Kawaii ASCII Art

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠱⠊⡱⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠒⠒⠤⢄⣑⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢰⣢⠐⡄⠀⠉⠑⠒⠒⠒⣄ ⠀⠀⠀⣀⠴⠋⠀⠀⠀⡎⠀⠘⠿⠀⠀⢠⣀⢄⡢⠉⣔⣲⢸⠀⠀⠀⠀⠀⠀⢘ ⡠⠒⠉⠀⠀⠀⠀⠀⡰⢅⠫⠭⠝⠀⠀⠀⠀⠀⠀⢀⣀⣤⡋⠙⠢⢄⣀⣀⡠⠊ ⢇⠀⠀⠀⠀⠀⢀⠜⠁⠀⠉⡕⠒⠒⠒⠒⠒⠛⠉⠹⡄⣀⠘⡄⠀⠀⠀⠀⠀⠀ ⠀⠑⠂⠤⠔⠒⠁⠀⠀⡎⠱⡃⠀⠀⡄⠀⠄⠀⠀⠠⠟⠉⡷⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠤⠴⣄⡸⠤⣄⠴⠤⠴⠄⠼⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢂⠀⠀⢱⠀⠂⠁⠉⡆⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠂⠀⠀⠀⠀⠐⠀⠀⠈⠀⠀⠀⡄⠃⠀⠀⠀⠀⠀⠀⠨⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢂⠀⠀⠀⠀⠀⠠⠀⢀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⢃⠀⠀⠀⣀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⡁⠀⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠳⠀⠁⠀⠀⠀⠀⠈⠑⢆⡀⠀⠀⡎⠀⠀⠀⠀⠀⠄⠀⡅⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⠔⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠠⠠⠒⠒⢄⠀⠀⠀ ⠀⠀⠇⡀⡀⠀⡀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀ ⠀⡠⠂⠂⠁⠁⠀⠀⠀⠀⠀⠀⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠌⣁⠀⠀⠀ ⡋⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄ ⠈⠢⠀⣤⠤⠄⠉⠀⠀⡐⠂⢀⠄⠀⠀⢆⠀⠀⡶⡄⠀⣀⠀⠀⠀⠀⠧⠀⠈⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜ ⡠⠊⠁⠀⠀⠀⠀⠀⠀⠁⠀⠰⠁⠀⠀⠀⠑⠜⠁⠘⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠪⡈⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀ ⠈⠁⠄⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠂⠢⠠⠄⠄⠄⠂⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠁⠀⠀⠉⠙⢦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢀⣴⣶⣶⣄⠀⠀⢳⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣾⣿⢯⣟⣿⡇⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁⠀⢀⣸⣿⣿⡯⠟⠀⠀⡸⠃⠀⠀ ⠀⢀⠤⠒⠙⠋⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⢀⣤⣶⣿⣿⣻⣽⣷⠀⠀⢴⠁⠀⠀⠀ ⠄⠀⠀⢀⣤⣤⣀⠀⠀⢳⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠁⠀⢀⣤⣾⣿⣟⣯⣷⢿⣽⡾⣿⡄⠀⠸⡇⠀⠀⠀ ⠀⠀⢰⣿⣿⣻⢿⣆⠀⠀⠀⠀⠉⠉⠉⠁⠑⠒⠒⠒⠠⠦⠤⠤⢠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡴⠁⠀⢀⣤⣾⣿⣟⡿⣾⣽⣳⣯⣿⣞⣿⣽⣧⠀⠀⢷⠀⠀⠀ ⠀⠀⠸⣿⣧⢿⣿⣿⣤⣤⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⣀⣠⠤⠟⠛⠛⠀⠀⠀⠀⠀⣿⣿⢿⣼⣻⢿⣧⢿⣻⣧⢿⣼⢿⣼⣿⠀⠀⢸⡀⠀⠀ ⢣⡀⠀⠉⠛⠛⠙⣿⣿⣻⣟⣿⣻⢿⡿⣿⢿⣿⣿⣿⣷⣶⣶⣶⣶⣤⡄⠀⠈⠧⠔⠚⠉⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣼⣿⣯⣿⣽⣿⢾⣟⡿⣾⣻⣽⢿⣞⣿⡇⠀⠘⣇⠀⠀ ⠀⠙⠢⢤⡀⣀⠀⠈⢿⣷⡿⣞⡿⣯⣿⡽⣿⣞⣷⣻⣾⡽⣯⢿⣽⣻⣿⡄⠀⠀⠀⣀⣤⣴⣾⣿⡿⣿⣻⣟⣿⠟⠋⠉⠉⠉⠉⠉⠛⢿⣿⣿⣿⣽⣟⣾⢿⣽⣾⣷⠀⠀⢻⠀⠀ ⠀⠀⠀⠀⠀⠙⢦⠀⠀⠻⣿⢿⣽⣟⡾⣟⣷⣯⣟⣷⣯⢿⣻⣯⣷⢿⡽⣿⣤⣶⣿⡿⣟⣿⣽⢾⣻⡷⣿⣽⠃⠀⣀⡀⠀⠀⠀⣀⡀⠀⢻⣷⣟⡿⣿⣿⣿⣞⣷⠟⠀⠀⣸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠙⣿⣷⣻⣟⣯⣷⣟⣾⣟⣾⣟⡿⣾⣽⣻⣿⣿⣟⣯⣷⢿⣻⡷⣯⣿⢯⡿⣷⣻⣧⡘⠿⠃⠀⠀⠀⠻⠟⣠⣿⣟⣾⢿⣽⢯⣿⣯⡁⠀⠀⢾⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠈⢻⣷⡿⣽⣾⣻⣾⣽⢾⣯⢿⣷⣿⣿⣻⣾⡽⣷⣻⢿⣽⣻⣽⡾⠟⠛⠿⢷⣿⣻⣶⣆⣰⣆⣆⣰⣾⣿⣿⠾⢿⣿⣾⣻⢷⣻⣿⣆⠀⠀⠳⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠹⣿⣟⣾⢷⣻⡾⣿⣽⣻⣿⣟⣾⢷⣯⣿⣽⣻⣯⣿⠟⠁⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣽⣟⡿⠟⠋⠀⠀⠀⠈⠙⢿⣿⣻⢾⣿⣧⠀⠀⢱⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠘⢿⣯⡿⣯⢿⣳⣿⣿⣟⣾⢯⣿⣞⣷⣯⣷⠟⠁⣠⣴⣶⣦⣀⡴⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⢀⣶⠟⠻⣶⣟⣿⣿⣞⣿⣇⠀⠀⢃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠈⢻⣿⣽⣟⣯⣿⡿⣞⣯⣿⣳⣯⣷⡟⠁⠀⣼⣿⣇⠀⣸⣿⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣤⣿⣿⡄⠻⣿⣞⣿⡄⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠉⠉⠉⢹⣿⣟⡿⣽⡾⣯⣷⠏⠀⠀⠠⣿⠋⢹⣿⠟⢿⣿⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⢿⣅⣨⣿⣄⣽⡇⠀⢻⣿⣻⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⢴⠀⠀⢸⣿⢾⣟⣯⡿⣷⡟⠀⠀⠀⠀⢿⣷⣾⣿⣷⣿⠏⠀⠀⠀⠀⠀⠀⢯⣄⣬⠇⠀⠀⠈⠻⣿⣿⣿⠟⠀⠀⠈⣿⣟⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢸⣿⣟⣾⢯⣿⣽⡇⠀⠀⠀⠀⠀⠙⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⣼⢰⠇⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠘⣿⣻⡾⣟⣷⣿⡇⠀⠀⡼⢰⠃⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠐⠃⠋⠀⣿⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢻⣿⣽⣟⡷⣯⣿⡀⠘⠁⠋⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⢀⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⢻⣷⣻⢿⣽⣻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⢠⡎⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠙⢿⣯⣟⣷⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠓⢶⡚⠙⠓⢦⡀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠙⢄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⠙⣿⣾⣿⡞⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢳⠀⠀⠀⢳⠀⢠⣴⡞⠉⠀⢠⡞⠉⢳⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⠄⠀⠀⠉⠛⠿⠷⣯⣿⣿⣷⣦⣤⣀⣀⣀⣀⣹⡀⠀⠀⠀⠀⣸⠀⠀⠀⣾⣿⡿⣿⢿⣿⣷⣾⣇⠀⣠⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢀⡴⠒⢲⣄⣤⣤⣶⣿⢿⡿⣿⡿⣿⢿⣿⠋⠛⠀⠀⠀⣰⡏⠀⠀⠚⠙⢿⣿⣿⣟⠛⠉⢀⣈⡉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠘⣇⣀⣠⠟⠛⠿⠿⠾⠿⢿⣷⡿⣯⣿⠃⠀⠀⠀⠀⣸⠃⠹⡄⠀⠀⠀⠀⢹⣿⣿⣿⣷⠋⠉⠹⡆⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠉⠁⠀⠀⠀⢀⣀⣠⣾⣿⣽⣿⣯⠀⠀⠀⠀⣠⠏⠀⠀⠳⡄⠀⠀⠀⠀⡇⠀⠀⠉⠳⠤⠞⠁⠀⢰⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠒⠖⣨⠀⠀⣞⠁⠀⢻⠉⠁⠀⠈⠳⠤⠤⠞⠁⠀⢀⡀⠀⠙⠲⠤⠴⠞⠁⠀⣠⣀⠀⠀⠀⣀⠴⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠙⠲⠖⠋⠀⢀⡦⡀⡀⠀⠀⢀⣠⠔⠋⠑⠢⣄⡀⠀⠀⣀⣠⠖⠁⠀⠉⠁⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⣀⢀⣀⠤⠊⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
pls note the ai inflicts emotional damage (ᵕ—ᴗ—)
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へ ♡ ╱|、 ૮ - ՛ ) (` - 7 / ⁻ ៸| |、⁻〵 乀 (ˍ, ل ل じしˍ,)ノ
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠻⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⢸⡿⣿⠇⠰⠟⠀⠀ ⠀⠀⠀⠀⣀⡤⣤⠶⠛⠉⠉⠀⠀⠉⠉⠛⠲⣤⣤⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⡼⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⢧⠀⠀⠀⠀ ⠀⠀⡼⢁⡆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢰⡈⢧⠀⠀⠀ ⢀⡞⠁⣸⠁⠀⢠⠬⠓⠀⣀⠀⠀⢀⠀⠛⠥⣄⠀⠀⡇⠈⢳⡀⠀ ⡞⠀⠀⠹⣆⠀⠀⠆⠀⠀⠓⠊⠙⠚⠁⠀⠀⠀⠀⣰⠇⠀⠀⢻⠀ ⣇⠀⠀⠀⠈⣹⠶⠦⠤⠤⣤⣤⣤⡤⠤⠤⠴⠶⣏⠁⠀⠀⠀⣸⠁ ⠈⠓⠲⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠶⠚⠁⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⠟⢿⣿⣿⣛⣛⣛⠛⠿⣿⣯⠈⣈⣤⡤⠤⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⠟⢿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡿⢀⣿⣿⣿ ⣿⣿⣿⣿⡁⢨⣤⣴⣿⣿⣿⠉⣿⣿⣿⣿⡄⢸⣿⡇⢉⣁⣀⠐⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠻⣿⠁⣄⠙⢿⡗⢸⣿⣿⣶⡌⢻⡟⢀⣿⣿⠏⠀⢿⣿⣿⠇⢸⣿⣿⣿ ⣿⣿⣿⣿⡇⠸⣿⠿⢿⣿⣿⠐⣿⣿⣿⣿⠃⣼⣿⣿⠈⣿⣿⣿⣿⣦⡌⢿⣿⣿⣿⣿⣿⣿⣿⣤⣉⣴⣿⡇⢸⣿⠘⣿⣿⣿⠇⢸⡇⢘⡿⢁⣴⡀⣾⣿⣿⣷⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡄⢲⣶⣾⣿⣿⣦⣭⣉⣉⣩⣼⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠏⣸⣿⣦⣙⣛⣉⣴⣿⣷⣈⣠⣾⣿⡀⢿⣿⣿⠛⠛⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣈⣀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡟⡃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⣿⣿ ⠃⣤⣌⠙⠻⢏⣴⡇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣴⡍⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⣴⣿⣧⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢠⠙⣿⣿⡿⢋⡴⢋⣾⣿⣿ ⣦⠙⢿⣿⣷⣿⣿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⣿⣿⣦⡈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣠⣿⣿⣿⣿⣦⠘⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⣧⡈⠛⢡⠎⣰⣿⣿⣿⣿ ⣿⣷⣦⣉⠛⣿⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣾⣿⣿⣿⣿⣦⢸⠻⠿⠿⠿⠿⠿⠿⠇⢰⣿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣦⠙⣷⡾⢃⣾⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣯⣼⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠹⢣⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⣛⠻⢋⣵⠀⣿⣿⣿⠇⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡂⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣷⣿⢋⣾⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠻⢿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡟⢿⣿⣿⣿⣧⡈⠛⣡⣿⣿⣿⣿⣿⣿⠎⣻⣿⣿⡇⠀⠀⢹⣿⣿⣿⣿⢿⣿⣿⣿⣿⡁⠄⢀⣿⣿⣿⣿⡿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡍⣛⠋⠀⢰⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣏⣉⣉⠀⣹⣿⣿⡿⠷⣶⣿⣿⣿⠟⢀⡉⢿⣿⣿⣿⣿⣿⡿⢿⠟⠛⣻⣇⢠⣬⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡄⠟⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢀⡿⠑⣋⡄⣼⣿⣿⣿⣯⣴⣿⣿⣤⣽⣿⣿⣿⣿⣀⣴⣮⣤⣾⠇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣠⠈⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣍⣙⡉⢹⣿⣿⡿⠿⣿⣿⣿⡿⣡⠂⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⠙⡿⠉⠀⣿⣿⣿⣿⣷⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣼⣿⣿⣿⣿⣿⣿⠀⣶⣄⢙⢋⣼⢏⣼⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⠁⣌⠙⠛⠇⠸⠁⠀⣰⢡⣿⣿⣿⣿⣿⣿⣷⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢿⣿⣿⣿⣿⣿⣧⠈⢿⣿⣿⢇⣼⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡆⢻⡇⠐⠀⠀⠀⢠⠃⣾⣿⣿⣿⣿⠋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠻⣿⣿⣿⣿⣿⣷⣤⡙⢋⣼⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡌⠁⢀⡆⠀⠀⡎⣼⣿⣿⣿⠿⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠘⢿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣦⡘⠃⠀⡸⣰⣿⣿⡟⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿ ⣿⣿⣿⣿⣿⣿⠛⢿⣦⣄⢡⣿⡿⠏⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠘⢿⣿⣿⣿⣿⣿⠿⠻⠿⠿⠟⣡⡆ ⣿⣿⣿⣿⣿⣿⣆⠀⡙⠿⠀⡿⢁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠻⣿⣿⣿⣧⠐⣿⣶⣶⣾⡿⣸ ⣿⣿⣿⣿⣿⣿⣿⣧⡊⢷⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⠿⣿⣿⣧⡌⠻⠿⢿⢡⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⠀⢿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠙⣿⣿⣿⣷⣶⣾⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⢁⣼⣃⢿⣿⣿⣿⣿⢉⣠⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⣍⡙⠻⣿⣿⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠃⣼⣿⣗⢸⣿⠟⠁⣨⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢺⣿⣿⣦⣉⠻⣿⣿⣿⣿⠞⢉⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢂⠹⢿⣿⡈⢏⣴⣾⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣶⣄⣁⣠⣤⣴⣾⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣶⣶⣬⣩⣥⠾⣿⣿⣿⣿⣿⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
