⠯⡋⢱⠈⠀⠆⠀⠙⠦⡟⠉⠑⢹⠌⠠⠡⡀⠀⠳⠀⠱⠙⡕⠁⠀ ⠈⠏⠉⠀⠀⡇⠈⢠⠈⠀⠀⠈⠢⠘⠀⠀⢆⠌⠀⠀⠈⠄⠣⠀⢀⠂⠀⠀⠀ ⠀⠈⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠑⠀⠀⠌⠀⠀⠀⠀⠈⢀⠡⠀⠀⠀⠀⠀

⠄⠐⠀⠀⠀⠀⠈⠇⠀⡇⡇⠀⠀⣠⡐⠀⠈⢸⠁⠉⢉⠉⠉⠉⠉⠙⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠗⠉⠁⠀⠉⠁⠉⠑⠺⣤⠤⠤⠤⣤⣤⣤⡆⢸⣤⣤⣤ ⠀⠀⠀⠀⠀⢀⢀⠜⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⢀⢸⠀⠀⠀ ⠀⠀⠀⣀⣀⣸⠃⠀⢀⢐⢆⠀⢠⠈⢆⣀⣀⠀⠐⡄⢃⡀⣀⣀⠀⢸⢸⠀⠀⠀ ⣀⣠⣤⣤⣤⢂⢡⠀⣸⡞⠚⡄⠈⡄⠈⠺⡦⡈⡂⢰⠈⡏⠉⠉⠉⢹⢸⠉⠉⠉ ⠑⢄⠀⠀⢸⠎⠀⠰⠀⣧⣴⡌⡄⠰⠘⢿⣯⢳⣇⠀⡄⠰⡀⠀⠀⢸⢸⠀⠀⠀ ⠑⢄⠳⡄⢻⠘⢰⠀⡿⡟⣿⡇⠏⠢⢣⠘⠛⠀⡟⠀⡇⠠⣹⠛⠛⢻⢸⠻⠟⠓ ⠀⠀⠑⢌⠻⡀⣿⣷⣽⣄⠀⠀⠀⣀⣀⡀⠀⠰⡇⠀⡇⡘⣗⢵⡄⢸⢸⠀⠀⠀ ⠀⠀⢀⠜⣡⢀⣳⢻⠏⡧⡀⠀⠫⣁⡠⠃⠀⡰⠇⢀⢇⢠⢹⠛⠛⢻⢸⠛⠛⠛ ⡠⢔⣡⠞⢹⠊⡼⢸⢀⡇⢸⠒⠀⡤⠤⠐⡏⢸⡀⢸⢸⡀⠆⢇⠀⢸⢸⠀⠀⠀ ⡠⠋⠀⠀⢸⠀⠇⢌⢈⢿⡚⣦⡔⠣⠤⠂⣉⣎⠁⣆⢎⠫⠜⡈⢶⣼⢸⣤⣤⣄ ⢆⡀⠀⠀⢸⡘⢸⡄⠀⢊⢷⡏⠀⠁⠀⠁⠀⡏⢰⡇⠁⠁⠶⠐⡈⢾⢸⠀⠀⠀ ⢄⠉⠢⡀⡘⠀⡜⢌⢄⠀⡏⡧⣀⠀⠀⢀⣠⠁⢸⡁⠀⣨⡔⠱⡈⢄⠻⣤⣤⣤ ⠀⠉⠂⡸⠁⡾⡤⠏⢧⣼⠀⢡⣠⣩⣽⣿⡟⠀⢸⣿⣿⢁⠗⢞⣃⠀⠡⡙⢄⠀ ⠀⠀⠐⠀⡾⡏⠀⠘⡿⠃⠀⢸⣿⣿⣿⣿⡇⠀⢸⣿⣿⠋⠀⢸⡏⢦⠈⢎⢮⡢

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠤⠴⠶⠤⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡴⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀ ⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀ ⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⢠⠃⢀⣸⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠈⡇⠀ ⢸⠀⢰⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⢸⡀ ⠸⡆⢾⣒⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡴⠃⠀⡇ ⠀⢣⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢀⡇ ⠀⠀⢦⠀⠘⠧⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⠀⠀⡼⠀ ⠀⠀⠈⠣⡀⠀⠀⠉⠙⠛⠒⠲⠶⠖⠚⠋⠁⠀⠀⢀⡜⠀⠀ ⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠶⠶⠖⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⡠⢺⢀⠞⠁⠀⠀⣿⠀⠀⠙⡌⡏⠢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡞⠁⢸⡎⠀⠀⠀⠀⢸⠀⠀⠀⢱⣣⠀⠹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠏⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠽⡀⠀⠀⠀⠀ ⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠇⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⢀⠀⠀⢀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀ ⠀⢀⡠⠤⠒⠊⠉⠑⠲⢭⢯⡒⠨⠷⠦⠭⢶⡶⠶⠖⠒⠶⠾⣄⡀⠀⢀ ⢠⡏⣀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⢀⡄⠙⣆⡞ ⠸⣧⡀⣠⠤⠄⠤⡀⠀⣠⠏⠀⠀⠀⠀⠈⢇⠀⠀⢀⡠⠤⣀⠀⠀⣸⣁ ⠀⡏⡎⠀⠀⠀⠀⣹⡞⠥⡤⠒⢒⣒⣒⣂⡠⠽⣶⠃⠀⠀⠀⠙⡶⡏⠁ ⠀⡇⠣⣀⡀⠀⠐⠁⠑⢤⣇⠀⠀⠁⠀⢸⢀⡤⠯⠣⠀⠀⠀⢀⠇⡇⠀ ⠀⢣⡀⠀⢳⠀⠀⠀⠀⠀⠐⠓⠒⢤⡐⠚⠋⠉⠀⠀⠀⢉⢻⡥⢠⠇⠀ ⢀⡠⠕⠂⣺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⢤⣤⠋⠀⠀ ⠉⠉⢉⡝⣁⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠲⢬⠽⠆⠀ ⠀⠀⢛⠞⠉⣈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠳⡆⠽⠆⠀ ⠀⢀⠯⢄⣼⢡⡷⠤⠤⠤⠀⠠⠤⠤⠤⠤⠤⡤⠤⠤⣠⡇⠀⣿⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡠⠔⠒⠒⠒⠒⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⣋⣉⠅⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠄⠀⣰⠓⠠⣮⢿⠋⡆⠀⢱⡔⠉⠙⢢⠀⠀⠤⢄⠘⠢⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠃⢠⣞⣮⣮⣤⡁⠀⢞⣇⣠⣀⡈⠀⢠⠀⠀⢣⠀⠈⢢⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⢺⣞⣧⣼⣿⣾⣦⢾⣿⣿⣯⣿⣒⢤⠁⠀⠀⠀⠀⠀⢣⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠸⣷⠏⠀⠈⡹⠋⢿⡋⠁⠩⢙⡷⠋⠀⠀⠀⠀⠀⠀⠀⢇ ⠀⠀⠀⠀⣀⡇⠀⠀⠀⢹⠓⠒⡚⠄⠀⢀⠹⢂⠒⢻⠁⠀⠀⡀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠎⠀⣈⡳⣶⡍⣋⢆⠀⠙⢏⠹⠀⡈⠊⠀⢈⡆⠀⠀⠘⡄⠀⠀⠀⠀⠀ ⢀⢴⣹⠀⣜⠑⠢⢜⡏⠁⠀⠑⠢⣀⠀⠀⠀⣀⡴⠋⢣⠀⠀⠀⢱⠀⠀⠀⠀⣄ ⣸⠱⣀⠄⢎⡱⠆⠈⣿⠄⠒⠠⠤⢄⣉⡖⢿⠯⠐⢂⠹⡄⠀⠀⢸⠒⠚⠒⠢⡏ ⠘⢫⡾⠓⠡⡁⠀⠀⣇⠀⠀⠀⠀⠀⠀⠱⣈⡄⢀⡀⢶⠇⠀⢀⡜⠀⠀⢀⡀⠌ ⠀⠀⠑⢤⠀⠀⠀⢠⣌⠢⣤⠄⠀⠀⠀⠀⠀⠉⣀⣠⣞⣀⠴⠊⠀⢠⠞⠁⠀⠀ ⠀⠀⡎⡯⠤⢤⠒⠈⣾⠉⠀⠀⠀⢠⣶⣦⠀⣠⣤⡄⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀ ⠀⢀⢇⣇⠀⠀⣆⠠⠚⡧⠀⠀⠀⠘⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀ ⠀⠎⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⢿⣿⣿⠏⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠶⠶⠶⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠛⠁⠁⣡⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⠀⢀⣰⢞⣿⡿⣯⡀⠀⠀⢤⠀⢀⡴⠶⠶⣤⡀⠀⠀⠀⠀⠀⠀⠈⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠒⠄⠀⢀⣾⠏⠀⠀⣻⢯⡞⡿⠁⢸⡇⠀⠀⠀⣷⠟⠀⠀⠀⠈⢻⡄⠀⠀⠄⠒⠶⣤⡀⠀⠙⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⢀⣴⠏⡾⢰⣇⡀⠈⠃⠀⠀⣰⢿⡇⠀⠀⠀⠀⠈⠇⠀⢠⠀⠀⠀