/ᐢ⑅ᐢ\ ♡ ₊˚ ꒰ ˶• ༝ •˶꒱ ♡‧₊˚ ♡ ./づ~ :¨·.·¨: ₊˚ `·..·‘ ₊˚ ♡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⠤⣦⢴⠟⠋⠁⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⣀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⠀⠀⠀⠀⠀⢴⣾⡙⣻⡷⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠘⢿⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠆⠀⠀⢰⣿⣦⠤⠔⠀⢹⣧⣀⣀⠀⠀⠀⠈⠀⡀⠀⠀⠀ ⠀⠀⣸⣆⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⣀⡀⠀⠀⠀⠀⠾⠂⠀⠀⠀⢻⡏⠀⠀⢾⡛⠻⣯⣉⠁⠀⠀⠀⢀⡿⣤⣀⡀ ⠠⣴⣟⣻⡷⢶⠀⠀⠀⣾⠀⠀⠀⢰⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠠⠀⠈⠛⠛⠛⣿⠛⠂⠀⠐⠻⣷⣼⠟⠉ ⠀⠀⠹⡿⠀⠀⠀⠀⠀⣿⣠⣀⣒⠀⢋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠔⠀⠀⠀⠀⠈⠋⠀⠀ ⠀⣠⠀⠀⠀⠀⠀⢀⣤⣿⠟⣿⡉⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⡿⢶⣤⡀⠀⠘⠟⢁⣿⡞⠛⠉⠀⠀⠀⠀⠀⠀⠀⣰⣤⣤⡶⠤⣤⣄⠀⠀⠀⠀⠺⣧⡀⠀⠀⣴⠟⢿⡆⠀⠀⠀ ⠛⢷⣾⠋⠀⠀⠀⠀⣾⠛⢷⣤⣀⡀⠀⠀⠀⠀⠀⣼⠋⡁⢻⡀⢀⠀⠉⠀⠀⠀⠀⠀⠈⢻⣤⠀⣿⠐⢸⡇⠀⠀⠀ ⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣷⠄⠀⠀⠀⠁⠀⢀⣸⡷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡏⠀⣾⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣼⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣤⣶⣾⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠻⢷⣶⣦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⣿⠟⠃⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣀⡀⠀⠀⠘⠻⣧⡀⠀⠀⠀⠀ ⠀⠀⢀⣾⡟⠁⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣦⡀⠀⠘⣷⣄⠀⠀⠀ ⠀⠀⢸⣿⠁⠀⢰⡿⠃⣄⠘⢿⣿⣿⣿⣿⣿⠃⢠⡀⠈⢿⣿⡄⠀⠘⣿⡀⠀⠀ ⠀⠀⢸⣿⡤⢶⣿⠃⣼⣿⣷⣄⠙⣿⣿⣿⠃⢠⣿⣿⣦⡀⠹⣷⠶⠶⣿⣧⡀⠀ ⠀⣴⡟⠁⠀⣸⠃⣸⣿⣿⣿⣿⣧⣄⣀⣀⣀⣾⣿⣿⣿⣿⡆⢻⡄⠀⠀⠙⣿⡄ ⢰⣿⠃⠀⢀⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⣧⠀⠀⠀⢹⡇ ⢸⣿⠀⠀⢨⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡀⠀⠀⠈⡿ ⢸⣿⡀⠀⠸⡇⢸⣿⠋⠉⠹⣿⣿⣿⣿⣿⣿⣿⡿⠉⠈⠹⣿⠇⢸⡇⠀⢀⣼⡏ ⠀⠻⣷⣤⣀⣷⠀⢿⣄⣀⣴⣿⡟⢻⡿⢿⡟⢻⣿⣤⣤⣼⠟⢀⣿⣧⣴⠿⠋⠀ ⠀⠀⠀⠙⠛⢻⣷⠀⠙⢻⣿⣿⣿⣬⣴⣶⣤⣾⣿⣿⡟⠁⢠⣿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠷⣦⣤⣄⣉⣉⠋⠙⠋⠙⠋⣉⣁⣠⣴⠿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠘⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⢀⡾⠁⢠⠖⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣁⠀⣾⠃⠀⠨⠄⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠉⠁⠀⠉⠳⡀⠀⢀⣀⣀⣀⣀⣀⡀ ⠀⠀⠀⠀⠀⢠⠮⣉⡿⠀⠀⠀⠀⠀⠀⣽⠟⣋⠥⠒⠛⢶⣤⡽ ⠀⠀⠀⠀⠀⠸⡂⢰⣰⡂⠀⠀⠀⠀⠀⠀⢙⣧⣦⣔⡾⠟⠋⠀ ⠀⣀⡐⢢⠀⠀⠘⡬⠒⠂⡄⢿⡿⠀⠀⢀⡽⠃⠀⠀⠀⠀⠀⠀ ⠘⢦⣁⢸⠀⠀⢠⠞⠀⣄⣙⣒⣀⣤⡴⣿⡁⠀⠀⢀⡀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠘⣻⣧⠀⢰⠃⠼⢄⠀⠀ ⠀⠀⠀⠀⠀⢀⡷⠠⠞⠃⠀⠀⠀⠐⠒⠦⢿⡀⠑⠒⠂⠋⠀⠀ ⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢹⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⢾⠟⠉⢷⡀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⢸⡵⢀⣟⣸⣇⡼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠓⠒⠒⠒⠚⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠃⣈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⣀⡀⠙⠞⠁⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⡏⢻⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡐⡄⣸⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣿⠀⠀⠀⠀⠀ ⠀⠀⣀⠠⢝⡜⣿⣿⡟⢉⣭⡝⢿⣿⣿⣿⡟⣭⣭⠉⢻⣿⡿⡠⠒⠀⠀⠀ ⡴⣟⣿⣻⣆⢰⣿⣿⠀⢸⣿⣿⢸⣿⣿⣿⠙⣿⣿⠇⠈⣿⣿⠱⠭⠄⠀⠀ ⢷⣿⡀⣸⣿⡞⣿⣿⣄⠀⠉⠁⣼⣿⢿⣿⣧⠈⠁⠀⣰⣿⣿⣠⣴⣶⣦⣄ ⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠒⠓⠒⠛⠛⠛⠛⠛⠛⠓⠻⡏⣿⣿⠿ 🔥🧸😉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣽⡿⠿⠿⠿⢯⣿⣿⣿⣿⣿⡿⠿⠟⣛⣛⣛⣛⠻⠿⠿⠛⠛⣛⡛⣛⡻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⣀⣤⣤⠤⠄⠈⠛⣿⣿⠃⣶⣿⣿⣿⣿⣻⣷⡾⢟⣻⣿⣿⣿⣿⣿⣿⣷⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⠆⢸⣿⡇⢿⣿⣿⣿⣿⣟⣫⣶⣾⣿⣿⣿⣿⡿⠿⠛⠛⣿⡈⠻⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣀⣴⣄⠛⠿⣿ ⣿⣿⣿⣿⣿⡿⠋⠁⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢰⡜⣿⣿⠸⡿⣿⣭⣿⣿⠿⣩⣾⣿⡿⠟⠉⠐⣲⣿⣿⣿⣿⣷⣦⡙⢿⣿⢿⣿⣿⣿⣦⡐⢾⣿⣿⣿⣿⣿⠂⢀ ⣿⣿⣿⠟⡁⢀⣠⣾⣿⣿⣿⡿⢟⣩⣿⣿⣿⡿⠋⠀⢀⡛⣰⣿⠋⠀⣰⣿⣿⡿⣣⣾⣿⡿⢋⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠙⠿⠿⠿⣿⣿⣷⡄⢿⣿⣿⣿⣿⢠⣿ ⣿⣿⣷⣊⣴⣿⣿⣿⣿⡿⢋⣤⣿⣿⣿⡿⢋⡠⠂⣰⠸⣇⣿⠇⠀⢸⣿⡿⢋⣴⣿⡿⢁⣶⣿⣿⡿⢛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠙⣿⣷⣌⢻⣿⡇⠟⣛⣛⣛⠻⢸⣿ ⣿⣿⣿⣿⣿⣿⣿⠟⣩⣶⣿⣿⣿⡿⠋⣤⠞⢀⡄⡏⠀⠀⠠⠤⠀⠛⢛⣀⣺⣿⠋⣴⣿⣿⠿⢋⡵⢋⣽⣿⣿⡟⣻⣿⠿⣿⣿⡏⣿⣦⡈⣿⣿⣦⢙⡒⣿⣿⣿⣿⣿⣾⣿ ⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⠞⢁⢠⡟⢰⠀⢠⡖⣰⣿⣿⠐⣰⣶⡿⢡⣾⠿⢋⡡⢚⣡⣶⣿⣿⡿⢋⣼⡿⢁⣼⣿⣿⡇⣿⣿⣿⡘⣿⣿⣆⠻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⣠⡎⠀⢸⡟⠃⡞⠀⣾⢁⣿⣿⡟⢀⣹⡿⠶⢛⣡⠞⣁⣴⣿⣿⡿⠟⣋⣴⡿⢋⣴⣿⣿⣿⣿⢇⡏⣿⣿⣷⠸⣿⣿⣆⠨⣙⠻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡟⢋⠔⢠⣾⣿⡇⣰⢸⡇⣸⠃⢼⡇⣸⣿⡯⢐⣿⡏⣤⣴⠟⣃⣴⣿⡿⠟⢋⣤⣶⣿⠋⣴⣿⣿⣿⡿⢩⡏⣸⣿⣿⣿⣿⡇⢿⣿⣿⡀⢹⠗⣸⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡾⢃⣾⣿⣿⣿⡇⣿⠸⢠⡇⢀⣴⢠⣿⣿⠇⠾⠟⠐⠟⠡⠾⣿⣿⣿⣵⣺⣿⣿⣟⣱⣾⣿⢟⣿⡟⢱⡿⢰⣿⣿⣿⣿⣿⣿⢸⣿⣿⡇⠀⣾⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⢋⣴⣿⣿⣿⣿⣿⡇⠈⢀⡞⢠⣞⠁⢸⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣷⡿⠿⣋⣠⣾⡟⠰⢿⠇⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⡟⢸⡿⢸⣿⣿⣿ ⣿⣿⣿⣿⣫⣴⣿⣿⣿⣿⣿⣿⣿⣷⠀⡜⠀⣿⣿⠐⠸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⣀⣽⣷⣶⣴⠞⣡⣾⠏⢀⣴⡷⢀⣿⢃⣿⢿⣿⡿⢻⡿⢿⣿⣷⠹⢁⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡏⠋⢩⣿⣿⣾⣯⣄⠀⠀⢹⠃⣰⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣭⣿⣯⣥⣾⡟⠁⣠⣾⡿⢣⣿⠃⣼⡿⢸⣿⡇⣸⡷⣼⣿⣿⡇⢿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡆⠎⢿⣿⣿⣿⣿⣷⡀⢸⠈⠻⠀⢿⣿⠀⡙⠡⠀⣀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡿⣋⡴⠯⠽⠿⢁⣾⠃⡸⢻⢁⣿⣿⢡⣿⠇⣿⣿⢻⡇⠈⠻⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⡌⣿⣿⣿⣿⣿⣿⡈⠀⠀⢠⢸⣿⡄⣼⣶⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢸⠏⡼⢣⠇⣸⣿⠃⣜⡿⠀⣿⡇⡈⣹⣦⡐⠛⢿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⡇⢳⣄⠀⠘⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢐⣾⠀⣀⡜⣡⠃⣴⡿⠃⣼⣿⢇⠁⣿⡇⡇⣿⣿⣿⣦⠀⣻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⣥⣶⣦⡍⠙⠻⣁⣴⣶⡶⠀⠙⢷⠀⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⡇⠂⠀⢀⣾⣷⣿⠋⡰⢃⣾⡟⠁⢰⣿⠏⣼⠀⣟⡇⢡⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣠⡀⢌⠉⡻⢴⣿⠀⡌⢧⢻⣿⣿⡏⣤⣶⠄⣹⣿⣿⣿⣷⣈⣠⡾⣿⣿⣿⠞⣡⣿⡟⠠⢠⣿⠏⣼⡇⡸⣸⠁⣸⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢢⠙⣦⠹⣧⣼⣄⠺⣿⣿⣇⣋⣵⣾⣿⣿⣿⣿⣿⣿⠟⣰⣿⡿⠁⣨⣽⠟⣰⣴⡿⢫⣾⡟⠀⣰⡏⢠⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢢⢹⣷⡙⢿⡟⠗⣈⠻⣿⣿⣿⣿⠿⠿⠛⢛⣋⣥⡾⠟⣩⣴⣿⠟⣡⣾⣿⢋⣴⣿⣿⠁⣴⣿⢃⣾⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⡇⢻⣿⣌⢻⣄⡛⠷⡘⠿⣿⣿⣿⣿⣿⣿⣋⣵⣾⣿⣿⡟⣡⢾⡿⢋⣴⣿⣿⡿⢃⣾⣿⠟⣼⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢻⡈⣿⣿⣦⡙⢿⣷⡸⣷⣬⡙⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣁⣤⣾⣿⣿⣿⠟⣱⣿⣿⡟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢸⣇⡙⠻⣿⣷⡈⢿⣧⠘⣿⣿⠐⡜⣯⣍⡛⢿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣞⢿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣿⣿⣿⣆⠀⢈⣙⠳⠶⢍⡛⠦⠹⡇⣿⣿⣧⢡⠸⣿⣿⣦⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣦⣬⣤⣶⡂⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⣿⠀⢸⣿⡿⠷⠦⠤⠑⠠⠀⠙⠿⠿⠎⢃⢻⣿⣿⣷⣌⠻⣿⣿⣿⣿⣿⣿⣿⡟⢠⣿⣿⣿⣿⣧⡙⢿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡿⠀⠈⣿⣷⡆⠀⠒⠂⠀⠀⡌⠉⠩⣀⡚⠺⣿⣿⣿⣿⣧⡱⣯⣝⠻⢿⣿⡟⠀⠾⢿⣿⣿⡿⠟⣋⣤⣽⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣷⡈⢛⠛⠻⠿⢿⣿⣿⣿⣇⡿⢋⣴⣿⡆⠃⣿⣷⣼⣿⣿⠟⠀⠀⢀⠀⢺⣷⣦⣀⠙⣿⣿⣿⣿⣿⣿⣿⣶⡙⣿⣿⣿⣶⡈⠋⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣄⠫⣍⣛⡲⢤⣉⠻⡇⢰⣿⣿⣿⣇⠀⣿⣿⣿⠟⠁⠀⠀⠀⠘⣷⣤⣿⣿⡇⢀⣼⣿⣿⣿⣿⣿⣿⣿⢣⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡙⣿⣿⡆⣈⠳⡀⠸⣿⣿⣿⡏⠀⠙⠛⠛⠀⠀⠀⠀⡀⠠⠘⣿⣿⣿⠀⢿⣿⣿⡿⠟⣩⣿⣿⡟⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⣿⡇⣿⠷⠃⣠⡈⠻⣿⣿⢂⡀⠀⠀⣤⡄⠀⠂⣧⠀⠀⢸⣿⡇⢸⡈⣿⢏⣴⣾⣿⣿⣿⣿⣮⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⣀⣴⣆⠘⢿⢆⠁⢿⡈⢁⡏⢘⡇⠁⠘⢄⠙⢧⠀⠀⣉⠀⠸⠋⢃⣾⣿⣿⣿⠟⣋⣥⣶⡂⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠁⣿⣿⣿⣷⣀⣠⣐⣦⣙⣿⣧⠘⣿⡀⢠⣈⣷⣄⠀⠀⠈⠳⢄⠀⢿⣿⠿⢛⣡⢾⣿⣿⣿⣿⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀ ⢸⡤⠚⠁⠀⠲⣤⡏⠀⣖⠒⠋⠀⠀ ⢸⠙⣄⡀⠀⣠⠍⠁⠀⠈⠉⠳⡄⠀ ⠀⠀⠀⠉⠐⠎⠀⠀⠀⠰⠤⠤⠴⠃
bunny rabbit comp credits too the people who made them! ⚠️none if these are mine! {\__/} ( • w •) / > 🍬 ʏᴏᴜ ᴡᴀɴᴛ ɪᴛ? {\_/} ( • ^ •) 🍬< \ ɢᴇᴛ ɪɴ ᴛʜᴇ ᴠᴀɴ. ______________________ ♡ ☆ .♡‧₊˚ ☆ .♡ ‧₊ ♡‧₊ ☆ .♡˚ ╭◜◝ ͡ ◜◝╮ ㅤ ╭◜◝ ͡ ◜◝╮. ( ) ♡ ( )☆ ♡ ╰◟◞ ͜ ◟◞╭◜◝ ͡ ◜◝╮ ͜ ◟◞╯♡ . ☆ ㅤㅤ( )☆ ♡ ♡   ╰◟◞ ͜ ◟◞╯ ♡ (\_(\ /)_/) ( ) ( ) ૮/ʚɞ |ა ૮| ʚɞ\ა ( ◌ | | ◌ ) _________________________ ૮₍ ˶ᵔ ᵕ ᵔ˶ ₎ა (˶ᵔ ᵕ ᵔ˶) ૮₍˶ •. •⑅₎ა♡ ૮ • ﻌ - ა⁩ (>﹏<) (˶˃ ᵕ ˂˶) ฅ՞•ﻌ•՞ฅ ૮꒰ ˶• ༝ •˶꒱ა ૮₍ ˶•⤙•˶ ₎ა ૮₍´˶• . • ⑅ ₎ა♡ ฅ^•ﻌ•^ฅ ૮ ˶ᵔ ᵕ ᵔ˶ ა‧ ૮꒰⸝⸝> ̫ <⸝⸝꒱ა☆⋆。 °‧★ᶻ 𝗓 𐰁( 。 •̀ ᴖ •́ 。) ૮₍ ˶ᵔ ᵕ ᵔ˶ ₎ა ૮₍ ˃ ⤙ ˂ ₎ა ૮꒰ ˶• ༝ •˶꒱ა ♡ ૮ ˙Ⱉ˙ ა rawr! ≽^•⩊•^≼˚ /ᐠ - ˕ -マ (,,>﹏<,,)૮ ◞ ﻌ ◟ ა ૮ • ﻌ - ა⁩ ( ꩜ ᯅ ꩜;) ฅ՞•ﻌ•՞ฅ ૮₍˃̵֊ ˂̵ ₎ა ٩(ˊᗜˋ*)و ♡૮ • ﻌ - ა ₍ᐢ. ̫.ᐢ₎ ૮₍ ´• ˕ •` ₎აა ____________________ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⣄⣴⡾⠟⠿⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣾⠋⣀⣤⣴⣿⣿⣶⣶⣶⣤⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠋⣉⣿⣿⡿⠿⠛⠋⢉⠉⡥⣉⠙⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡶⢶⣤⣴⡿⠛⠛⠻⢷⣄⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣸⣿⣴⣾⠿⠋⠁⠀⠀⠀⠀⢼⡙⠶⠌⣇⠀⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣁⣤⣴⣾⣿⣷⣶⣶⣶⣾⣿⣭⣀⡀⠙⢿⣄⣀⣤⣠⣤⣤⣤⣤⣤⣤⣴⣤⣴⡾⠋⣉⣿⡿⠋⢠⣄⣀⠀⠀⠀⠀⠀⠚⣤⢠⡸⡝⠀⢸⣿⣷⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠋⠉⠁⣡⢌⡁⠉⠉⠉⠛⠛⠿⢿⣿⣿⣍⠉⠙⢻⣿⡟⣿⢻⣟⡿⡿⣿⣧⣼⡿⠋⢔⢋⡇⠌⢳⣠⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⢺⣿⣿⢻⡿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢀⡿⢀⠉⣘⢆⠀⠀⠀⠀⠀⠀⣈⡙⡿⣿⣶⣤⣿⣽⣾⠿⠿⠿⢿⣿⣿⠋⠀⠀⠘⣮⡑⣦⠜⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣯⢳⡝⣮⢽⣹⢻⢿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⠀⠀⠀⠀⢙⡖⠚⢦⠋⠀⠀⠀⠀⠀⣘⢡⡞⠀⢹⠩⣿⣿⠏⠀⠀⠀⠀⠀⠹⣿⣷⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠀⢼⣿⣯⢳⡝⣮⢳⣭⣛⡞⣶⣹⢻⢿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣇⠀⠀⠀⠀⠉⠉⠈⠁⠀⠀⠀⠀⠀⠠⢏⡼⣰⠎⠋⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⣶⣶⣾⣷⣶⣶⣄⠀⠀⠀⠀⠰⡉⣀⠃⠀⠀⢸⣿⣯⢷⡹⣎⠷⣎⢷⡹⢶⣭⣛⠾⣜⡻⢿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡟⣯⡝⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣿⣿⠀⠀⢠⠐⠂⡄⠀⢸⣿⡟⠛⠉⠉⠁⠉⠉⠁⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⣿⣿⣷⡹⣞⡽⣚⢧⣛⠷⣮⣝⡻⣼⡹⣏⢾⣻⢿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣟⡻⢶⡹⢶⡹⡽⣿⣷⠀⠀⠀⠀⢀⠆⢒⡀⠀⠀⠀⣴⡿⠟⠛⠋⠙⠉⠻⣿⣧⠀⠰⣘⠲⠈⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣳⡝⡾⣭⢳⣏⡟⡶⣭⢳⢧⡻⣜⢧⣛⢮⣛⠿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⡿⣏⠷⣮⡝⣧⣛⢧⡻⣵⣻⣿⡇⠀⠀⠀⠐⠢⡍⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⣄⠀⠀⣀⣴⣿⡟⠀⠀⠀⠀⢰⡲⠉⣓⢲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣏⠷⣭⢳⢮⣝⡳⣭⣛⢮⡳⣝⡮⣝⡮⣝⡻⢶⣹⢻⢿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣾⣿⡿⣏⠷⣭⣛⢶⡹⣖⢯⡳⣝⠶⣽⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⢨⣿⣿⣿⣿⡿⣿⣿⣿⣦⣀⠀⠀⠱⣦⡀⡜⢋⡜⠀⠀⠀⠀⠀⡔⢂⡆⠀⠀⠀⢹⣿⣯⢻⡜⣯⢞⡼⣳⢧⣛⢮⢷⡹⣞⡵⣻⢼⡹⢧⣏⡟⣮⣝⡻⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⣿⣿⡹⣎⡟⣶⡹⣎⢷⡹⣎⠷⣭⣛⢾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢋⠼⣮⣿⡟⢹⣷⣣⢟⡼⣿⡌⠛⢿⣷⣦⣀⡁⠉⠉⠃⠀⠀⠀⠀⠀⠀⠰⠤⠙⠀⠀⢀⣾⣿⢿⣷⡻⣜⢯⡞⣵⢫⡞⡽⣎⢷⡹⣞⡵⣫⣝⡳⢮⣝⠶⣭⢳⢧⣛⢿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣟⠶⣝⡮⣝⡶⣽⡹⣎⢷⣹⣛⠶⣭⢿⣿⣿⣤⠀⠀⠀⠀⠀⢀⠄⠤⠀⠀⠀⠀⠀⠐⢯⣠⣾⣿⠏⢀⣼⡿⣜⢯⡞⣽⣻⢷⣶⣿⡿⠿⣿⣿⣶⣤⣄⣀⣀⠀⠀⠀⠀⠀⣀⣠⣴⣾⡿⠃⢀⣿⣳⡝⣮⡝⣮⢳⣝⡳⣝⢮⡳⣝⢾⡱⣮⣝⡳⢮⣻⡜⣯⢞⡽⣺⣜⡻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣏⠿⣜⡳⣝⢾⣱⢻⡜⣧⡳⣭⢻⡜⣿⣿⡗⠎⠀⠀⠀⠀⠀⠘⠎⣄⠣⠀⠀⠀⠀⣠⣿⣿⠟⣿⡿⣟⢯⡳⣝⡮⣝⢶⡹⣎⢷⡻⣷⣄⣀⣉⣻⣿⠿⠿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣯⣤⣴⣾⢿⣱⣛⢶⡹⢧⡻⣜⡳⣽⢺⡝⣮⢳⡝⡶⣭⣛⢧⡳⣝⢮⡻⣜⡳⣎⠷⣭⢻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣎⠿⣼⡹⣎⠷⣭⡳⣽⢲⡝⣧⣛⡞⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⠟⠁⣠⣿⡳⣝⢮⡳⣝⣾⣹⣎⣷⣹⣎⣷⣹⣛⣿⢻⣛⡿⣶⣤⣤⣴⣿⣧⣄⣀⣠⣼⡿⣝⢯⡝⣮⢳⢧⣛⢮⣝⡳⣿⣿⡵⣫⢷⡹⣎⢷⣹⢳⢧⣛⢮⣝⢮⡳⣝⢮⣳⢭⡟⣼⢳⣎⠿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⣯⡟⣶⡹⣞⡽⣲⡝⣮⢳⡽⣲⡝⣞⣿⢿⣿⣦⣀⡀⠀⠀⢀⣀⣠⣴⣾⣿⡿⠟⢻⣿⡶⣿⢟⣳⣽⣾⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣷⣿⣽⣭⣗⣧⢻⡽⣛⢯⣏⢷⡹⢮⣝⢮⣛⢮⡝⡾⣜⡳⡽⣿⣿⡵⣫⢷⡹⣎⢷⣫⢞⡽⣺⡜⣧⢟⣮⢳⡝⣮⡝⣮⢗⣮⢻⣜⣻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⣿⣿⣷⣽⣎⣷⣣⣟⣼⣣⣟⣵⣻⣜⣿⣆⠉⠛⠿⣿⣿⣿⡿⠿⠿⢿⣯⣥⣤⣴⣿⣳⣽⣾⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣷⣯⣽⡞⣼⢣⣟⡳⢮⡻⣜⢧⡻⣵⢫⢷⡹⡽⣿⣿⣧⢏⡷⣹⢎⡷⣫⢞⡵⣻⡜⣯⠞⣧⣛⠶⣝⢮⡻⣜⡳⣎⢷⣚⣿⣿⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⠻⣦⣤⣤⣶⡿⣏⠿⣭⣷⣿⠟⠋⠁⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣷⣮⣝⡳⣝⢮⡳⣝⢮⣛⢮⡳⣽⡹⣿⣿⣾⡱⣏⡾⣱⢏⡾⣱⢧⡻⣜⡻⢶⣭⣛⢮⢷⡹⣎⢷⡹⣎⠷⣎⢿⣿⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⣱⢻⣜⣿⣿⠟⠁⠀⢠⣴⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣾⣽⣎⠷⣝⣮⢳⣭⡳⣽⢲⡽⣹⢿⣿⣷⡝⣾⡱⣏⢷⡹⣎⠷⣭⣛⠷⣮⡝⣮⢳⣝⢮⣏⠷⣭⣛⢮⣳⢻⣿⣿⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠷⣭⣳⣾⣿⠃⠀⠀⣰⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣜⢮⡳⣎⠷⣭⡳⣝⢧⣛⣿⣿⣿⣶⡹⣎⠷⣝⢾⡹⢧⣏⡟⣶⡹⣎⠿⣜⡳⣎⡟⡶⣭⡳⣭⢳⡻⣿⣿⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⡶⣿⣿⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣧⡟⣼⣛⠶⣝⣮⢳⡝⣶⢻⣿⣿⣷⣭⣛⢮⡳⣝⡳⢮⣝⠶⣝⢾⡹⣎⢷⡹⣞⡵⣳⡝⣮⢷⡹⡽⣿⣿⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣯⢽⣿⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣵⢫⡟⡼⣎⢷⡹⣎⢷⣛⣿⣿⣷⡽⢮⣝⢾⣹⢳⣎⡟⣮⢳⡝⣮⢏⡷⣹⢞⡵⣻⡜⣧⢻⡵⣻⣿⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣯⢿⣿⠂⠀⠀⠀⠀⠈⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣶⡀⠀⠀⠀⠻⣿⣧⡻⣵⢫⣞⡳⡽⣎⢷⣚⢿⣿⣿⣿⣜⢧⣏⠷⣮⡝⣞⢧⡻⣜⢯⡞⣵⢫⡞⣵⢻⡜⣧⢻⡵⣿⣿⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⠛⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠹⣿⣷⢭⡳⣎⠷⣝⢮⡳⣝⢮⣛⣿⣿⣿⣷⣎⡟⣶⡹⣎⢷⣹⢮⡳⣝⢮⡳⡽⣎⢷⡹⣎⢷⡹⣽⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠹⣿⣷⡹⣞⡽⣎⠷⣝⣮⢳⡝⣶⣛⢿⣿⣿⣿⣶⡹⣝⢮⡳⣏⢷⡹⣎⠷⣝⢮⡳⣽⡹⣎⠷⣽⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢿⣿⣳⡝⡾⢭⣛⠾⣜⢧⣛⢶⡹⣎⣿⣿⣿⣿⣿⣾⣧⡻⣜⢧⣻⡜⣯⡝⣾⡱⢧⣻⡜⣯⣿⣿⡏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠘⣿⣷⡹⣝⢧⣏⡟⣮⢻⡜⣧⣛⣾⣿⡿⠁⠈⠛⢿⣿⣿⣿⣮⣷⣹⢶⡹⣖⢯⣛⣶⣽⣾⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣦⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡳⣝⠾⣼⡹⣎⢷⡹⣶⣿⣿⡟⠁⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣷⣦⣀⠀⣠⣾⠟⠋⠁⠀⠀⠉⠙⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢵⣫⢟⡶⣹⢎⣷⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣟⢮⡳⣏⢾⣵⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣶⣾⣷⣿⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⣎⣷⣽⣾⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡟⡿⣭⢯⡽⣹⣛⠿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⢀⣀⣠⣴⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣤⠀⠀⠀⠀⣠⣿⣿⣛⢶⣹⢳⡝⣮⢳⢧⣏⡟⡶⣭⣛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠁⠀⠀⣠⣾⣿⢿⡱⣏⢾⡱⣏⢾⡱⢯⡞⣼⣹⢳⢧⣏⠿⣼⡹⣟⡿⢧⣏⠿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⡀⠀⠀⠀⠀⠀⢀⣤⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣶⣶⣶⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡗⠀⠀⠀⠀⠸⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⠟⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⣶⣶⣾⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣶⣶⣶⣶⣶⣾⡿⡿⠿⠿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣾⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀________________________________________________________________________________________________________________________⠀⠀ /)/) ( . . ) 🤍𝓁ℴ𝓋ℯ 𝓎ℴ𝓊🤍 (づ⊂) ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀_______________________________________ /) /) ( -. -) Yes, today is Opposite day! 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⠀⢀⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠒⢤ ⠀⠏⠀⠀⠀⠈⠳⡄⠀⠀⡠⠚⠁⠀⠀⠀⠘⡄ ⢸⠀⠀⠀⠤⣤⣤⡆⠀⠈⣱⣤⣴⡄⠀⠀⠀⡇ ⠘⡀⠀⠀⠀⠀⢈⣷⠤⠴⢺⣀⠀⠀⠀⠀⢀⡇ ⠀⠡⣀⣀⣤⠶⠻⡏⠀⠀⢸⡟⠙⣶⡤⠤⠼ ⠀⠀⢠⡾⠉⠀⢠⡆⠀⠀⢸⠃⠀⠈⢻⣆ ⠀⠀⣿⣠⢶⣄⠀⡇⠀⠀⠘⠃⣀⡤⢌⣈⡀⠀ ⠀⠀⠀⠀⠀⠙⠼⠀⠀⠀⠀⠿⠋
.    ◌.      ◝       °˛            )ノ °   ⊹            ⊹    ((              ◜ᥥ ᥥ  ˛           ) )     ⊂ (•ˋロˊ•˶)    ╭ ◜◝ ͡ ◜◝ ⊹.    ⊂   ◝   ) ̄ ̄ ̄ ̄ ̄(   (_ ("  )ᦱ (_____________)   U  ◝_)    \/          \/
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⠀⣠⠴⠚⡙⠙⠲⣤⣠⠖⢋⡛⠙⠲⣄⠀⠀ ⣴⠃⣰⠟⠉⠙⢦⡈⢁⣾⡟⠉⠳⣆⠸⣇⠀ ⣿⠀⣿⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⡿⠄⣿⠄ ⠸⡄⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣰⡏⠀ ⠀⠙⣆⠙⢧⡀⠀⠀⠀⠀⢀⡴⠃⣰⠏⠀⠀ ⠀⠀⠈⠳⣄⠙⠶⣄⣀⠴⠋⣠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⠓⢦⡈⢡⣰⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⡾⠛⠳⠶⣤⣀⣠⣤⣤⣴⡟⠁⠀⠙⣷⠟⠋⠉⠉⢿⡀⠀⠀⠀ ⠀⠀⠀⣾⠁⠀⠀⠀⠀⠉⠀⠀⠀⡿⠀⢠⣟⣿⠿⠳⢦⣤⡴⣼⣇⠀⠀⠀ ⠀⠀⠀⢻⣤⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⣽⣏⠀⠀⢸⣷⡄⠀⣿⠀⠀⠀ ⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠓⢾⡟⠛⢁⣼⣟⠀⠀⠀ ⠀⢀⣼⣇⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣙⣿⣿⣥⣽⢤⠀⠀ ⣀⣈⣷⣏⣁⠀⠀⢀⠀⠉⠙⠻⣶⣾⣳⣶⠟⠉⠁⢀⠀⠀⠀⠶⢻⡟⠒⠒ ⠀⠀⠸⣇⣀⠀⠀⠛⠉⠂⠀⢀⡿⣉⣉⢿⡄⠀⠒⠉⠋⠀⠀⠠⣼⠧⢤⠀ ⠀⠐⠛⠻⣍⣀⡀⠀⠀⢀⣠⠞⠙⠧⠼⠈⠳⣄⡀⠀⠀⠀⣠⣴⣟⡀⠀⠀ ⠀⠀⣠⠴⠛⢿⣭⠿⠿⢯⡅⠀⠀⠀⠀⠀⠀⣠⣭⣩⣭⣭⣿⣋⠈⠙⠂⠀ ⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⣿⠶⠶⠶⠤⠶⣾⠇⠀⠘⣧⠀⠀⢹⡇⠀⠀⠀ ⠀⠀⠀⠀⠸⣇⠀⠀⣰⠾⠋⠀⠀⠀⠀⠀⣧⡀⠀⠀⢿⣄⣤⡾⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠚⠋⠁⠀⠀⠀⠀⠀
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⠁⡈⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠃⡇⠀⠀⠀⠀⣿⣽⢳⡽⣟⡾⣜⢶⣫⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢿⡱⣏⣷⣭⢳⡝⣾⣻⠵⣣⢳⠀⡏⣔⣣⠖⠦⢌⠱⣄⠀⠀⠀⠀⠀⠂⢄⠁⠂⠄⣀⠀⠀⢛⡀⠀⠀⠠⢘⠢⡙⢁⠊⢀⠂⠡⠀⠀⠀⠀⠀ ⠰⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⢠⠒⠂⠀⠰⢠⠇⠀⠀⠀⠀⡘⢀⠁⢀⠀⠀⠀⠸⣿⡧⢯⣝⡳⣝⣮⢳⣻⣿⡽⣫⢶⢦⡤⣤⢀⣀⡀⠀⠀⠀⠀⠀⢀⠤⠊⢸⣻⢎⣷⣹⢻⣜⢧⡻⣜⣿⣳⢥⢻⡀⢹⠴⠀⡁⠀⠈⢀⠬⠢⠀⠀⠀⠀⠀⠀⠈⠲⢤⢀⠈⠒⠨⢇⠀⠤⠀⡠⢊⠔⠢⡑⢢⡈⠄⠐⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⢉⢡⡀⠄⢀⠀⠀⡑⠢⠉⠁⠀⢡⠏⠀⠀⠀⠀⢠⠁⠘⠀⡄⠀⠀⠀⠀⢻⡟⡼⢮⡝⡾⣜⡯⣽⣿⣽⣻⢮⣷⡹⣿⡄⠀⠈⠉⠉⠀⠀⠈⠁⠠⠀⣾⣽⢫⣶⢫⢿⣚⢧⡻⣼⣹⢞⣬⢣⡇⢰⠘⣇⠀⠀⡠⠂⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠑⠈⠒⠠⡀⠈⠂⢎⠔⡃⢜⠠⠌⡑⢌⠢⡀⠀⠀⠀⠀ ⠐⠀⠀⡄⢝⢂⡨⡎⠲⠄⠀⠀⠀⠁⠀⢖⠉⢏⢄⠄⠀⠀⢂⠆⠀⠇⠀⡇⠀⠀⠀⠀⠈⣿⣙⢧⡻⣵⢫⡾⣽⣿⢯⣗⣯⡶⣟⠲⡇⠀⢂⠐⠀⠡⠈⠐⠈⠠⠀⡿⠮⣟⣼⢫⣿⡝⣮⢳⣇⢿⡺⢴⠣⣇⢨⠀⢹⡀⠊⠀⠀⠀⠁⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠈⢀⢠⠁⠢⡀⠱⡌⡖⠒⣂⠄⠀⠑⠨⠀⠀⠀⠀ ⢢⠄⠒⡸⢌⠲⡐⢄⢣⡱⡀⠀⠀⠀⠀⡠⠏⠄⠈⡄⠀⠀⠌⠀⢸⠀⢸⠇⠀⠀⠀⠀⠀⠸⣎⢷⡹⣎⢯⡗⣿⣯⠷⣞⡼⢁⠈⠣⢇⣀⠀⠄⠀⡁⠀⠂⢈⠀⡁⡇⠈⡟⣮⢏⣿⢞⡵⣫⢎⣿⡹⢎⡳⢹⢀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠙⠄⠀⡄⠃⡱⠁⠀⠈⠑⠢⡀⠀⠀⠀⠀⠀ ⠡⢌⡀⢣⡉⢖⡙⢄⠂⠱⡈⠂⠀⢀⠔⠁⠀⠀⠀⠀⠀⠌⠀⠀⣆⠀⢸⢼⠀⠀⠀⠀⠀⠀⢻⡎⢷⣭⣳⣽⠿⣎⠿⡼⠃⠀⠁⠢⠄⡈⠙⠒⠦⢄⡐⢀⠠⠀⢠⡵⢊⠠⠚⢿⡯⣞⡵⣫⢞⣼⡝⢮⡱⡛⢠⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠈⢂⠋⠀⠘⡆⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀ ⠓⢦⠘⠤⡹⡖⢆⢞⢄⠁⠀⢣⢔⠁⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⢡⠀⠸⣝⡇⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠉⠐⠠⠝⢀⠀⠀⠀⠀⠀⠀⠉⠐⠂⢠⢜⢣⣀⠂⡼⢩⠁⠀⠀⠀⠙⡶⣽⡜⡭⣾⡹⢲⡱⡇⠈⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀ ⡉⢦⠉⡔⢛⣁⡂⢘⢸⢀⠜⠁⠀⢕⠂⠄⠀⠀⠀⠌⠀⠀⠀⠀⠘⡀⠀⢫⠛⡄⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⢳⠄⠀⠀⠀⠀⠀⠀⠀⢸⡈⢆⠈⠹⡇⠀⣇⠀⠀⠀⠀⡇⠈⠋⠑⠫⠵⣃⣷⠁⠆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀ 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⠀⠀⠸⣀⠕⠊⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⢀⢞⣏⡷⣵⠷⣻⠀⠀⠀⠀⡠⡡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠃⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠹⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠙⠀⠈⡦⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠒⠥⠅⠀⠒⠀⠒⢣⠡⠀⠀⠀⠔⠈⠀⠀⠀⠀⠀ ⠀⠀⠔⢣⡠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⡲⠜⣶⢫⠳⣍⡆⠀⢀⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠅⠈⠢⠀⢆⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠈⢅⠀⠙⢄⠠⠀⠀⠀⠂⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀ ⠀⠀⠐⡨⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢣⢎⡵⣻⡏⢧⣛⠔⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠈⠉⠉⠙⠛⠆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠑⣀⠀⠈⠑⢅⠌⠲⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣆⠳⣊⣶⡿⣘⡷⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠱⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢎⠲⣌⢳⢏⢾⡱⡹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡘⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢥⢊⡳⡬⢫⣏⠶⣱⢃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢠⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠃⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⡠⠀⠀⡇⠀⠀⠀⠀⠈⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⡘⢦⣙⡔⣱⠯⣜⠣⡇⡟⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢰⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⢀⠆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⡘⠀⠀⠀⠀⠀⠀⠀⠈⠄⠠⠀⠀⠀⢀⠀⢤⠘⠂⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣀⣌⣱⣢⠋⣔⣣⣝⣬⡇⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡇⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⡌⢀⠇⢸⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⡢⠢⡀⠀⠀⢁⢈⠔⠁⠀⠀⡠⠊⠀⠠⠊⢀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⡰⠃⡇⣀⢲⡔⢁⡼⣡⢏⡭⢫⢄⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⣧⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⡰⠀⢸⠀⢘⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡆⠀⠀⡲⡀⠀⠀⠀⠀⠀⠀⢁⠑⢄⠀⠀⠁⢆⠀⠀⢀⠌⠀⢀⠄⢀⠔⠁⠈⠨⠂⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⢎⡑⡂⡗⣤⠋⢀⠞⡴⢣⠞⣜⢣⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢣⣿⢿⡆⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠠⠁⢀⡏⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡇⠀⠀⠘⢥⠀⠀⠀⠀⠀⠀⠈⡄⠀⠑⢀⢁⠈⢀⠔⠁⢀⠔⢁⠔⠁⠀⠀⠀⠀⠙⡤⡇⢀⠀⠀⠀⠀⠀ ⠀⠀⠰⠃⠆⡌⣁⢾⠃⠀⡎⢎⡵⣋⢞⡬⢳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣼⡿⣯⣿⡄⠀⠀⠈⠄⠀⠀⠀⠀⣠⠆⠀⠀⠀⡠⠊⠀⠀⣠⠃⠀⡸⠁⠀⡆⠀⠀⠀⠀⠀⠀⠀⡀⠔⡙⠀⡁⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠑⠍⡁⣀⡔⠁⢀⠁⠀⢈⠀⠁⢀⠰⡸⢍⠀⠰⠈⠀⠀⠀⠀ ⠀⠀⢆⡉⢀⣰⢋⠃⠀⡜⠘⡜⡴⣩⠞⡜⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢠⣿⣿⣽⣯⣿⡄⠀⠀⠘⡄⠀⢀⠂⡍⠀⠀⠀⠀⠁⠀⠀⠌⠀⠀⢀⠁⠀⠀⠃⠀⠀⠀⠀⡀⠒⠉⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⢃⠐⠄⡀⠀⠀⠂⢄⠢⢀⡀⠠⢈⠀⡀⠁⢂⢉⠜⢂⡠⠀⠀⠀⠀⠀ ⡀⢎⠰⡀⡖⢡⠁⠀⡀⠀⡰⣐⠖⣦⢛⡜⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣾⣟⣾⣿⣯⡿⣷⡀⠀⠀⠘⠂⢁⠜⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠌⠀⠀⠸⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⢀⢢⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠈⠄⠀⠘⢔⠄⡀⠀⠀⠂⠌⡑⠢⠀⠤⣅⣀⣀⣈⡘⣂⠀⠀⠀⠀⠀ ⠌⠢⢁⠞⢀⠃⠀⢰⠇⡸⣑⢮⡙⢦⢫⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢠⣿⢯⣿⣿⣟⣿⡿⣷⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢸⡄⠡⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠰⠀⠀⠀⠑⠠⡁⠂⠄⣀⠀⠁⠐⠂⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢔⠎⠀⠆⠀⢀⠧⢆⠳⣍⠶⣩⢏⡞⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⣸⣿⣻⣿⣿⣿⣻⣽⣿⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⣉⠜⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣣⠀⠀⠀⠀⠀⠑⠢⢀⠈⠁⠀⡒⠀⠤⠀⠍⠀⠀⠀⠀⠀⠀⠀ ⢈⠋⠀⠰⠀⠀⡼⡘⢎⡳⢬⣓⡳⢎⡜⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⢠⣿⢷⢿⣿⣿⣾⢿⣯⠇⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⢀⠤⠊⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣗⢄⠀⠀⠀⠀⠀⠀⠈⠐⠠⢀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀ ⠈⠀⠀⠃⠀⢀⠧⣙⠦⣙⠶⣥⢛⡮⡱⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⣼⢯⠏⣿⡿⣾⣟⣯⡿⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠄⠊⠁⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⡱⢦⡀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢐⢣⡹⣌⠳⣎⢧⢳⣱⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢀⣯⠏⣸⡿⣽⡿⣞⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠌⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡼⣈⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠢⠱⢎⠳⣍⠮⣓⠆⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣸⠏⢠⣿⣽⡿⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢎⡰⢑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢤⠳⣌⢳⢎⡵⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⣼⣳⣯⣿⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣖⡶⠧⠖⠒⠒⠛⠋⠁⠀⠀⠀⠀⠑⡀⢀⡆⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡦⡘⢥⠊⡍⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡚⢬⠳⣌⠳⣎⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠷⣯⣷⣿⣳⣧⡀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⣾⣿⣿⣶⣶⣶⣶⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⢠⣿⣳⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡙⢆⡹⣐⢃⠆⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠤⣙⢮⡱⢎⡳⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢸⣻⡽⣷⣿⣻⣾⣟⣧⣀⡀⠀⠀⢀⣀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣧⣻⣇⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠱⢢⡉⠦⣑⠢⡉⠢⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⚝⠀⠀ ⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣷⣦⣀⣀⠀⠀⠀⠀ ⠀⢀⣴⢿⣿⣿⣿⡟⠉⠙⠛⠛⠛⠻⣿⡷⠸⣿⣏⠉⠙⣿⣿⣿⣿⣦⡀⠀ ⢀⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢸⣿⣷⚝⣿⡿⠀⢸⣿⣿⣿⣿⣿⣷⡄ ⢸⣿⣿⡿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠀⠀⠘⣿⣿⣿⣿⣿⣿⣇ ⠸⣿⣿⣿⣿⣿⣿⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⡇ ⠀⠹⣿⢿⣿⣿⡿⡄⠀⠘⠇⠀⠀⠠⡄⠀⠀⠺⠀⠀⢠⡿⣿⣿⣿⣿⡿⠃ ⠀⠀⠙⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠈⠁⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⠟⠀⠀ ⠀⚝⠸⣿⣿⣿⣿⣿⣿⣿⣋⠰⢶⣶⣒⣶⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣯⡏⠀⠀⣏⣉⣽⠛⠛⢿⣿⣿⣿⣿⣷⠀⠀⠀ ⠀⠀⠀⠸⣿⣿⣿⡏⠉⢉⣁⡇⠀⠀⣹⣀⣹⠀⠀⢸⣿⣿⣿⣿⠏⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⣿⣷⣶⣾⣷⣮⣿⣿⣥⣤⣽⣦⣶⣿⣿⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠟⠛⠋⠉⠙⠛⠿⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠋⠙⠻⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡿⠛⠛⠲⢦⣀⠀⠀⠀⠀⠀⣾⣁⠀⠀⠀⠈⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⠇⠀⠀⠀⠀⠈⠳⠦⠤⣤⠴⠛⠋⠀⠀⠀⠀⠀⠀⠙⠳⡀⠀⠀⠀⠀⠀ ⠀⡀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠌⢦⡀⠀⠀⠀ ⣸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⣀⣠⡙⢦⠀⠀ ⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣟⣛⠉⠀⠀⠈⡆⠀ ⢸⡇⠀⠀⠈⠉⠛⠛⠛⠓⠲⠶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢶⣤⡀⣿⡒ ⢸⡇⠀⠀⠀⠀⣀⣤⠴⠖⠚⠉⣡⠾⠉⠀⠀⠀⠀⠀⣀⣠⣤⣄⠘⠀⡄⠀⣿⣿ ⢸⡇⠀⠀⠀⠈⠉⠀⠀⠀⣠⠞⠁⠀⠀⢀⣠⠴⠞⠋⠉⠀⠀⣿⠀⢠⣥⣷⡿⠍ ⣼⡇⠀⠀⠀⠀⠀⠀⣰⠞⠁⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⣰⠏⣠⣾⡯⠞⢳⣤ ⠻⢿⠀⠀⠀⢀⡔⠋⢀⠀⠀⠀⣰⠀⠀⢷⡀⠀⢀⣀⣤⡾⢿⣽⠟⠋⠀⠀⢸⣿ ⠀⠈⣆⠀⠀⠈⣧⡀⠈⢧⣤⠞⠁⡀⣀⣨⣿⠿⠛⠋⣽⠞⠛⠁⠀⠀⢀⣴⠋⠀ ⠀⠀⠘⢶⣄⡀⢀⣥⣤⣤⣖⡲⣿⡿⠛⠉⠀⠀⠀⠀⢇⠀⠀⣀⣤⠾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⣹⠏⠀⠀⠀⠀⠀⠀⠀⢸⣿⡋⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⢠⠄⠀⠀⠀⠀⠀⠀⠘⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⢀⣟⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢾⡃⠀⠀⢠⣾⣟⡇⠀⠀⠀⠀⠀⢀⣸⣼⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⠦⠶⠿⠙⢱⡏⠀⠀⠰⡖⠀⠉⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣦⡀⠀⣽⣿⡶⢶⠟⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢋⣩⣉⢻⣿⣿ ⣿⣿⣿⠀⣿⣶⣕⣈⠹⠿⠿⠿⠿⠟⠛⣛⢋⣰⠣⣿⣿⠀⣿⣿ ⣿⣿⣿⡀⣿⣿⣿⣧⢻⣿⣶⣷⣿⣿⣿⣿⣿⣿⠿⠶⡝⠀⣿⣿ ⣿⣿⣿⣷⠘⣿⣿⣿⢏⣿⣿⣋⣀⣈⣻⣿⣿⣷⣤⣤⣿⡐⢿⣿ ⣿⣿⣿⣿⣆⢩⣝⣫⣾⣿⣿⣿⣿⡟⠿⠿⠦⠀⠸⠿⣻⣿⡄⢻ ⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⠇⣼ ⣿⣿⣿⣿⣿⣿⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣰⣿ ⣿⣿⣿⣿⣿⣿⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿ ⣿⣿⣿⣿⣿⠏⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿ ⣿⣿⣿⣿⠟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿ ⣿⣿⣿⠋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿ ⣿⣿⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿ ⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⢸⣿ ⡏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⢻⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣼⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⣦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠈⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠙⠻⠷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢯⣓⣲⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⢁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡟⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠉⠲⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⡖⣿⣷⡀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠓⠚⠀⠛⢷⢀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⣴⡇ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢺⡏ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⢳⠃⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢸⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡟ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⣿