⠈⢳⡀⠀⠀⠙⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣼⢧⣼⣿⠛⣿⡿⣿⣦⡀⠉⠁⣾⣿⣺⣿⣗⣶⣤⡀⠀⠈⢧⡀⠀⠀⠈⠇⠀⠀⠀⠈⢷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠈⣿⣶⢻⣿⣠⣾⣿⣾⣿⣷⣶⢾⣿⣿⣿⣿⣶⣭⣿⣟⠖⢶⡄⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢸⣿⡳⣿⠟⠛⠛⠻⣿⣿⣿⣦⣿⣿⣿⠛⠿⣿⣿⣿⣨⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠸⣿⣷⠋⠄⠄⠀⢠⠞⠋⠀⠺⣿⡀⠀⠀⠠⠲⢀⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠁⠀⠀⠀⠀⢻⡟⠷⣦⣤⣤⢿⡀⠀⠀⠀⠈⠻⡷⣶⡶⠾⠻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹ ⠀⠀⠀⠀⠀⠀⡠⠄⠾⣄⡀⠀⠀⣀⣠⣸⣧⠀⠀⠀⢠⣤⣅⣀⡠⠤⠐⢫⠀⢸⠁⠀⠀⡇⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⠀⠀⡄⣀⣙⣶⣾⣏⠀⢻⡘⢦⠀⠀⠈⢿⣆⠀⢣⠀⠀⢀⡷⠁⠀⠀⠀⣷⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡤⢲⠃⠀⣠⢿⣏⡁⠀⢹⣿⡶⠞⠁⠈⠳⣄⡀⠀⠈⠑⠚⠓⠂⠁⠀⠀⠀⢀⣴⢿⡄⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡴⢻⣀⣎⠀⣠⣇⠀⠀⠉⠓⢏⢹⡀⠀⠀⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠈⣧⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⣿⣄ ⢀⡷⢯⠁⠀⢉⣡⡜⠓⢦⡤⠀⠀⣿⣿⣀⣠⣤⣄⣀⣀⠀⠈⠉⠳⡶⠶⣾⣿⣏⣀⠤⡴⠚⢻⡄⠀⠀⠀⠀⠀⣿⠴⠶⠶⠶⠦⣄⣸⠘ ⠾⣥⣤⠷⣞⣁⠀⣱⣠⠋⠁⠀⠀⣿⡏⠁⠀⠀⠀⠀⠉⠉⠛⠓⠚⢧⠀⢹⡁⠀⠀⠀⠹⡄⠈⡧⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠈⠻⣄ ⠀⠑⢪⡽⠶⠞⠋⠀⡇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⢣⡀⠀⠀⣀⡽⢾⡟⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⣀⣀⡘ ⠀⠀⠀⠹⡄⠀⠀⠀⠉⠀⠀⠀⠀⡟⢳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠗⠚⠉⠁⢀⣼⠁⠀⠀⣀⡾⠁⠀⠀⢀⣤⡞⠋⠁⠀⠀ ⠀⠀⠀⠀⠈⣲⡆⠀⠀⠀⠀⠀⢠⣷⣄⠙⣻⣶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣴⣞⣉⣠⡤⠞⠋⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⠋⣽⠃⠀⣀⣀⡤⠴⠚⢳⣼⠛⠉⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⢀⣀⣀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⡏⠉⠉⠀⢸⡄⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣄⣴⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣄⣳⠀⠀⠀⠀⢇⢀⣠⠶⠛⣿⠄⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡼⠁⠈⠉⠓⠒⠒⠒⠋⠉⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⡠⢚⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠑⢄⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⢀⣼⠁⠀⢀⡾⡇⠀⢀⡴⠊⢠⠎⠈⠀⠀⠀⢠⡧⢰⡦⣄⡀⠀⢹⣦⡀⠈⢹⣦⡀⢂⠀⠀⢣⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠀⢠⣾⡇⠀⣰⠋⢸⢀⡴⠋⠀⣰⡇⠀⠀⢇⠀⠀⡞⢹⠘⠓⢤⡉⠢⣄⠿⡝⢆⠀⢻⣽⠢⢕⡠⠈⣧⠄⠀⠀⠀⠀ ⠀⠀⠀⡼⠀⢠⢋⣿⠀⡜⠁⠀⡾⠋⣠⣴⣾⠿⡷⢾⡤⠘⡄⠀⠃⢸⢷⠀⠺⠿⢶⠾⢦⣷⡀⠙⢦⡙⠓⣞⠛⠉⢻⠀⠀⠀⠀⠀ ⠀⠀⢰⢁⡇⠃⢸⠈⠞⠀⠀⢠⡗⠋⢡⣾⠃⠀⢻⡈⡆⠀⠘⢄⠄⢸⣌⡆⠀⠈⠊⠳⣄⠈⡷⢄⠀⠈⠁⠀⠑⢤⣈⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⡏⠀⠀⠀⠀⢸⠀⢠⡋⢿⣶⣶⣞⣷⣿⣆⠀⠀⠀⠈⣿⣷⣶⣶⣶⣶⣿⣦⣾⠀⠁⠀⠀⠀⠀⠀⠈⠉⠁⣡⠂⠀ ⠀⠐⠀⡎⠀⠀⠇⠀⠀⠀⠀⢸⣠⣏⣽⠿⣿⣿⣹⡿⠿⡟⢦⡀⠀⠀⢯⢻⡿⠿⣿⣏⢹⣿⣿⣧⣀⠀⠀⠀⠀⣀⣠⡴⠋⠁⠀⠀ ⠀⠀⠀⠇⠀⠀⠁⠀⠀⠀⠀⣸⣿⡿⠉⣶⣿⣿⣿⡇⠀⢙⡞⠻⣦⣀⣸⡄⠁⣾⣿⣿⣾⠇⢻⣷⣝⣯⡉⢿⠉⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢰⣿⠁⠁⠀⢯⠀⠉⠘⠃⠀⢸⡷⠶⠿⢿⣟⠓⠀⣇⠈⠁⠘⠀⠈⢹⣿⠟⡟⢿⠦⣤⣬⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⢳⠀⠀⠀⠀⢽⣧⡀⠀⠚⠒⠒⠚⣀⣤⡿⠁⠀⠀⠀⢻⣦⣀⡙⠒⠒⠟⣀⣰⣿⠇⢀⣧⡟⠀⠻⠸⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⡆⠀⢠⠀⠀⠀⠀⠘⣏⠙⠛⠛⠚⠛⠛⠋⠁⠀⠀⠘⠀⠀⠀⠈⠉⠙⠛⠛⠛⠉⠉⣸⣠⢞⡿⡇⠀⠀⠐⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢳⣀⠘⡄⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣴⡏⠀⡷⠲⡄⠀⠀⠀⠀⠀⠀ ⠀⢀⠀⠀⣾⠈⠳⣧⠀⠀⠀⠀⢹⢻⣄⠀⠀⠀⠀⠀⢠⣶⣿⠷⠶⢾⣷⣦⠀⠀⠀⠀⠀⢠⡞⠉⡿⠀⠸⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⢹⡇⠀⣿⡄⠀⢿⡆⠀⠀⠀⠘⡄⢹⢷⣄⠀⠀⠀⠘⣷⠛⠋⠙⠛⢻⡟⠀⠀⠀⠀⣠⡟⠁⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⡀⡟⡇⠀⢸⢿⡄⠀⠀⠀⢣⣸⠀⠉⢳⣦⣀⠀⠘⠒⠤⠤⠖⠋⠀⢀⣠⢶⡻⡄⢳⠀⠀⣷⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⢀⠈⢷⠁⡇⠀⢸⠘⣿⡄⠀⠀⠘⡏⠀⢀⡇⢼⡟⠳⣤⣀⠀⠀⣠⣶⡿⢻⡿⠀⣇⢳⡘⡄⠀⢸⡇⢸⡄⠀⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⢢⡘⣳⢧⡀⢸⣧⢹⣿⣄⠀⠀⢿⠒⠺⠀⠈⠣⡀⠙⢿⣿⣿⣿⠟⢁⡞⠁⠀⡼⠤⠿⣷⠤⠞⠛⢉⡇⡇⢸⠙⠢⡀⠀⠀⠀ ⠀⠀⠀⢻⣁⣼⠇⢸⣄⡿⠁⢈⣧⡀⠈⢧⠀⠂⠀⠀⠈⠲⣄⠙⠋⣠⠔⢉⣴⣿⢀⠇⠀⠀⠘⡄⠀⠀⡜⢹⢰⠀⢆⣀⠇⠀⡀⠀ ⢀⡠⠤⠤⢭⣀⡤⠚⠙⠲⣴⠋⢠⠟⣦⠈⢆⢰⠀⠀⠀⢰⠙⡆⢀⡇⢀⢸⣿⠟⡞⠀⠀⠀⠀⠘⣄⣠⠖⠺⠤⢑⣂⣠⠴⠚⠉⠠ ⠈⢀⡀⢠⠚⣁⣤⣶⠦⡀⠈⢳⣡⡾⢻⠟⢮⣿⡆⠀⠀⣼⠀⢹⣼⠀⣸⠈⠃⡜⢣⠀⠀⠀⠀⠀⡜⡱⠉⠑⡠⠀⠀⣭⠇⣀⠀⠀ ⠃⠈⠉⠛⢿⣛⢟⡹⡗⠙⡆⠘⡇⠀⡸⠀⠀⠙⢿⡄⣰⣍⠗⠚⠓⠞⣉⣇⡜⠀⣈⢦⠀⠀⠀⢸⢣⠃⠀⠉⡍⠹⣏⡽⠋⠁⠀⠀ ⣷⣤⣀⡠⠴⠛⠋⢰⠃⠀⡇⠀⡇⠰⠁⠀⠀⠀⢀⠈⠁⢯⠀⠀⠀⠀⣿⠀⢠⠎⠀⠀⠱⡄⠀⢸⠘⠀⠀⠀⢰⠀⠙⡄⠀⠀⠀⠀ ⠈⡄⠀⠀⠀⠀⠀⢸⠀⠘⠀⣠⠇⠀⠀⠀⠀⠀⠀⠑⡄⠘⣆⠀⠄⠠⠇⡰⠃⠀⠀⠀⠀⠈⢆⠀⠳⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠑⠀⠀⠀⠀⠀⠈⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠇⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠈⢂⠀⠳⡀⠐⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⠿⠿⠿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣾⠿⠛⠛⠿⠿⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀ ⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀ ⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀ ⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀ ⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀ ⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀ ⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇ ⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇ ⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀ ⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣶⣦⣤⣴⣶⣶⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀ ⠀⠀⠹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀ ⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣶⡿⠟⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣿⣿⡿⠿⠿⠟⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣮⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠘⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠣⡙⢯⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢸⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⡂⠀⠀⠱⡀⠙⢷⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡟⠀⠀⠀⠈⡄⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡈⠁⠀⠀⠀⠑⡄⠀⠙⢗⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠿⠁⠀⠀⠀⠀⡇⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠸⡄⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡀⢸⠿⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⠀⠀⠀⢦⢄⣘⣟⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠺⠧⣀⣀⠀⢠⢧⡘⡆⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣧⣀⣀⣈⣣⡀⠉⠳⣄⠀⠀⠀⠙⢟⢦⡀⠀⢀⣀⢀⣀⢀⢸⡧⠀⠀⠀⠉⠛⠀⠱⡇⠀⠀⠀⢯⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⠬⠂⠀⠀⠀⠀⠀⠈⠳⣄⣀⠤⠔⠓⠛⡛⠉⠉⠉⠉⡝⠉⠀⠀⠀⠀⠄⣀⠀⠀⢻⠀⠀⠀⠈⣟⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢐⣞⡉⠀⠀⠀⠀⠀⠀⣀⠤⠖⠊⠁⠀⠀⠤⠒⠒⠉⠁⠀⠑⠢⡈⠉⠒⠤⣀⣀⡀⠀⠉⠁⢸⡀⠀⠀⠀⢱⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠻⣽⢀⡤⠖⠉⠀⠀⡔⠁⣠⠔⠊⠑⠒⠤⢄⡀⠀⠀⠀⠈⠢⡀⠀⢀⣍⡠⠤⠒⠒⠋⢦⠀⠀⠀⠀⢿⢆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⢄⠾⠋⠁⠀⠀⠀⢀⣎⡤⠊⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⡀⠀⠈⠢⡉⠀⢀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠱⡳⡀⠀⠀⠀ ⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⢠⠟⣹⠡⠤⠤⡄⠀⠀⠀⠀⢠⡤⠐⠀⠀⡈⠑⠢⣀⠈⢢⣸⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠘⣕⡄⠀⠀ ⠀⠀⢸⠀⢠⠃⠀⠀⠀⠀⣰⠃⡜⠉⠒⠤⠔⠁⠀⠀⠀⠀⠈⠳⠤⠒⠉⠀⠀⠀⠀⠑⠦⣹⠀⠀⠀⠀⠀⡠⠀⠘⣄⠀⠀⠀⠈⣞⠀⠀ ⠀⠀⠬⠀⡆⠀⠀⠀⠀⣰⢃⣘⡀⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣒⣠⣤⣤⡤⠀⠈⠘⡆⠀⠀⡼⠊⠀⠀⠀⠘⡄⠀⠀⠀⢸⢆⠀ ⠀⠀⡧⠘⠀⠀⠀⠀⣼⣧⣾⠟⠛⣛⡿⠶⣿⠀⠀⠀⠀⠀⢀⡿⠟⠛⣛⣉⣉⠛⢿⣶⣄⠰⡇⠀⠀⢰⠀⠀⠀⠀⠀⠹⡀⠀⠀⢸⠘⣆ ⠀⠀⡇⠀⠀⠀⠀⣼⣿⠏⠁⢰⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠐⢀⣛⣿⣿⣿⣷⡄⠙⢿⣷⣅⠀⠀⢸⠀⠀⠀⠀⠀⢀⡇⠀⠀⠠⠀⢸ ⠀⠐⡇⠀⠀⠀⣼⢹⣷⠀⢰⣿⠛⣿⣽⠛⠂⠀⠀⠀⠀⠀⠀⠀⢺⣿⣭⡟⢻⣿⣿⠀⢱⣿⠛⠒⠀⢸⠀⠀⠀⠀⠀⢸⠁⠀⠀⢸⠁⢸ ⠀⢘⡇⠀⠀⢠⣇⡼⠁⠓⠼⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠺⠧⡠⠎⢸⠀⠀⠀⢸⠀⠀⠀⠀⣠⠏⠀⠀⠀⡸⠀⡾ ⠀⢰⠃⠀⢠⢯⡏⣀⣀⢔⡂⠀⠀⠀⢀⣀⣀⣀⣤⡤⢤⣀⡀⠀⣀⡀⠀⠀⠠⣤⣤⣄⣀⣸⠀⠀⠀⢸⠀⠀⠀⡰⡿⠀⠀⠀⢰⢁⣞⡅ ⠀⣾⠀⢀⡞⠐⣯⠟⢡⠀⠀⠀⠀⠀⠀⣾⢯⡛⡱⢪⠕⡪⠵⢾⡙⣆⠀⠀⠀⢀⡉⠺⣭⡿⠀⠀⠀⢸⠀⠃⡰⢱⢳⠀⠀⢀⢧⡞⠎⠀ ⣰⡏⠀⡼⠀⠀⢧⣴⡏⠀⠀⠀⠀⠀⠀⡟⢦⠱⣑⢣⠚⡥⢋⠦⡑⢾⡀⠀⠀⠀⠹⣦⣌⡇⠀⠀⠀⢸⠀⡜⠁⡜⢰⠀⠀⣸⢺⠈⠀⠀ ⡿⠀⢠⠇⠀⠀⠈⣻⡇⠀⠀⠀⠀⠀⠀⣟⢢⠓⣌⠦⡙⠴⣉⠖⣩⢒⡇⠀⠀⠀⠀⢹⣾⠃⠀⠀⠀⢸⡜⠀⢠⡇⢸⠀⠀⡇⢸⡀⠀⠀ ⠁⠀⡞⠀⠀⠀⠀⡏⢳⡄⠀⠀⠀⠀⠀⠘⣎⡱⢌⠲⣉⠳⢌⢎⡑⢎⡇⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⣸⠀⠀⡼⣧⠘⡄⠀⡇⠈⡗⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣿⣿⣶⣶⣶⣄ ⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⡀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠙⠛⢿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣾⠋⠁⠀⠙⢷⡄⠀⠀⠀⣠⡾⠛⠛⠻⣶⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡇⢸⡇⠀⢰⣶⠀⠀⣿⠀⠀⣸⡏⢀⣤⡄⠀⠈⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⡝⠿⣿⣿⠀⠈⣷⡀⠀⠀⠀⣠⡿⠀⠀⣿⠀⠈⠋⠁⠀⢠⡿⢰⣿⣿⣿⡿⠋⡉⠙⢿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⣾⠁⠀⠈⠀⠀⠀⠈⠛⠷⠶⠞⠋⠀⠀⠀⠘⣷⣀⣀⣀⣴⠟⠁⢸⣿⣿⣿⡇⠸⣧⠀⠈⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠈⠻⠿⠿⠀⠀⠹⣷⠤⣼⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⣿⠿⠿⠿⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⢰⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣤⣤⡄⠀⠘⢷⡀⠀⠀⠉⠻⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠋⠀⠀⠀⣠⡟⠀⡀⠀⠀⠀ ⡤⠤⠤⠤⠴⠏⠀⠀⣿⠀⠀⠀⠙⢦⣄⠀⠀⠀⠈⠉⠛⠛⠶⠶⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⣠⣾⠏⢰⡟⠻⣧⣀⠀ ⠀⠀⠀⠀⠀⣴⡟⢻⡏⠀⠀⠀⠀⠀⠙⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣧⣀⠀⢻⣆⠈⠉⠛ ⠀⠀⠀⠀⣾⠟⠀⣼⣷⣄⡀⠀⠀⠀⠀⠀⣨⣿⣿⣶⣦⣤⣄⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⠻⣦⣄ ⠀⠀⢀⣼⣏⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣜⣿ ⠀⠀⣸⡇⠉⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁

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

⣀⣀⠤⠤⠤⠤⠤⠤⠤⠤⣀ ⠀⠀⠀⠀⢀⠴⠛⠀⠀⠀⠀ ⠀⠁⠀⠀⠀⠀ ⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀ ⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⡇⠀⠀⠀⢀⡶⠛⣿⣷⡄⠀⠀⠀⣰⣿⠛⢿⣷⡄⠀⠀⠀⢢⠀ ⠀⡇⠀⠀⠀⢸⣷⣶⣿⣿⡇⠀⠀⠀⢻⣿⣶⣿⣿⣿⠀⠀⠀⢸⠀ ⠀⡇⠀⠀⠀⠈⠛⠻⠿⠟⠁⠀⠀⠀⠈⠛⠻⠿⠛⠁⠀⠀⠀⢸⠀ ⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀ ⠀⠀⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣚⡁⠀⠀ ⠀⠀⠀⠀⠈⠙⠒⢢⡤⠤⠤⠤⠤⠤⠖⠒⠒⠋⠉⠉⠀ ⠈ ⢢⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸ ⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣤⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀ ⢸ ⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢠⣿⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀ ⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⢸⠘⡆⠀⠀⢸⣀⡰⠋⣆⠀ ⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠼⠀⠘⠤⠴⠃⠀⠀⠀⠈⠉⠁⠀

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⣿⣿⣿⣿⣏⡈⡀⣻ ⣿⣿⣿⣿⣿⠃⠈⠻ ⣿⣿⠛⠀⠸⠀⠀⠘⠀⢻ ⡋⣁⣴⣿⣿⣄⠀⠈⠀⠀⢿ 🏀 ⣿⡿⠀⠀⢀⡀⣷⠀ ⣿⣿⣿⡟⠀⢀🐔⢵⣿⣦ ⣿⣿⣿⡀⠀⣿⣿⣆⠀ ⣿⣿⣿⣿⣆⠈⢿⣿⠀⢻ ⣿⣿⣿⣿⠿⠃⠀⣿⡷⠘

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

⠀⠀⠀⠀⠰⢷⢿⠄ ⠀⠀⠀⠀⠀⣼⣷⣄ ⠀⠀⣤⣿⣇⣿⣿⣧⣿⡄ ⢴⠾⠋⠀⠀⠻⣿⣷⣿⣿⡀ 🏀 ⠀⢀⣿⣿⡿⢿⠈⣿ ⠀⠀⠀⢠⣿⡿🐔⡊⠀⠙ ⠀⠀⠀⢿⣿⠀⠀⠹⣿ ⠀⠀⠀⠀⠹⣷⡀⠀⣿⡄ ⠀⠀⠀⠀⣀⣼⣿⠀⢈⣧

⠀⠀⣀⣤⠶⠶⠶⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⠋⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⣴⣤⣄⡀⠀⠀⠀⠀ ⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡄⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀ ⠀⠀⠈⠻⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀ ⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⢀⡤⠶⠿⣿⣦⠗⠛⠒⣦⣀⠀⠀⠀⠀⠀⠐⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⡇⠀⢠⡇⠀ ⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠘⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣇⠄⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠐⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠹⣤⡀⢰⠞⠉⢳⡄⠠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠛⢶⣤⣀⣀⣀⣤⡴⠟⠃⠀⠀⠀⠀⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠠⡏⠀⠈⠓⡶⠊⠀⠀⠘⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠰⣸⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣧⣀⣀⣠⡾⢦⣤⣤⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⠀⠈⠉⠁⠀⠀⠀⣀⣀⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀ ⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⡴⠒⠒⣞⣁⡠⠽⠭⢄⣈⣳⣊⡉⠲⣄⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀ ⠀⠀⠀⠀⢸⡇⠀⡴⠋⢙⡵⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠳⢤⣀⣳⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠐⢺⡇ ⠀⠀⠀⠀⢸⡇⡮⢇⡾⠁⢠⣶⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⢹⣄⡀⠀⠀⠀⠀⠀⠀⠈⡇ ⠀⠀⠀⠀⠸⣿⡁⣼⠀⠀⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠈⠳⣄⢹⠦⠀⠀⠀⠀⠀⠀⣟ ⠀⠀⠀⠀⠀⠻⡟⢿⠀⠀⠈⠛⠉⠀⠀⠀⠀⣤⠤⣄⠀⠀⠀⠀⠀⣸⣿⣿⣧⠀⠀⠙⣎⠳⡄⠀⠀⠀⢸⢰⡏ ⠀⠀⠀⠀⠀⠀⠱⣜⣆⡤⠦⠤⣄⠀⠀⠀⠀⠛⠒⠋⠀⠀⠀⠀⠀⢻⣿⣿⡏⠀⠀⠀⢸⣤⠇⠂⠀⢠⢄⡾⠁ ⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠐⣾⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢸⠃⡃⠁⠠⣠⡾⠁⠀ ⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⣼⣦⣤⣠⠦⢄⠙⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⡞⣡⣤⠾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠸⣿⠉⠀⣹⣀⣙⣿⠏⠁⡽⠶⠤⣤⣤⣤⣤⣤⣴⡾⠅⠚⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠈⠛⣿⠿⣌⡝⠝⡍⣘⣧⣀⣀⣀⣀⣤⣴⣶⣾⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣳⡶⢻⠷⣮⣤⣤⣽⣥⣬⣭⣿⣿⢿⡖⠋⠉⠉⢳⡝⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣠⢺⣥⣧⣽⢂⡄⠀⠓⠀⠈⢻⡄⠀⠀⠀⠀⣿⣭⣧⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣋⠴⢺⠥⠚⠁⠀⠘⠦⣽⡒⢤⣄⣀⣼⢳⣤⡀⠀⠼⠃⣠⣷⡗⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠯⠜⠉⡏⠀⠀⠀⠀⠀⡄⣧⠉⠙⠲⣾⣯⣯⣏⣳⣶⣴⣾⣻⣉⣽⣵⡦⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣿⢄⠀⠀⠀⠀⠀⠀⠀⠉⢉⣽⡶⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠟⢦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⡀⠙⠒⠢⢴⣉⡦⠔⠚⠋⢸⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠦⠽⣉⣙⣟⠛⣛⠻⢿⠞⠿⡟⠿⣻⠛⣧⠀⠀⠀⠀⠁⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣉⣉⣻⣿⣃⠙⢍⣫⣁⠉⠉⠉⣉⣩⣿⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣉⣉⣿⡀⠉⠛⠛⠧⠜⠛⠛⠛⠉⢡⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠾⠶⠶⠶⠶⠞⠳⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢠⠔⠚⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠏⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡀⠀⠀⠀⡇⠀⠀⢀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢧⠀⠀⠀⢳⣾⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⢀⡀⠀⠀ ⠀⠀⠀⠀⠑⡶⠀⠀⠙⠛⠻⠿⣿⣿⣿⣿⠷⠶⠒⠚⠉⠉⠉⠓⡄ ⠀⠀⠀⠀⡼⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⡴⠲⢤⠇⠀⠀⠀⠀⣆⡸⠂⠀⠀⠐⠀⠀⠀⢶⣤⣀⣀⡤⠞⠁ ⠀⢧⡀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢈⡷⠒⢆⠀⠀⠀ ⠀⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⠀ ⢰⠒⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀ ⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀ ⠀⠙⠲⠞⠓⠢⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠳⠤⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣅⣀⢈⣩⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠴⣒⣤⣀⡲⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣿⣯⡿⠟⠋⠈⠻⡛⠋⠹⣗⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠊⢔⢉⢙⣹⡿⠳⣙⡊⣓⣉⣒⡤⡀⠀⠀⠀⠀⠀⣰⡟⣡⠟⠁⠀⠀⠀⠀⠀⠈⠑⠢⡍⡧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠐⡇⠀⠻⣿⠟⠁⠀⠀⠀⠉⠉⠻⣟⠋⠙⠓⢤⣠⡴⣶⡿⣛⣉⣁⠒⠢⣄⣀⠀⣀⣤⡶⢺⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠱⡀⢾⠁⠀⠀⠀⣀⡠⠤⠶⠒⣺⠿⣟⢠⣯⣃⣳⡾⠲⠷⣮⣥⣴⣮⣤⣤⣬⣿⣟⣻⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠢⣷⣦⣤⣾⣿⣷⣶⡂⢉⡤⢊⣥⣿⡿⠿⠿⢿⣦⣤⣀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⡤⢤⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠋⡴⣻⣿⠏⠀⠀⠀⠘⢿⢯⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⢽⣿⣦⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⣡⢁⡏⠀⠀⠀⠀⠀⠈⠫⣳⠄⢹⡆⠀⠀⠀⠀⣠⣴⣿⣿⣿⠞⠁⠈⢿⢿⡷⠀⠀ ⠀⠀⣰⣾⣏⠩⡉⠰⣄⠀⠀⠀⠀⢠⢂⡴⢛⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣾⣿⡀⠀⢠⣾⣿⣿⡿⠟⠁⠀⠀⠀⣸⣾⠃⠀⢀ ⠀⣰⡇⠈⠙⠤⣽⣧⣹⣷⣤⣀⣴⣡⡤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠛⠛⠋⠁⠀⠀⠀⣀⣴⣾⡿⠁⠀⠀⠘ ⢰⣟⣹⡄⠀⠀⠀⠉⠛⠻⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⡖⠁⢸⣿⠃⠀⠀⠀⠀ ⢹⡇⠂⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⠀⠠⣬⣧⣀⡜⠁⠀⠀⠀⠀⠀ ⠀⠱⡄⠀⠣⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢶⠃⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠢⢀⣙⠿⣿⡿⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡾⡄⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠑⠊⠁⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⢷⣿⣿⡶⠤⢕⡄⠀⠀⠀ ⠀⠀⠀⣠⠔⠂⢶⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀ ⠀⣠⡎⠀⣀⣠⡾⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀ ⠀⣿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⡾⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡾⠁⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠈⢳⣄⠀⠀⠀ ⠤⠒⠚⠁⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠙⠒⠂⠤⠐⠒⠋⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠈⠓⠒⠤ ⠀⠀⣀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡀⠀⠀⠀⢀⣠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⠀⠀ ⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠋⠉⠉⠉⠓⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠚⠉⠉⠉⠙⠒⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣀⠀⠀⢀⡀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⡀⠀⠀⣀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⣿⡄⠀⣾⡇⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⢸⣧⠀⢰⣿⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣀⡀⠀⠀⢿⠁⠀⢹⠇⠀⠀⣠⡄⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢀⣀⠀⠀⠸⡏⠀⠈⡿⠀⠀⢀⣤⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠙⠲⠤⢀⣀⠠⠴⠚⠁⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠈⠓⠦⠄⣀⡀⠤⠖⠋⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⡀⠀⠀⠀⠀⠀⣀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣀⠀⠀⠀⠀⠀⢀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠒⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠒⠒⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠒ ⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠀⠀⠀⠀ ⠀⣾⡆⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⣾⡆⠀⢸⣧⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⢠⣿⠀ ⠀⣿⡇⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⢿⡇⠀⢸⡿⠀⠀⢀⡀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⣀⠀⠀⠸⣿⠀ ⠀⠈⠀⠀⠘⣹⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢹⡟⠀⠀⠈⠀⠀⠀⠁⠀⠀⢙⡏⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⣏⠁⠀⠀⠉⠀ ⠀⠀⠀⠀⢠⠏⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠹⣄⠀⠀⠀⠀ ⠀⣀⣠⠔⠃⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠛⢤⣀⡀⠀⢀⣀⡤⠚⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠘⠣⣄⣀⠀ ⠁⠀⠀⠀⣀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢤⡀⠀⠀⠀⠉⠁⠀⠀⢀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣀⠀⠀⠀⠈ ⠤⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠤⠤⠤⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⣶⠀⠀⣰⡆⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢰⡆⠀⢀⣶⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⣿⠇⠀⢿⡇⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⢸⡿⠀⠸⣿⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢲⠦⠀⠀⠙⠀⠀⠘⠁⠀⠀⢺⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠐⡶⠄⠀⠈⠃⠀⠀⠋⠀⠀⠐⡟⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠙⢦⣀⠀⠀⠀⠀⢀⣠⠞⠁⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠈⠳⣄⡀⠀⠀⠀⠀⣀⡴⠋⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠈⠉⠐⠒⠈⠉⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠉⠁⠒⠂⠉⠁⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⢄⣀⣀⣀⡤⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⠤⣀⣀⣀⣠⠤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀ ⠀⠀⠉⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠀⠀⠀⠈⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠁⠀ ⠀⣤⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⢠⡄⠀⢀⣄⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⢀⣄⠀ ⠀⣿⡇⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⣿⡧⠀⢸⣿⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢸⣿⠀ ⠀⠿⠁⠀⢠⣶⡆⢨⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢴⡦⠀⠀⢹⡇⠀⠘⣟⠀⠀⣠⣤⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠱⢠⣤⡄⠀⠘⡟⠀