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⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⠞⠁⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠏⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⡆⠀⠀⠀⢸⠁⠀⣀⣀⣀⣀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠳⣄⠀⠀⠈⢳⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀ ⠀⠀⠀⠀⠈⢳⠆⠀⠀⠉⠛⠛⠿⠿⠿⣿⣿⡿⠷⠶⠒⠚⠋⠉⠀⠈⠙⢢⠀ ⠀⠀⠀⠀⢠⠏⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃ ⢀⡴⠦⢄⡞⠀⠀⠀⠀⠀⣄⣀⡗⠀⡀⠀⠖⠀⠀⠀⠐⣤⣀⣀⣀⣠⠴⠋⠀ ⠘⣇⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⣹⡤⠯⣍⠀⠀⠀⠀ ⠀⠈⠓⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⠟⠀⠀⠀⠀ ⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠉⠀⠀⠀⠀⠀ ⣠⡤⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠇⠀⠀⠀⠀⠀⠀ ⣏⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀ ⠘⢦⣀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣅⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⠉⠉⠒⠒⠶⠦⠤⠤⡤⠤⣤⡆⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⡟⢁⣍⣉⠛⠻⠛⠛⠛⠛⢀⣤⣀⢋⣁⣠⡄⢹⣿⣻⣻ ⣿⣿⣿⠃⣾⣿⣿⣿⣶⣾⣿⡿⠀⣮⢀⠀⣀⠈⠚⠚⠈⢿⣿⣿ ⣿⣿⣿⡆⢉⣿⣿⣿⣾⣿⣿⣷⡐⠞⠀⠀⠿⠏⠀⠙⡽⢰⣿⣿ ⣿⣿⡿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣆⠲⠒⠁⣾⣿⣿ ⣿⠿⠇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠘⠛⢿ ⣷⣶⣆⠰⢾⣿⡇⠀⣿⣿⣿⡿⢿⣿⣿⣿⠀⣹⣿⡿⠇⠸⠿⣿ ⣿⣯⣴⡄⠺⢻⡿⠿⠿⢿⣿⣐⣂⣽⡿⠿⠿⢿⣿⠛⠀⣿⣶⣿ ⣿⣿⣋⣤⣦⠌⣴⣶⣶⣦⠹⣿⣿⡏⢠⣶⣷⣦⡈⣠⣷⣦⣽⣿ ⣿⣿⣿⣿⣿⡄⠻⠟⠛⠋⣠⣤⣤⣤⡘⠛⠛⠿⢁⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⢤⠶⠶⠶⢦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡤⠴⠶⢤⣄⡀⠀⠀⠀⢀⣤⠶⠛⠋⣁⣀⣤⣤⣤⣤⣤⣤⣤⣀⣈⠉⠛⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠞⢁⣠⣤⣤⣤⣀⠙⠲⣤⠖⠋⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡈⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠃⢠⣿⣿⣿⣿⣿⣿⣷⡦⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡏⠀⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢱⣶⡎⢿⣿⣿⣿⣿⢣⣾⣆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⢦⡀⠀⠀⠀⠀⠀⠀ ⠈⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡇⢸⣿⣿⣿⡏⢸⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⢧⠀⠀⠀⠀⠀⠀ ⠀⢹⡆⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⠀⢸⣿⣿⣿⡇⠀⠉⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠘⡇⠀⠀⠀⠀⠀ ⠀⠀⢿⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣇⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠹⣆⠀⠀⠀⠀ ⠀⠀⠀⠙⣆⠈⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⣾⣿⣿⣿⣿⡀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠈⢦⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⡟⠉⠉⠉⠙⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢧⡀⠀ ⠀⠀⠀⠀⠘⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠰⣿⡷⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠸⡇⠀ ⠀⠀⠀⠀⠀⣧⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⠀ ⠀⠀⠀⠀⠀⢻⡆⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢠⡿⠀ ⠀⠀⠀⠀⠀⠈⣿⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⠿⠋⢀⡞⠁⠀ ⠀⠀⠀⠀⠀⠀⣸⠇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⢤⣤⠶⠋⠀⠀⠀ ⠀⠀⠀⢀⡴⠋⠀⣴⣾⣦⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣰⣷⣦⣄⠉⠳⣄⠀⠀⠀ ⠀⠀⡴⠋⠀⠐⠋⢹⣿⣿⣿⣦⡙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣠⣾⣿⣿⡏⠉⠓⠄⠈⢧⡀⠀ ⠀⣼⠁⣰⡇⠀⣀⣼⣿⣿⣿⣿⣿⣦⣌⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣉⣴⣿⣿⣿⣿⣿⣷⣄⡀⢀⣆⠀⢧⠀ ⠀⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣍⡙⠛⠛⠿⠿⣿⡿⠿⠟⠛⠛⣉⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⢸⡆ ⠀⠻⣄⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠓⠀⣠⣤⣄⠀⠐⠚⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⢀⡼⠁ ⠀⠀⠈⠛⠶⣤⣤⣀⣀⣉⣉⣉⣉⣉⣀⣀⣀⣠⣤⣤⠴⠖⠋⠁⠀⠈⠙⠲⠶⣤⣤⣄⣀⣀⣀⣉⣉⣉⣉⣉⣁⣀⣤⣤⠴⠞⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠉⠙⠉⠉⠀⠀⠀⠀⠈⠉⠉⠓⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣯⣽⣲⣶⣦⣾⣷⣤⠾⠋⠁⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣾⣽⢻⣿⣿⣿⣿⣯⠿⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣷⣤⣤⣤⡄⠀⠀⠀⠀ ⠘⣿⢯⠽⢿⣿⣿⣿⣿⠆⠀⠀⢸⠇⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⠀⠀⢦⠀⠀⠀⢸⢹⡟⣽⣿⣿⣿⣿⣳⣤⣤⣀⡀ ⠀⢿⡀⠀⠈⠻⠛⠁⠀⠀⢀⣠⣺⡄⢀⡀⠛⠋⠀⣤⣀⣀⢀⡀⠀⠀⠸⣿⡿⠀⠀⠘⢧⡀⠀⠈⠙⠓⠛⣿⣿⣿⣻⣿⣿⠵⣞⠃ ⠀⠈⠹⢧⣄⣀⣀⣠⣤⠶⠛⠉⠀⠙⢦⣍⡁⠀⠀⠈⠉⠙⠉⠁⠀⠀⠀⠀⢀⠀⠀⠀⠈⣷⣄⠀⠀⠀⠀⠻⠛⠻⣿⣼⣾⠧⢻⠀ ⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣶⡶⠀⠀⠠⠤⠤⠤⠤⠤⣤⣤⣴⣶⣾⣋⠈⠳⢦⣀⡀⠀⠀⠀⠈⠉⢃⣤⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⣰⠿⠉⠀⠀⠈⠙⢧⠀⠀⠉⠙⠓⠶⠶⠶⠶⠟⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⢼⣇⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⣠⡤⣤⡀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠉⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢤⣤⣄⣀⣀⣀⣀⣀⣀⣈⣣⣀⠀⠀⢀⣼⣣⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠛⠛⠉⠉⠉⠁⠀⠀⠈⠉⠉⠙⠛⠿⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀ ⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠹⣧⡀⠀⠀⠀⡏⠉⠙⠋⢹⡆ ⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠉⠛⠿⣦⡀⠀⠸⣷⡀⠀⠀⠹⣄⠀⠠⡹⠃ ⠀⢀⣿⠃⠀⠀⠀⠀⣠⣶⠾⠟⠛⠉⠉⠛⠿⣶⣄⠀⠀⠀⠀⣰⠃⢀⣠⣤⣄⠀⠈⢻⣦⠀⢻⣧⠀⠀⠀⠈⠓⠋⠀⠀ ⠀⢸⣿⠀⠀⠀⣠⣾⠋⠁⠀⠀⢀⣠⣤⣤⣤⣈⠙⣷⣄⠀⢠⣏⣶⣿⣿⣿⣿⣿⣦⠀⢻⣧⠘⣿⢀⢸⡛⠛⢲⠀⠀⠀ ⠀⣾⡇⠀⠀⢠⡿⠁⠀⠀⣠⣾⡿⢿⣿⣿⣿⣿⣷⣌⢿⣆⢸⣿⡋⠉⢉⣿⣿⣿⣿⣧⠈⣿⠀⣿⣿⠀⠹⠶⠋⠀⠀⠀ ⠈⡟⣿⠀⠀⢸⠇⠀⢀⣼⣄⠈⠀⣸⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣶⣿⣻⣿⣿⣿⣿⣤⣿⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⢷⢹⡆⠀⢸⡄⠀⣾⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣇⣿⢹⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠏⣸⢧⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣇⢳⡀⠈⢧⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⢁⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢎⠃⠀⠈⠳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠟⠁⠀⠀⠈⠻⣿⣿⣿⣿⡿⠟⠁⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⣄⠀⠀⠈⠙⡻⠿⢿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⣀⡀⣰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡤⠬⣷⣄⡲⣤⣈⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⢛⡵⠚⠁⠀⢀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣇⠀⠀⠀⢻⣿⠒⠭⣟⣷⢶⣤⣤⣤⣤⣤⣤⣤⣤⣶⢾⣟⠯⠗⠊⠁⠀⠀⠀⣾⠟⠁⠀⢘⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣧⠀⠀⠈⣿⡄⠀⠀⠈⠉⠛⠛⠛⠛⠛⠒⠋⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣿⠇⠀⠀⠙⠛⠛⠒⠒⠛⠛⠛⠻⠿⢷⡢⣤⣔⡶⠿⠟⠛⠛⠛⠻⠿⠽⠟⠁⠀⠀⢺⡿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢿⣿⠒⠲⠛⠙⠲⠦⢼⣿⡿⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⢸⣇⡇⠀⠀⠀⠀⠀ ⠀⠀⠹⠿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⡻⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⢀⡾⡿⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⢀⣠⣴⢯⠞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⠶⣖⡿⠚⠁⠀⠀⠀⠀⠀⠀⠀⠘⠮⣷⣶⡤⡤⠴⠾⠟⠋⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠋⠙⢦⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠛⠉⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀ J⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⢀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣠⣴⣶⡿⢿⣷⣤⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠟⠋⠉⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠟⠻⣷⠀⠀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⢀⣿⣤⡾⠛⠉⠈⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡟⠁⣠⣶⣆⣸⡟⠋⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⢀⣴⡾⠛⢹⡿⠀⢰⣿⠿⠛⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⡇⠀⢀⣴⠟⠁⠀⠀⣿⡇⢠⡿⠁⠀⠀⢀⣿⠟⠻⢷⣦⠀⠀⠀⠀⠀⠸⣟⠻⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣴⡿⠁⠀⠀⠀⠀⠙⠷⢾⡇⠀⠀⢠⣾⣯⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⠀⠈⢻⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⣶⣟⢃⡿⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢹⣧⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠙⠋⠁⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠹⣧⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⢀⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⣻⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠂⠸⣿ ⠀⠀⣴⣶⣄⠀⠀⢠⣿⠀⠀⠀⢀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠠⠀⠀⣿ ⠀⠀⣿⣿⣿⠀⣰⠾⣿⠀⠀⠀⠹⠿⠿⠶⠃⠀⠀⠀⠀⠀⠐⠶⠶⠶⠶⠶⣶⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⢀⣿ ⠀⠀⠈⠉⠁⠀⠻⣤⣿⡄⠀⠀⠀⠀⢀⣴⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠂⠀⠀⢸⡿ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠘⠓⠾⣷⡾⠃⠀⠀⠛⠷⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠙⠛⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠄⢀⣾⡟⠐ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀ ⠀⠀⠀⢀⣠⣴⡾⠟⠉⠀⠀⠀⠙⠻⣶⣤⡀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⣴⡿⠃⠀⠀⠀ ⣤⣶⣾⣿⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⣄⣀⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠉⠀⠀⠀⠀⠀ ⢻⣇⠀⣹⢹⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢁⡼⢛⣿⡿⠶⣶⣶⣶⣦⣤⣶⣶⣶⠶⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣶⢇⣾⠇⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⢸⣿⠛⠁⣼⠋⠑⢄⣈⠙⣷⡤⠠⠠⣀⠿⣷⣶⡶⠾⢶⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣿⡾⠃⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⢸⡏⠀⠀⣿⠀⢀⣤⣾⠷⢿⣿⠀⡜⠁⠀⢸⡏⠀⠀⣸⣿⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⢹⣷⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⢸⡇⠀⠒⠾⣿⡟⠉⠀⠀⠀⢻⣦⡐⢄⣀⡈⠻⣶⣾⣿⣥⣿⣿⡆⠀⠀⠀⠀ ⠀⠀⠘⣿⣧⣤⡶⠶⠾⠛⠁⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⢘⣿⡄⠀⠀⠀⠀⠹⣷⡤⢤⣀⣠⣴⡿⠋⣻⣧⣾⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀ ⠀⡴⠈⠉⠦⡀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠑⣄⠀⠀ ⠣⠀⠀⠀⠀⠀⢣⣠⠤⠤⠤⡈⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⡂⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⢀⡀ ⠀⠀⠀⠀⠈⠀⠀⠀⣄⣠⠆⠀⠀⠀⠀⠀⡞⢠⠃⠀ ⠀⡏⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠀⠀ ⠀⠀⠐⡄⠀⠀⠀⠆⠀⠀⠀⠀⠘⠄⠀⠀⢘⠀⠀⠀ ⠀⠀⠀⠉⢄⡠⠎⠀⠀⠀⠀⠀⠀⠘⠢⠜⠁⠀⠀⠀
⣿⣿⣿⣿⣿⣿⡻⠝⢫⣟⠟⠻⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⢿⠝⠲⠁⠀⠀⠉⠀⠀⠘⠯⢟⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣛⢯⡟⠁⠈⠱⠏⠃⠑⢺⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣯⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡕⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣞⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢲⣻⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣞⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣷⡳⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣭⡯⠓⠫⠞⠑⠚⠓⠚⠍⢻⣽⠯⢯⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣯⣗⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⢻⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣤⡤⡶⠖⠶⢶⠲⢖⡶⠶⣒⣖⣦⡤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⢯⢇⠀⠀⠀⠀⠀⠀⠀⣀⣴⡲⠯⠓⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠫⠶⣢⢄⠀⠀⠀⠀⠀⠀⠀⠀⣹⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⡝⠉⠉⠀⠀⠀⠀⠀⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣢⠀⠀⠀⠀⠀⠀⠈⠳⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⣥⠀⠀⠀⠀⠀⢀⣞⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣄⠀⠀⠀⠀⠀⠀⣺⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣙⠀⠀⠀⠀⠀⢠⡟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⡄⠀⠀⠀⠀⠈⠚⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⡜⠁⠀⠀⠀⢠⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣞⡇⠀⠀⠀⠀⠀⣸⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡇⠀⠀⠀⠀⣾⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢘⡆⠀⠀⠀⠀⢰⢯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⡞⠁⠀⠀⠀⣸⡅⠀⠀⠀⠀⠀⣴⣿⣻⢷⣆⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠀⠀⣰⣿⣻⣽⣳⡄⠀⠀⠀⠀⢈⣾⠀⠀⠀⠀⣼⢾⠿⣿⢿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿ ⣿⡵⡄⠀⠀⠀⢹⠥⠀⠀⠀⠀⠀⢿⣳⢯⣟⡾⠀⠀⠀⠀⠀⣠⣶⣦⡄⠀⠀⠀⠀⠀⠹⣷⣻⢾⡽⠁⠀⠀⠀⠀⠘⢾⠀⠀⠀⠀⢸⢚⠛⠒⠋⠺⣍⣻⠜⠒⠣⣛⣿⣿⣿⣿⣿ ⣿⣯⡛⠀⠀⠀⠘⡷⡀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠂⠀⠀⠀⢻⣟⣾⠁⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢰⡛⠀⠀⠀⣴⢏⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣿⣿⣿⣿⣿ ⣿⣿⡵⣄⠀⠀⠀⠺⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢀⣴⣿⠟⠽⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⠃⠀⠀⢀⣽⡞⡮⣀⣀⣀⠀⠀⠀⠀⠀⠀⠫⡝⣿⣿⣿⣿ ⣿⣿⣿⣷⢻⠃⠀⠀⠫⢖⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⢠⢯⢇⠹⡑⠟⢲⣭⠇⠀⠀⠀⣀⣀⠀⠈⢣⢻⣿⣿ ⣿⣿⣿⣿⣯⣖⣲⠀⠀⠈⠋⢽⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⡾⠛⠃⠀⠀⣤⣴⢻⠁⢎⠰⡁⢎⡘⣭⢆⣀⡤⣞⠧⣯⠤⡀⠀⢳⢎⣿ ⣿⣿⣿⣿⣿⣿⣷⣓⢤⣠⣄⠀⠉⠐⠫⠖⣲⣰⣢⢤⢄⣀⣀⡀⣀⣀⣠⢄⡠⣴⣠⡖⠴⠟⠛⠛⠈⠉⢀⣀⣠⣤⣲⢳⡁⢆⡉⢆⠱⡈⢆⡘⢌⠳⠞⢣⠑⡌⠌⢷⣓⣄⣀⣏⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣯⣖⣺⣆⣤⢤⣄⡠⣄⣀⣉⣈⣁⡙⠈⢁⣉⣉⣈⢤⣀⣠⡖⣤⢤⡲⠷⠲⠾⠋⠉⠁⠈⢣⢿⢠⠘⡄⠣⠁⠈⡒⢌⠢⡉⢆⠱⡈⢜⠠⢚⠲⡵⢪⢽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠧⡏⠉⠉⠁⠈⠙⠒⠁⠚⠛⠛⠊⠁⠈⠃⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡞⡄⠣⢌⠱⢠⡐⢌⠢⡑⢌⠢⡑⡸⠂⠳⣈⠒⡌⣝⢮ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢧⡤⢤⡤⢤⣰⣚⠧⢛⠰⣈⠱⡈⠦⢡⠘⡄⢣⠘⡄⢣⠘⢣⣀⢐⠡⢊⢴⣫⣾ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢳⢚⠓⡊⢍⡡⢌⡘⢄⡣⠤⡃⠜⡠⢃⠜⡠⢃⠜⡠⢃⠜⡄⠢⠜⡰⢡⡾⣵⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⡞⣥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢿⣈⢆⣉⣦⡔⢢⠘⡴⠀⠀⡕⢡⠑⡌⢢⢱⠊⠒⡡⢊⠔⡨⠑⡬⣰⡟⣼⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡿⢯⠗⠉⠈⠀⠃⠱⡟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣶⢹⠋⠛⠒⠿⡲⣅⠒⡡⠑⡌⢢⠑⡌⢂⠮⡀⢄⠱⡈⢆⢡⡳⡞⣵⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣟⠇⠀⠀⠀⠀⠀⠀⠈⣟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⠀⠀⠀⠈⣯⡧⢘⠰⡉⠔⡡⢊⠔⡡⠒⡌⢢⠑⣌⡦⣏⣷⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⡞⡄⠀⠀⠀⠀⠀⠀⣀⣯⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡟⠀⠀⠀⢀⡗⡏⡄⢣⠘⡌⠔⡡⢊⠔⡱⣈⣦⢷⣹⣼⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⣢⣀⣀⠀⣀⡤⣻⢫⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡗⡇⠀⠀⣀⡼⣺⠵⣼⢤⣣⡼⣬⠴⣥⠾⣝⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣧⣯⣵⣿⣿⣷⣶⣵⣏⣖⣒⣖⣒⣖⣲⣒⣲⣜⣫⣯⣧⣷⣾⣼⣭⣯⣽⣵⣿⣿⣿⣿⣾⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⡀⠀⣠⠴⠃⣠⣴⣾⣷⣄⠀⠂⣤⣶⣶⣤⡀⠀⢀⣤⣶ ⠀⠀⠀⠀⠈⠙⡇⠈⢦⡀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⡇⠀⢰⣿⣿⣻⣿⣿⣷⣼⣿⣿⣿⣿⣷⠀⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠘⢿⣀⠝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠈⠿⣿⣿⣿⠟⠈⢻⣿⣿⣿⣿⠏⠀⠻⣿⣿ ⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠱⡄⢰⠈⡟⣇⠀⠀⠀⠳⡈⠁⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⢱⡿⠀⢣⠸⡄⢀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⣀⠀⠀⡜⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⢧⠀⡜⢠⢧⠈⣧⠀⠀⠘⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣸⣉⠳⣼⣱⡥⢧⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⡄⡇⡜⢸⡀⢹⢧⠀⠀⠸⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡴⢻⠋⠙⢄⠘⡆⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⢣⠇⠈⡇⠈⡆⠳⡀⠀⢹⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⡇⠀⠀⠈⢧⢹⡄⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⣯⠤⠒⠒⠒⠽⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⢳⠎⠀⠀⡇⠀⢹⠀⠙⢆⠀⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣸⠀⠀⠀⣀⢀⣑⠷⡀⠀⠀⠀⠹⡷⢄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠉⠀⠀⢸⠀⠀⠀⡇⠀⠀⢧⠀⠀⠑⠾⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣇⡇⠀⢀⠞⡡⠔⠚⠋⠹⣆⠀⠀⠀⠱⡄⠙⠦⣄⠀⠀⠙⣟⡶⠤⣄⣠⡤⠤⠤⣈⠙⠫⣅⢳⠀⠀⠀⠀⠀⢸⠀⠀⢸⠃⡄⠀⠈⢇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⠈⣇⠀⠀⢻⠀⠀⡾⠋⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠙⣄⠀⠀⠙⠢⢴⣉⡷⣟⣽⣿⣿⡯⣭⡉⠛⢯⡁⠸⡆⠀⠀⠀⠀⠘⣆⣀⡎⠀⢷⡀⠀⠘⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢧⠀⠸⡄⠀⢸⡀⠀⠀⠀⠀⠀⠀⠠⠴⣶⡄⠈⠢⡀⠀⠈⢦⠀⠀⠀⠠⢿⣿⠏⠘⠉⠈⢷⣞⢹⣿⣦⡙⣖⡇⠀⠀⠀⠀⠀⣇⡙⡇⠀⢸⠙⣄⠀⠘⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡆⠀⠹⡄⠀⡇⠀⠀⣠⡴⠒⠚⠓⠲⣯⣄⣀⠀⠈⠲⣄⠀⢳⡀⠀⠀⠀⢻⢠⡄⠀⣠⣠⣿⢿⢿⡏⢷⣽⡇⠀⠀⠀⠀⠀⣇⡱⢹⠀⣼⠀⠈⠳⢄⡘⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢱⡀⠀⡟⢦⢳⢤⡼⢏⣾⠟⠛⣿⣶⢿⣿⡀⠀⠀⠀⠀⠙⠲⠽⠀⠀⠀⠘⠈⣿⡽⢻⣿⣾⣿⠈⡇⠘⢉⡇⠀⠀⠀⠀⠀⡇⠀⢸⠀⡇⠀⠀⠀⠀⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠣⠀⡇⠈⠙⢸⣣⡟⡁⠀⠀⣸⣿⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠉⠛⠁⣰⠃⠀⢸⠁⠀⠀⣠⠀⠀⡇⢀⡏⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠚⢻⣼⡅⢰⣤⣾⣿⣳⣿⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢒⣲⡎⠁⠊⠀⡼⠀⠀⡰⡏⠀⠀⣧⡎⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡘⡄⠈⠻⠇⠈⣿⡘⠿⠵⠟⠐⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⡼⢹⠃⠀⠀⡇⢣⡜⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠱⡄⠀⢲⡀⠀⠀⠳⡜⣆⠀⠀⠀⠈⠳⢤⣀⣤⡜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡠⢺⢠⠏⠀⠀⠀⡇⠘⣇⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢆⡀⢷⣄⠀⠀⠘⢮⣆⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡎⠀⠀⠀⢀⡇⠀⠘⣇⢀⣀⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠺⠈⢳⠢⢄⣀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⢸⡇⢀⠴⠚⠉⠀⠀⠈⢳⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠙⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⡇⠀⠀⠀⠀⢸⠞⠁⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠹⣶⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣇⠀⠀⣴⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡞⠁⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠈⢹⣠⡀⠘⡄⠀⠈⢷⡶⠤⢤⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠔⠚⠉⠀⡼⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⣇⠱⣄⠹⡄⠀⠀⠳⡀⠀⣾⠀⠀⠈⠉⠉⢿⣍⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡀⠈⠲⣹⡄⠀⠀⢳⢰⢻⠀⣀⡀⠀⠀⠀⠉⠳⠤⣀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⠀⠑⠦⡀ ⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⡇⠀⠀⠈⢱⡀⠀⠈⣿⣌⡿⠁⢹⠀⠀⠀⠀⠀⡼⠛⠋⠱⡄⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⢁⡜⠁⠀⠀⠀⠙ ⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⢀⣠⢿⣰⠃⠀⢠⠀⠀⠀⠀⣸⡁⠀⠀⠀⣼⣆⣠⠤⠖⠒⣚⢺⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡤⠚⠉⠉⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠈⣇⠀⠀⢀⡽⠋⠀⠀⠈⢧⠀⢸⠓⠉⠉⣉⡙⠛⠲⠉⢙⠋⠁⡀⠤⠖⠋⠁⣸⠇⠀⠀⠀⠀⠀⠀⠀⢠⠞⡡⠞⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡰⠋⢦⣀⠀⣀⠀⢹⠀⡰⠋⠀⣀⡤⠤⡄⠘⡇⣸⡀⠀⠀⠀⣉⣩⢷⠤⡞⠓⣖⠒⠒⠒⠒⢤⢿⠀⠀⠀⠀⠀⠀⣲⡴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀ ⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣌⡉⠻⡙⠦⣷⠁⠐⠋⠀⠀⠀⠹⡄⢣⢹⠙⠒⠚⢉⡏⠀⡟⠀⢸⡀⠘⢆⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠳⠧⢤⠃⠀⡠⠖⠋⠉⢳⡀⢰⡜⠘⡄⠀⠀⡜⠀⢀⡇⠀⠈⢇⠀⠈⢧⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀ ⠀⠀⣖⠊⠘⠉⠉⠉⠉⠓⠢⢄⠀⠀⠀⣠⠔⠚⢉⢉⠩⠙⢃⢳⣤⠀⠀⠀ ⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⡜⢃⠀⡃⠄⠄⡀⠇⡘⠀⢿⡀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢀⠂⠤⠁⠌⡐⢀⠒⠠⢁⠂⢳⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⠈⠄⣁⠢⠐⡈⠄⡁⢂⠘⣈⡆⠀ ⠸⡀⠀⡤⢠⠦⠤⠲⠠⢤⡀⠀⠀⣼⠀⣇⡬⠤⠖⠧⠚⠦⢤⠁⡂⠤⡇⠀ ⠀⠙⠭⢄⡙⠀⠄⠀⠀⠐⠛⢢⠜⡼⢀⢳⡚⠀⠀⠀⢀⠙⣠⠼⠐⡐⢧⡀ ⠀⠀⢀⠜⠁⠒⠦⠤⠀⠰⡒⠊⣴⠁⠌⠌⡱⠒⠲⠶⠎⠂⡛⣄⢂⠡⠌⢧ ⠀⠀⡇⢠⠃⠀⠀⠀⠀⢁⠈⠑⢬⠚⡯⠊⠀⠆⠀⠀⠱⡂⠈⢺⡄⣸⠒⠋ ⠀⠀⠈⡎⠀⠀⠀⠀⠀⠸⡓⠤⣂⣕⡍⡢⢴⠀⠀⠀⠀⠀⠉⢧⠋⠁⠀⠀ ⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⢣⠀⠀⠉⠈⢀⠏⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀ ⠀⠀⠀⠙⡄⠀⡖⡖⠒⡖⠉⠀⠀⠀⠀⠀⠑⠒⠒⢲⠒⢲⠂⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠒⠃⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠛⠒⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠚⠉⢉⣩⠽⠟⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠄⢤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠀⠀⠀⣀⣤⠴⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢳⡄⢀⡴⠚⠉⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠹⡏⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢬⣳⣄⣠⠤⠤⠶⠶⠒⠋⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠈⠉⠛⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢃⠈⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⢀⢾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠮⣄⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠋⠀⠀⢀⡤⡴⠃⠈⠦⣀⠀⠀⠀⠀⠀⠀⢀⣷⢸⠀⠀⠀⠀⢀⣀⠘⡄⠤⠤⢤⠔⠒⠂⠉⠁⠀⠀⠀⠑⢄⡀⠀⠀⠙⢦⡀⠀⠀⠀ ⠀⠀⠀⠀⣼⠃⠀⠀⢠⣞⠟⠀⠀⠀⡄⠀⠉⠒⠢⣤⣤⠄⣼⢻⠸⠀⠀⠀⠀⠉⢤⠀⢿⡖⠒⠊⢦⠤⠤⣀⣀⡀⠀⠀⠀⠈⠻⡝⠲⢤⣀⠙⢦⠀⠀ ⠀⠀⠀⢰⠃⠀⠀⣴⣿⠎⠀⠀⢀⣜⠤⠄⢲⠎⠉⠀⠀⡼⠸⠘⡄⡇⠀⠀⠀⠀⢸⠀⢸⠘⢆⠀⠘⡄⠀⠀⠀⢢⠉⠉⠀⠒⠒⠽⡄⠀⠈⠙⠮⣷⡀ ⠀⠀⠀⡟⠀⠀⣼⢻⠧⠐⠂⠉⡜⠀⠀⡰⡟⠀⠀⠀⡰⠁⡇⠀⡇⡇⠀⠀⠀⠀⢺⠇⠀⣆⡨⢆⠀⢽⠀⠀⠀⠈⡷⡄⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⠁ ⠀⠀⢸⠃⠀⠀⢃⠎⠀⠀⠀⣴⠃⠀⡜⠹⠁⠀⠀⡰⠁⢠⠁⠀⢸⢸⠀⠀⠀⢠⡸⢣⠔⡏⠀⠈⢆⠀⣇⠀⠀⠀⢸⠘⢆⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠀⡜⠀⠀⢀⡜⡞⠀⡜⠈⠏⠀⠈⡹⠑⠒⠼⡀⠀⠀⢿⠀⠀⠀⢀⡇⠀⢇⢁⠀⠀⠈⢆⢰⠀⠀⠀⠈⡄⠈⢢⠀⠀⠀⠈⣇⠀⠀⠀⠀ ⠀⠀⢸⡀⠀⢰⠁⠀⢀⢮⠀⠇⡜⠀⠘⠀⠀⢰⠃⠀⠀⡇⠈⠁⠀⢘⡄⠀⠀⢸⠀⠀⣘⣼⠤⠤⠤⣈⡞⡀⠀⠀⠀⡇⠰⡄⢣⡀⠀⠀⢻⠀⠀⠀⠀ ⠀⠀⠈⡇⠀⡜⠀⢀⠎⢸⢸⢰⠁⠀⠄⠀⢠⠃⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⡆⠀⠀⣶⣿⡿⠿⡛⢻⡟⡇⠀⠀⠀⡇⠀⣿⣆⢡⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⢠⡏⠀⠉⢢⡎⠀⡇⣿⠊⠀⠀⠀⢠⡏⠀⠀⠀⠎⠀⠀⠀⠀⠀⡇⠀⡸⠀⠀⠀⡇⠀⢰⡆⡇⢸⢠⢹⠀⠀⠀⡇⠀⢹⠈⢧⣣⠀⠘⡇⠀⠀⠀ ⠀⠀⢸⡇⠀⠀⠀⡇⠀⡇⢹⠀⠀⠀⢀⡾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠃⠀⠀⠠⠟⡯⣻⣇⢃⠇⢠⠏⡇⠀⢸⡆⠀⢸⠀⠈⢳⡀⠀⡇⠀⠀⠀ ⠀⠀⠀⣇⠀⡔⠋⡇⠀⢱⢼⠀⠀⡂⣼⡇⢹⣶⣶⣶⣤⣤⣀⠀⠀⠀⣇⠇⠀⠀⠀⠀⣶⡭⢃⣏⡘⠀⡎⠀⠇⠀⡾⣷⠀⣼⠀⠀⠀⢻⡄⡇⠀⠀⠀ ⠀⠀⠀⣹⠜⠋⠉⠓⢄⡏⢸⠀⠀⢳⡏⢸⠹⢀⣉⢭⣻⡽⠿⠛⠓⠀⠋⠀⠀⠀⠀⠀⠘⠛⠛⠓⠀⡄⡇⠀⢸⢰⡇⢸⡄⡟⠀⠀⠀⠀⢳⡇⠀⠀⠀ ⠀⣠⠞⠁⠀⠀⠀⠀⠀⢙⠌⡇⠀⣿⠁⠀⡇⡗⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠁⠁⠀⢸⣼⠀⠈⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠁⠀⠀⢀⡠⠔⠚⠉⠉⢱⣇⢸⢧⠀⠀⠸⣱⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠦⡔⠀⠀⠀⠀⠀⢀⡼⠀⠀⣼⡏⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠋⠀⠀⠀⢀⡠⠤⣿⣾⣇⣧⠀⠀⢫⡆⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⣠⠇⠀⠀⢀⡠⣶⠋⠀⠀⡸⣾⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡄⠀⠀⠀⠀⠠⠊⠁⠀⠀⢸⢃⠘⡜⡵⡀⠈⢿⡱⢲⡤⠤⢀⣀⣀⡀⠉⠉⣀⡠⡴⠚⠉⣸⢸⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢧⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠚⣤⣵⡰⡑⡄⠀⢣⡈⠳⡀⠀⠀⠀⢨⡋⠙⣆⢸⠀⠀⣰⢻⡎⠀⠀⡎⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢷⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡸⢌⣳⣵⡈⢦⡀⠳⡀⠈⢦⡀⠀⠘⠏⠲⣌⠙⢒⠴⡧⣸⡇⠀⡸⢸⠇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠢⡀⠀⠀⠀⠠⠄⡖⠋⠀⠀⠙⢿⣳⡀⠑⢄⠹⣄⡀⠙⢄⡠⠤⠒⠚⡖⡇⠀⠘⣽⡇⢠⠃⢸⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⠃⠀⠀⠀⠀⠀⢀⡼⣄⠀⠀⠀⠀⠀⠑⣽⣆⠀⠑⢝⡍⠒⠬⢧⣀⡠⠊⠀⠸⡀⠀⢹⡇⡎⠀⡿⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡼⠁⠀⠀⠀⠀⠀⠀⢀⠻⣺⣧⠀⠀⠀⠰⢢⠈⢪⡷⡀⠀⠙⡄⠀⠀⠱⡄⠀⠀⠀⢧⠀⢸⡻⠀⢠⡇⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⡏⣿⠀⠀⠀⠀⢣⢇⠀⠑⣄⠀⠀⠸⡄⠀⠀⠘⡄⠀⠀⠸⡀⢸⠁⠀⡾⢰⡏⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠐⢦⡀⠀⠀⠀⡠⠒⠀⡀⠀ ⠀⠀⠀⡤⠤⡀⠈⠣⡀⢰⠁⠀⢠⠎⢳⠀ ⠀⠀⡸⠁⠀⠙⢆⢸⣾⢠⠴⠋⠀⠀⢹⠀ ⠀⠀⡇⠀⠀⠀⠀⠙⣯⡇⠀⠀⠀⠀⢀⡇ ⠀⠀⢙⡲⠶⠀⠀⠀⣿⠁⠀⠢⠄⣖⠊⠁ ⠸⡍⠉⠀⠀⠀⢀⡼⣿⢄⠀⠀⠀⠀⡹⠆ ⠀⠀⠙⠒⠂⠋⠁⠀⠉⠀⠈⠉⠉⠁⠀⠀
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⢀⠂⠄⠀⠀⠠⠀⠄⠀⠄⠠⠀⠄⠠⠀⠄⠠⠀⠄⠠⠀⠄⠠⠀⠄⠠⠀⠄⠠⢀⠠⠀⠄⠠⠀⠄⠠⠀⠄⠠⠀⠄⠠⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠄⠠⠀⠄⠠⠀⠄⠠⠀⠄⠠⠀⠄⠠⠀⠄⠠⠀⠄⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠠⠀⠄⠠⠀⠄⠠⠀⠄⠠⠀⠄⠠⠀⠄⡀ ⠠⢈⠀⠀⠀⡐⠀⠂⠌⠐⡀⠂⠐⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠄⠂⠀⠡⠐⢀⠂⠌⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠟⠛⠛⠛⠒⠦⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠄⠂⠐⠠⠈⠐⡀⢂⠐⢀⠂⠐⠠⠁⡐⠀⢂⠐⡀⠂⠐⡀⠁⠄⠠⠀⢂⠐⠈⠄⠂⡐⠀⠂⠄⠡⠐⠠⠈⠐⡀⠡⠐⢀⠂⠐⡀ ⠐⠠⠀⠂⠀⠀⠂⠁⠐⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⢀⡤⣀⡀⠀⡠⠜⠚⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠁⠀⢀⠀⠂⠄⠂⡁⠐⠠⠀⠌⠀⠄⠐⠀⡁⠠⠐⠈⢀⠐⠀⠂⡐⠀⠂⠄⡈⠄⠂⠐⠠⠁⠂⠁⡐⠠⠐⠠⠐⠠⠀ ⠀⠐⠀⠄⠀⠁⠀⠄⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠁⠀⠀⠀⠀⠀⠀⢧⢠⠬⠨⠔⢺⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠐⢀⠈⠐⠀⡐⠀⠌⠀⡐⠈⠀⠄⠈⠄⠂⠀⠀⡀⠀⠀⠌⠀⠀⠀⠐⠀⠁⡐⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠦⠀⠀⠐⠒⠒⠶⠶⠶⠶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢠⠇⠀⠀⠘⢦⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠁⠄⠈⠄⠂⢀⠐⡀⢂⠈⠀⠀⠀⠀⠀⡐⠀⠀⠠⠀⠀⠄⠈⡀⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠶⣤⡀⠀⢀⣀⣠⣤⣤⣼⡋⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⣞⣀⣓⡒⢄⢠⢞⡩⣽⡖⠛⠛⠛⠛⠛⠛⠷⠶⠶⢦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢂⠀⠂⠄⠂⡐⠀⠌⠀⠈⠀⢀⠀⠁⡀⠄⠈⠀⠄⠀⠀⠐⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡟⠉⠉⠉⠉⠉⠻⣦⡀⢀⠖⠋⡙⣳⠄⠀⠀⠀⠀⠀⠐⢌⢃⠎⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠈⠀⠈⠀⠄⢀⠀⠀⠀⠠⠐⠀⠀⠂⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠬⢹⣦⠀⠀⠀⠀⠀⠈⢻⣇⠠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⢙⣏⠉⠉⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⡀⠠⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀ ⢇⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⢧⠀⠀⠀⠀⠀⠈⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠋⠈⠉⠉⠉⠛⠫⢷⡦⣄⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⢼⠋⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⣦⠀⠀⢐⡀⠀⢸⡇⠀⠀⢀⣀⣤⣦⠤⡤⠤⠤⠤⠤⣄⣀⣀⣀⠀⠀⠸⣆⡟⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣳⡄⠀⠀⠀⣹⣦⡀⠀⠀⠀⢠⠶⠛⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⣦⡟⢀⣴⠿⠿⢷⡾⡷⣾⣯⣭⣩⡅⡄⠒⠠⠡⢈⠔⡀⠠⢐⠈⡉⠛⣶⡄⡷⢻⡈⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠘⣿⣄⣤⠞⠁⠈⣷⣄⠀⠀⠘⠦⣀⣀⣀⠴⠃⠀⠀⠀⠀⠀⠀⠀⢀⣤⡞⣭⠟⠊⠄⠻⠛⠁⠄⠀⠀⠀⠀⠀⠀⠈⠙⠪⣍⡛⠓⠦⢥⣐⣀⠑⡈⢄⢁⣖⣽⡿⠁⠘⡇⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣽⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠢⡄⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠈⢟⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡤⣖⣚⣹⡶⢋⠡⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣇⣄⡀⠈⠙⠛⠋⠛⠉⠁⠀⠀⠀⢸⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡆⠀⢿⣍⣀⠀⠀⠀⠀⠀⠀⠀⢩⢿⣄⠀⠀⣤⣶⠛⠋⠍⡉⠄⢄⣐⣾⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⢦⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⣀⠤⠔⣮⠀⠀⠀⠈⢉⣿⣷⢶⣤⡀⠀⠀⠀⠁⠻⣦⡸⡟⢁⠐⡈⠐⣠⣼⣶⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢶⣄⠀⠀⠀⠀⠀⠀⢰⡇⠄⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢇⣀⡠⠃⢀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⢶⡉⠀⠀⠀⠓⠦⣀⣠⡾⣛⠽⠁⠀⠙⣿⡄⠀⠀⠀⠀⠈⠛⠿⠷⠾⠾⠿⠛⣩⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣷⣄⠀⠀⠀⠀⣸⠡⠀⠀⠀⠀⠀⣀⣄⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⠀⠠⡀⠂⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣹⣦⣀⠀⢀⣴⠾⣫⡾⠋⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣿⣝⢷⣄⡀⢠⡟⠃⠀⠐⣸⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠠⠀⠘⣁⡨⠂⡞⠉⠳⠤⠓⡀⠀⠘⣯⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢢⡞⠁⠀⢈⣷⡟⠁⣼⠏⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⢠⡼⢋⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡈⠛⠛⠀⠀⠀⢀⡿⢷⣄⠀⠀⠀⠀⠀⠐⠈⠄⢁⠂⡐⠠⠁⠈⠄⡀⣠⠞⠁⠀⠀⠀⠰⡁⠀⠀⢹⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⡿⠃⠀⠘⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀⠀⣴⠟⢁⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⣸⠇⠀⠙⠻⣦⣄⠀⠀⠌⠀⠌⢀⠂⠀⠀⠀⠀⠐⠀⢉⠢⢤⠀⠀⢀⣀⡘⠂⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⠏⠀⠀⠀⠀⠈⠙⠿⣦⣄⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⢠⣾⠋⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⢠⡟⠈⠀⠀⠀⠈⠙⠿⣶⣄⡈⠀⡀⠐⡀⠄⠀⢀⠐⡀⠂⠠⠀⢇⡤⠉⢀⠀⢀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡶⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠻⣶⡿⠁⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⡻⢷⣦⣀⡀⠀⠀⠀⠠⠀⠁⠂⠐⢀⠀⡐⠀⠀⠀⣼⡻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠉⠙⠻⠟⣶⣦⣤⣀⣀⣀⠀⠀⣀⣀⣠⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡄⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⠀⣰⠦⢄⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠶⠒⠒⠒⠒⠒⠂⠐⠀⠒⠒⠈⠉⠐⠦⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠙⠒⠋⠉⢹⠁⠀⠀⣀⣤⡶⠶⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀⢠⠾⠋⠀⠀⠀⠀⠀⠀⣎⣤⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢋⡀⠀⠀⠀⠀⠀⠠⢾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⢁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠷⠀⠀⠀⠀⢠⠀⠀⠈⣹⠶⠀⠀⠀⢀⣀⣀⣀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠂⡐⠠⠀⡀⢀⠀⢀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⡈⢻⠉⠉⠁⠀⠣⣀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⡀⢀⣀⣤⣴⡄⠀⠀⠀⠀⢹⡇⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⠠⠁⠐⡀⠂⠌⣀⠂⠄⡁⢂⠈⠄⡁⠀⢠⡾⠇⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⢿⣝⣯⡾⠟⠁⠀⠀⠀⠀⠀⣿⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠄⠁⠂⠄⢁⠂⣤⢌⡒⢀⠂⠌⠀⠔⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠞⢒⣶⠄⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠡⠐⠠⠁⠈⡤⢆⢸⡁⠀⡵⠀⠈⢀⢈⣶⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠒⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠂⠀⠦⠞⠀⡉⠉⢀⠈⠀⣤⡿⣿⡈⣇⠀⠀⠀⠄⠂⢀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣣⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉⠀⣠⣶⠿⠛⠋⠉⠉⠁⠈⠉⢩⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⠿⠽⠯⢟⣳⣖⡤⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⣠⡴⠒⠦⢤⣤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣁⣀⣀⣠⠤⠤⢤⡀⠀⠉⠚⢭⣳⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⡾⠅⡆⠀⢀⠎⠀⠀⠀⠈⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⠀⠀⢹⠀⠀⠀⠈⢢⠀⠀⠀⠈⢻⣣⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣧⣄⣀⢰⣀⣀⠼⠀⠼⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