⠀⠀⠀⠀⠀⠀⠑⢶⣄⠀⠀⠀ ⠀⢠⣾⣿⡟⠁⠀⠀⠙⣷⡄⠀ ⠀⠻⡿⠛⢿⣦⣀⠀⠀⢹⣷⠀ ⠀⠀⠁⠀⠈⠛⢿⣦⣀⣾⡿⠀ ⠀⢠⣴⢷⣤⣀⣠⣽⣿⣿⣃⠀ ⣴⡟⠉⠀⠉⠛⠛⠛⠉⠈⠻⡷

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⠉⢹⣿⣏⠉⣹⣿⣿⣿⣧⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⣸⣿⣿⣿⣿⣿⣦⣤⣤⣾⣿⣿⣿⣿⣿⡀⠀⠀ ⠀⢠⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀ ⠠⠿⣿⣿⠿⠿⠿⠟⠋⣀⡈⠛⠿⠿⠿⢿⣿⠿⠇⠀ ⣤⣤⣤⣤⣤⣤⣴⣶⣿⣿⣿⣶⣶⣤⣤⣤⣤⣤⣤⡀ ⣿⣿⣿⣿⣿⣿⣿⠿⠏⠀⠈⠿⢿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⡁⠀⣰⣿⣦⠀⠀⣿⣿⣿⣿⣿⣿⠃ ⢸⣿⣿⣿⣿⣿⣷⠀⠘⠻⠛⠀⢸⣿⣿⣿⣿⣿⡟⠀ ⠀⢻⣿⣿⣿⣿⣿⣦⣤⣶⣤⣴⣿⣿⣿⣿⣿⣿⠃⠀ ⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀

⠀⡴⡞⠓⠢⣄⠀⠀⠀⣤⠞⠉⢲⡀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠨⡷⣷⠀⠀⠹⣷⡀⢸⣥⠀⠀⠠⡇⠀⠀⠀⠀⣰⣾⡿⠛⠋⠁⠀⠀⠀⠈⠙⢿⣿⣆⠀⣠⣴⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⢿⡏⣧⠀⠀⠈⢷⣿⡇⠀⠀⢰⡇⠀⠀⠀⣾⣿⠟⠁⠀⠀⠀⢀⣀⠀⠀⠀⠀⢻⣿⣿⡿⠛⠋⠉⠛⠻⢿⣿⣦⣄⠀⠀⠀ ⠀⠀⠻⣦⡐⠆⠀⠈⠛⠁⠀⢀⡿⠀⠀⠀⠀⣿⣯⠀⠀⠀⢠⠎⠁⠀⠉⢢⠀⠀⠸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣦⡀⠀ ⠀⠀⠀⠈⠻⢤⣄⠂⢀⠀⢠⡾⠁⠀⠀⠀⠀⣿⣧⠀⠀⠀⢸⡀⠀⠀⠀⣸⠀⠀⠀⠿⠇⠀⠀⡠⠔⠢⢄⡀⠀⠀⠙⣿⣷⠀ ⠀⠀⠀⠀⠀⠀⠙⠲⢧⣠⡿⢁⣠⣴⣶⣶⣶⣿⣿⣧⣀⠀⠀⠑⠂⠤⠒⠁⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢱⠀⠀⠀⢹⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⣿⡿⠛⠉⠉⠉⠙⠻⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⣠⠎⠀⠀⠀⣼⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⠀⠀⠀⡠⠤⠤⣀⠀⠀⠀⠀⠀⠀⡠⠒⠀⠐⠲⢄⡀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢠⣾⣿⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⡜⠀⠀⠀⠈⢣⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠉⢢⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⠳⡀⠀⠀⣠⠆⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⣾⣿⠿⠛⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠈⠢⢀⣀⣀⡀⠤⠔⠊⠁⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣶⣤⣀⣀⣠⣴⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠟⠛⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀@𝗻𝗲𝘂𝗿𝗼𝗹𝗶𝗻𝗮

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⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⢉⣕⡞⣼⣿⣿⣿⣿⣿⡟⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣳⡀⢻⣤⣴⣴⣶⣶⣶⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⣼⢧⣿⣦⠬⡜⣼⡝⣿⢹⣿⣿⡟⣁⡀⣴⣿⡟⣹⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣗⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢰⣿⢀⣿⢀⠨⢳⣷⢴⣧⣸⣟⡟⠉⢁⡾⠋⣀⡴⢃⡠⣠⣿⣻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⠋⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣾⣧⢸⣻⠀⢩⡏⠀⣸⣯⣿⡿⠒⣲⠟⠘⣩⠿⣠⠏⣴⣿⢯⣟⣹⣄⡿⣿⣿⣿⠏⣿⣿⣿⣧⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠘⢸⡇⣰⣿⠏⣿⣀⡼⠧⢶⣶⣳⡞⢳⠞⣿⣣⠏⠀⢠⣞⣀⣸⣿⣿⠀⢻⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡦⣿⣷⣿⢹⠀⣯⣞⣧⣔⣯⣿⣯⡾⢃⣾⠟⠁⢀⣴⡟⢀⣼⡟⣾⡿⣐⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣸⣿⣧⢹⣾⣴⣿⠋⡇⢸⣸⣿⣿⣿⣿⣿⣿⣯⣶⠟⠋⢀⣴⣫⢏⣴⠟⣽⣿⡟⠀⠈⢹⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢳⠇⣿⣿⣿⣿⢹⡀⠃⢸⡜⣿⢹⣿⣷⣿⣿⡿⣷⠶⠚⠛⢛⡿⠋⣠⣾⣿⣿⣤⣦⣀⢸⡟⣠⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢠⡞⣸⢻⣿⣿⣿⣾⣗⠄⠘⡇⣿⠚⠻⠿⠯⠿⠅⠀⠠⢄⠍⢨⡙⠊⠑⣿⣿⣯⣿⡿⠻⣿⢡⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣾⢣⡟⢸⠀⣿⣿⣷⣿⣦⠀⣷⣹⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠛⠿⠿⡿⣁⣼⣿⡟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢠⣇⣼⣿⣾⠀⣿⣿⣮⡛⢿⣧⣽⡿⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠶⠆⣰⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⡼⣼⣿⡏⡟⣼⣿⣿⣿⡻⣿⠃⣸⡟⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢰⢳⢻⡿⣠⡷⣿⣿⣿⣿⡏⢻⣴⠏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣼⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⡞⡞⣼⣷⢻⡇⣸⣿⣿⣿⡿⡟⠅⣴⣿⡟⢤⣀⠀⠀⠀⠀⠈⢿⡟⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢠⢻⢁⡿⠇⣸⠇⣿⣿⣿⣿⣇⣿⠞⣡⣿⣧⣤⣽⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⡞⣸⠃⢀⣿⢀⣿⣿⣿⣿⣿⢥⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠒⠺⠷⣏⡀⣼⡿⢸⣿⣿⣿⣏⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣯⠀⠀⠀⠀⣀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠻⣿⣿ ⠀⠀⠀⠀⠈⠙⠳⢿⣿⣿⡟⢉⣰⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⢿⣿⣿⣷⣤⠖⠛⠉⠉⠀⠀⢸⡏⠁⠀⠀⠀⠀⠀⠀⣿⣿ ⠀⠀⠀⠀⠤⢄⣀⠀⣨⡿⠟⢋⣿⡿⢯⣶⣝⣛⣛⣿⠿⢿⣿⢥⣠⠼⠻⣿⣟⣿⣿⣿⢿⣿⣿⡋⢤⡀⠀⠻⣌⣉⣻⣦⣀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⢀⣼⡟⠛⣛⣿⡿⠀⠉⢛⣻⣿⠿⠋⠀⢸⢹⠀⠀⠀⠀⠘⣾⣦⠉⠛⠷⢿⣿⣻⣦⡌⠢⡀⠘⣧⣙⡛⣿⣗⡚⠉⠉⠉⡇⠀⠀⢀⣀⣀⣠⣴⣿⣿ ⠀⠀⠀⢀⡤⡶⣿⠋⣽⠛⣿⡿⢁⣤⢶⡋⠉⠁⠀⠀⠀⢸⠾⠆⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠙⠛⣿⣦⡙⣏⠁⠈⣯⣙⠛⢿⣆⠀⣼⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢠⡟⢸⣷⣿⠉⡇⢀⣯⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠻⢿⣟⢧⡤⠶⠛⠋⠉⠻⣿⣽⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣴⣶⣿⣧⣿⢃⠏⠀⡇⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣀⠀⠀⠀⢻⡝⢿⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣟⢿⣯⣎⠤⠔⡇⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢴⣿⣿⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣿⣿⡄⢿⠦⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡉⢿⣻⡄⢻⣿⣿⣿⣿⣿⣿⣿ ⠀⢸⣿⣿⣾⣇⠀⠋⡏⠀⠀⠀⠀⣀⡤⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣭⣻⣎⠀⠹⣵⡟⠙⠛⢿⣿⣿⣿⣿ ⣴⣿⣿⣿⣻⣿⣆⢰⠁⠀⠀⠀⠘⠁⣶⠿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠀⠀⢻⣠⣴⠀⣼⡟⠛⠛⠛ ⣿⣟⠙⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠙⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣾⣿⠁⠀⠀⠀ ⡏⠁⠀⠘⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀ ⣄⠀⢀⡀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣤⣀⠀⠀⠀ ⣿⣷⣌⢿⣷⣍⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠈⠊⣙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⣎⣻⣼⣷⡆⠀ ⣿⣿⣿⣷⣽⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠊⠉⠛⠷⢶⣤⣄⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣷⣿⣿⡿⠿⠃⠀ ⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⡦⢶⣄⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠙⣄⠀⠀ ⣸⣷⣿⣿⣿⢿⣿⣿⣿⣿⣿⡄⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀ ⠿⠿⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳ ⠀⠀⠀⠁⠚⠉⠛⠙⠛⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢹⡟⣿⣿⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⢹⣏⠀⠉⠓⠤⣄⣀⡠⠖⠋⢳⣀⣀⣀⣀⣀⣀⣾⣐⣈⣦⣀⣀⡤⠤⠖⠒⠒⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢸⠇⠸⣿⡄⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠷⠶⠾⡊⠦⣄⣀⡤⠖⠉⠀⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⢧⠟⠀⠀⠙⢧⡵⠀⢀⣀⠠⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤⣤⡴⠛⠉⠙⡆⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠒⠚⠛⠛⠛⠛⠒⠒⠒⠒⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠋⠀⢀⣴⡾⠃⢀⠇⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⣜⠁⢀⣼⠛⠛⠤⣰⣫⠖⠀⡄⢸⡦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠘⢄⢸⢑⡷⢿⡿⢶⣄⠀⢈⠳⡄⣴⡧⢸⡏⠉⠳⡖⠲⠤⠤⢤⣄⣀⣠⡤⠴⠚⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠖⣚⣿⠀⠀⢄⡀⠙⠲⣍⣠⠋⠐⣠⣾⣿⢧⣴⣣⠏⣰⡿⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⠉⠁⠀⠀⠀⠀⠀⠈⢷⡀⠐⠭⣗⡀⡴⢁⢀⣼⣿⠂⠉⠢⣴⣁⡾⠋⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠑⠦⢄⣀⠀⠀⠀⠀⠀⢀⣠⡤⢒⠯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⢄⡀⠙⠧⣴⡋⣠⠟⠒⣤⣠⢀⠝⣄⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠉⠉⠉⢉⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣜⡽⠡⣤⣼⡯⣍⡉⢲⠊⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡰⠟⠋⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢀⡇⡀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⣤⢞⡞⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡉⡏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡍⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