⣤⢦⡀⣀⠀⢸⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠶⣤⡄⠀⠀⠀⠀⠀⠀⣴⣿⣿⢿⣿⣶⠶⠟⠛⠛⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠉⠛⠷⠾⠛⠛⠛⢻⣿⣿⣻⣾⣽⣿⣆⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣞⣿⣿⣿⡿⣿⣿⣶⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⣯⠿⣿⣽⣷⣻⣿⣿⣷⣻⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⣿⣿⡟⣷⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⠿⠟⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠛⣿⠛⠃⠀⠀⢰⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⠀⠀⠀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣤⡤⠀⠀⠈⠏⠁⠀⠀⠀⢀⡤⣤⡀⠀⠀⠀⠈⠹⠁⠀⠀⠀⢹⡿⠿⠧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢳⣄⣠⠄⠀⠀⠀⠀⠀⠀⠈⠓⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⣦⣾⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠛⢻⡷⠚⠛⠛⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠛⠛⠺⣯⠀⠉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⡏⠀⠀⠀⠀⠀⢈⡷⠶⠦⣤⣤⣤⣤⠶⣏⠀⠀⠀⠀⠀⠈⡷⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣀⠀⣀⣀⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⣀⡀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣶⣦⣄⠀⢀⣤⡴⠾⠛⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣻⢞⣳⢯⣿⣿⡋⠁⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡴⠶⠶⠶⣤⣤⣄⡀⢀⣀⣤⣤⠶⠶⠞⣿⡿⣞⡷⣯⣿⣿⣼⣿⣷⣤⣄⡀⠀⣀⣠⣸⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠀⠀⣿⡿⣽⡽⣻⣿⣽⣿⢿⢯⣟⠿⣿⣿⣿⣻⣟⡿⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣧⢿⣽⣻⣿⡿⣯⣟⢾⣻⡽⣿⣷⣿⣞⣽⣳⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢾⣿⣾⠷⠟⢿⣷⣯⣟⣳⣿⣿⣿⡿⣞⣧⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣽⣳⠿⣽⣾⠿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠛⠋⠁⠀⢹⡆⠀⠀⠀⠀ ⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣿⣤⡤⠦⠴ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⣿⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⢶⣤⠀⠀⠀⠀⢠⣤⣿⣤⣤⣀⡀ ⢀⣀⣤⣼⣷⡤⠤⠄⠀⠀⠀⢀⣠⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀ ⠉⠉⠀⠀⢻⡄⠀⠀⠀⠀⠀⠘⠏⠀⠀⠉⠀⠀⠀⠀⠀⢠⡖⠒⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣾⣁⡀⠀⠀⠀ ⠀⠀⠀⣀⣨⣿⡶⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠉⠉⠙⠛⠒⠀ ⠀⠀⠘⠉⠁⠈⠻⣦⣀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡾⠿⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠉⠛⠛⠶⠶⠦⣤⣤⣤⣤⣤⣤⠴⠶⠶⠶⠚⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⡀⣀⡤⢤⡄⡀⠀⠀ ⠀⠀⠀⠈⢠⠞⠉⠓⡶⠄⠀⠀⠀⢠⠏⠀⢀⢹⠅⠀⠀⢷⠀⠄⠀ ⠀⠀⢀⠀⢼⠀⢀⠁⠀⡀⠀⡀⠀⢸⠀⠐⢵⠉⠉⢳⡚⠛⢳⠀⠀ ⠀⠀⠀⠀⠘⡁⠀⢀⠁⠂⡀⠀⠂⠉⠛⢛⠛⠦⣤⠾⠜⢀⡾⡀⠃ ⠀⠀⠐⢠⠃⠡⠀⠀⠀⠀⠀⠀⠀⠠⠀⡘⠀⠀⠀⠛⠒⠋⣀⢄⠃ ⠀⠀⠠⢬⣧⠤⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⠍⠉ ⠀⠀⠀⢀⣿⡴⠒⠘⠛⠀⠀⠀⠐⠒⡄⠀⠀⠉⠈⠯⢀⣜⡏⠉⠀ ⠀⠀⠀⠀⣀⡵⢾⣀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣀⡴⠋⠙⠂⠀ ⠀⠀⠀⡾⢭⣱⢀⡭⠟⡶⢶⠶⠤⠤⠤⠴⠶⣾⠻⢭⡀⠀⠀⠀⠀ ⢀⣠⠎⢀⠐⠞⣝⣩⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠉⠒⢦⠀⠀ ⠸⣌⣧⣛⣙⡼⢡⠏⡀⠀⢀⠀⡀⠀⢀⠀⡀⡀⢀⠙⡀⠀⣩⠀⠀ ⠀⠀⠀⣎⣘⣦⡼⠒⠈⠀⠁⠈⠈⠀⠁⠁⠈⠀⠁⡒⢣⠒⠁⠀⠀ ⠀⠀⠀⠀⠀⠸⣇⢄⠄⣀⢀⡀⠀⠀⢀⢀⢀⢠⠨⡰⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠃⠁⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠦⠄⣀⣄⣀⠥⣀⣀⣀⠠⠴⠊⠀⠀⠀⠀⠀
⠀⠀⠀⠄⣠⡶⠶⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠈⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⡟⠙⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⢶⣾⠛⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠉⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⢻⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⠀⠁⠄⠀⠀⠀⠈⠙⠻⣦⣤⠔⠂⠈⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⢿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠙⠻⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⠟⠁⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⢸⣇⣀⣠⣤⣴⡶⠶⠶⠶⠶⣼⣧⣄⣀⠀⠠⠀⠀⠀⠀⠀⠈⣿⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢸⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢷⣦⡀⠐⠀⡀⠀⠸⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣷⣄⠐⠀⣠⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡾⠋⠀⠤ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣦⣤⡄⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣄⠀⠁⠐⠘⢷⣄⠀⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠄⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢻⣆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⡏⠀⢸⣿⣿⡏⠀⢹⣿⠀⠀⠀⠀⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠂⠀⠂⠀⠀⠂⠀⠀⢐⢀⡀⡂⣀⣢⣦⣆⣀⠘⠷⣤⣾⣿⣿⣷⣤⡾⠃⣀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠁⠀⠀⡀⠀⠀⠀⠀⠌⠁⣠⣶⠾⠋⠙⠐⠋⠛⠷⣦⡸⡛⠛⠻⢏⣠⡷⠟⠛⢷⣄⠀⢸⡧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⢘⣴⡿⠋⢀⡀⣀⣀⣀⠀⠀⠀⠈⠛⠷⣮⡾⠟⠻⠀⠀⠀⢀⠹⣷⣸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠐⣾⠋⠀⠈⣳⢟⠉⠉⠙⣷⡀⠁⠀⠀⠀⠀⠀⠀⢀⡵⠚⠛⣾⠆⢸⣿⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠂⠀⠀⢽⡏⠀⠀⣠⢅⣤⡥⡠⠀⠙⠁⠀⠀⠀⢰⡋⠉⣷⠘⡃⠀⢠⣿⢀⣾⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠽⢿⣦⡀⡁⠜⣷⡀⠼⢡⢫⢎⡜⠀⠀⠈⠀⠀⠀⠤⡖⡛⠭⡆⠀⡃⢠⢻⣷⡟⠁⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡾⣄⠀⠀⠀⠀⠀⠈⣛⣷⣶⣽⣷⣄⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⣷⣠⣎⠀⣁⣤⡿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠀⢀⡼⠀⠙⢶⡄⠀⡞⠉⢱⣿⣯⣤⣤⣭⣽⣿⡟⠛⠛⢿⣶⡶⠞⠛⠻⣯⠁⠈⠻⣿⠋⠁⠀⠀⠀⠀⠁⠀⠀ ⠀⠀⢠⠞⠁⡰⣿⣥⡄⠀⢶⠛⠂⠉⠛⠉⡉⣩⣿⠋⠀⠀⠙⢷⣄⣴⠿⠋⠀⠀⠀⠀⢹⡇⠀⣠⡿⢻⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⠃⢠⠞⡠⡇⠈⢷⡀⠈⢷⡀⠀⠀⣠⡾⠫⠁⠀⠀⠀⢰⡏⠉⢳⠀⠀⠀⠀⠀⢠⣿⠁⢸⡟⠒⠋⢈⠀⠀⠀⠀⠁⠀⠀ ⢠⠇⣠⠟⠋⠀⠓⠒⠒⠳⣄⠀⠙⢦⣼⡋⠀⠀⠀⠀⠀⡀⠈⠙⠒⠋⠀⠀⠸⣷⡀⠀⢀⣴⠟⠁⠀⠀⠀⠄⠀⠀⠀⠂⠀⠀ ⢸⠀⢹⠳⣄⠀⡞⠉⠓⠲⠬⣙⣶⣤⣀⣉⣻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡾⠟⠋⠀⠀⠀⠀⠀⢈⠀⠀⠰⠁⠀⠀ ⣸⠀⢸⠀⠈⠑⠇⢀⡤⠒⠋⣉⡿⠾⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀ ⠹⡀⠈⢦⠀⢸⠓⠋⢀⡴⠋⠁⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀ ⠀⢳⡀⠀⠀⢸⠀⠀⢘⣦⠄⠀⠀⠀⠀⢻⡆⠀⠀⠸⣦⠀⠀⠀⠀⠀⠀⠀⠸⠿⣦⣄⠀⠀⢀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀ ⠀⠀⠉⠀⠀⠸⠔⠊⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀⠀⠀⠁⠠⠠⠠⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣤⣤⣬⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡖⠋⠉⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⢏⣀⠀⠀⠀⠀⠀⠈⣷⣠⡤⠶⠶⠶⠶⠶⠦⣤⣴⡋⠀⠀⠀⠀⣀⣤⣌⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠈⠉⠙⠳⡄⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣤⠞⠁⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡄⠀⠀⣠⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⣠⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠳⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡞⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⣿⣿⣆⠀⢀⠄⣀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠈⠛⠛⠃⠀⠁⢸⣿⣇⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠤⠊⠀⠀⠘⠟⠉⠙⠓⠀⠀⠀⠁⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⣴⡋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠙⠳⡤⢤⠤⠤⣤⣤⣤⣤⡤⠄⢤⠞⠉⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⠀⠀⠓⡔⠳⡀⣠⣶⣶⢤⠀⠀⠀⠀⠀⢀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣻⠀⠀⠈⢏⢉⡿⣿⢿⣼⣄⣀⠤⠠⣼⣟⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⠀⠈⠂⡞⢹⠿⠁⠀⠀⠀⠀⠨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠙⠛⠛⠳⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⡖⠀⠀⣀⠀⠙⣧⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠆⣼⠉⠀⣸⡇⠀⣰⠏⠁⠊⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣰⠀⠀⡆⠀⠀⠀⠀⢠⣯⠓⠧⣄⠐⣣⣴⠾⠿⡶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⢀⠀⠘⡄⣀⣤⠶⢞⢛⡲⢤⣠⢞⡡⠞⠋⡙⠓⣟⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠙⢶⡿⠋⠈⠀⠀⣼⣿⣿⣿⡻⣿⠡⠀⠈⣀⣼⣦⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢷⡀⢠⣠⡀⠙⠟⠁⣀⠿⣽⣋⣉⣉⣭⠴⣿⠷⠶⠦⠤⠤⠤⢤⣤⣄⣀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⢿⣷⣙⡷⠄⠘⠃⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠛⢶⣝⢷⡄⠀⢀⢄⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⠀⢻⡄⠈⠛⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⣷⣆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣎⣧⠂⠀⠙⡶⠀⠀⢘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢟⣖⣳⣶⠦⣤⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⡿⠀⠀⣴⣧⣀⣀⣸⣾⡷⠄⠀⠀⠀⢤⣤⣤⡴⠾⠚⠛⠉⠍⠙⠛⣻⣤⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠴⠶⠚⠉⠀⠈⠉⠉⠙⠓⠶⠶⠶⠞⠋⠉⠁⠀⠀⠀⠀⠠⣞⣿⣟⣻⡴⠋⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢷⡼⣧⣤⣤⣤⡤⠀⠀⢀⣤⠞⢩⣶⣿⣿⣿⡹⣭⢯⡝⢫⣭⢷⣩⢯⠙⣔⣷⣿⡿⣟⡻⢏⣟⣹⢏⡟⣽⢫⣴⡟⡠⢬⢇⣨⢭⣹⡉⣧⢈⢿⣷⡌⢿⡜⢯⣙⣏⢿⣯⡿⣿⣿⣶⣈⠱⢦⣘⠈⡥⣉⣉⠛⣯⣟⢻⢯⣗⠀⠉⠷⣤⡈⠲⣤⣤⣀⡀⠘⣿⡇⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡠⠤⠐⠒⠒⠒⢒⣒⣀⣶⣴⢿⣷⢻⣯⣿⠏⣀⣤⣶⡿⠃⣴⢡⢿⠉⠀⠘⢷⡇⡋⣬⡗⣏⡶⢉⠦⣽⡿⣯⢷⡙⢶⡙⢎⠶⡱⣎⣞⠣⣳⡟⡰⢹⡏⢆⠯⡖⢧⢳⠹⡎⢌⢻⣿⡄⢻⣇⠳⡜⠲⣌⠳⣌⠿⣽⢿⣦⡌⠹⣶⡀⠆⡐⠢⠈⠹⣎⡝⣿⣦⡀⠀⠙⢿⣦⣙⢿⣿⣿⣶⣾⣴⠿⢶⢖⣂⠒⠒⠒⠂⠀⠤⢀⣀⠀ ⠀⢀⠞⣁⡠⠴⠖⢚⡻⠟⢋⣉⣠⣴⠚⠉⣿⣯⣿⣿⡾⣿⣿⠋⣠⣾⣷⠏⠀⠀⣄⠀⠘⣷⠾⡹⡜⠎⡐⣥⣿⢿⡽⣋⢦⡛⢤⡙⢎⡱⢓⡜⠬⣱⡿⢱⢡⣛⡜⣌⠣⡝⢎⡳⢘⣳⠈⡆⢿⣿⡄⢯⡳⡘⠧⢌⠓⡸⢦⠙⣿⢞⣷⡔⡈⢻⣦⡀⠑⠌⠀⠸⣆⠹⣎⢻⣄⠠⣄⠹⣿⣿⣷⣟⡾⣽⣿⠄⠈⢷⣤⣉⠛⠭⣉⠉⠀⠐⠀⣤ ⢀⣡⠞⠁⢀⠄⢊⡥⢶⢚⡏⣭⣿⠿⣾⣿⣿⣿⣷⣯⢿⡽⢁⣼⢏⣾⢻⣄⡀⠣⠍⢳⠞⠉⢳⣯⣁⣢⣽⡿⢯⡟⢡⣲⠏⡜⢢⡉⠦⡑⢞⣨⣳⣿⠱⡉⢆⡳⠐⡌⠣⠜⢢⢙⠢⣙⠖⡈⠆⢿⣷⡀⢿⣅⠣⢌⡘⠤⡉⢷⠘⢿⡜⣿⣆⠄⠹⣿⣆⠈⡐⠀⠘⠧⣞⠂⠹⣦⠹⣦⡘⣿⡾⣽⠿⢷⠷⢲⣤⠼⣿⣝⡻⢳⠶⣕⠢⣀⠀⠈ ⣱⠏⡠⠊⢀⡾⢫⡜⣣⣫⡼⣿⣇⠀⠀⠉⠑⣦⣼⣿⠟⢀⡾⢡⣾⡿⠏⠻⠛⠛⣷⣯⡠⣀⢮⡀⠀⠈⠉⠻⡏⠐⣵⠋⡔⡈⠆⡘⢠⠙⢤⣿⣿⠃⢆⡙⢢⠇⡑⠌⡑⢨⠁⠎⡰⢈⡇⢘⡈⠌⣿⣇⠘⣷⡈⠆⠨⢐⠁⢎⢣⠘⣿⡸⣿⣧⠀⠸⣯⢒⠰⡀⠀⠀⠙⢀⡤⣜⣧⡹⣿⣤⢿⡿⣿⣷⠖⠉⠀⠀⢹⣯⣝⣣⠟⣜⢳⣄⠑⢄ ⡿⠊⠀⣰⠋⡴⢳⣼⠗⢁⣼⡟⠉⠀⠲⠤⣼⡿⣯⠏⣠⡟⣡⣿⡿⢁⠍⠱⢈⠰⡼⢃⣻⣧⠀⠉⠀⠀⢤⣼⠃⣾⠏⠐⡀⠂⠄⠡⢂⢍⣾⣿⠣⠍⠠⡸⠰⢁⠰⢈⠐⠠⠘⠠⢐⠂⢭⠐⡀⠎⢸⣿⡄⠘⣷⠈⡁⠂⠌⢂⠐⡂⠘⣷⡙⣿⣧⠀⠘⣧⢒⣹⡄⠀⠴⠋⢧⡘⣟⢷⡘⢿⣮⢻⡗⣿⣧⠀⠀⢀⠘⣿⣷⡬⢟⡬⢣⢎⠳⡄ ⠀⠀⠠⠃⣘⡶⠛⠁⣰⣿⣿⣷⠀⠀⠀⣼⣿⣻⠏⣠⡟⢠⡿⣾⠃⡈⠄⠃⡀⠰⢡⠣⠏⠘⢦⡀⠰⣡⡞⠁⣰⡟⠀⠂⠀⡁⢈⠡⠂⡾⣿⡟⡰⠈⠄⡃⠜⠀⠂⠄⡈⠄⡁⠂⢄⠈⠒⡌⠐⡀⠂⢻⣧⠀⢻⣇⠐⠈⠀⠠⠐⢀⠀⠘⣧⠘⣿⣷⠈⠻⣏⢧⠳⡤⠀⠀⠈⢷⡘⣯⢷⡌⢿⣇⠹⣯⢿⣧⠒⣁⡔⢻⣾⣻⣎⢲⢃⠮⣑⠻ ⠀⠀⢀⡱⠊⠁⣠⣿⣿⣿⣿⡃⠀⠠⢴⢻⣷⠋⣰⡟⢠⡿⣽⠃⠐⢀⠂⠄⠠⢁⠦⠃⠀⢠⣿⣿⣿⠏⠀⢰⡿⠁⠀⠀⠁⠀⠄⡚⢐⣻⣿⢡⡇⠐⠠⡁⠎⠀⠁⠠⠀⠀⠐⠈⠀⢈⠐⠆⠡⠀⠈⣈⣿⠀⠈⣿⡆⠀⠠⠀⠀⠀⠀⠀⠹⣆⠸⣿⣧⠀⢹⣎⠒⣷⠀⠀⠀⠈⢷⡸⣇⢿⡈⣿⣆⠹⣟⠼⡟⠁⢀⣾⡜⡛⠿⢷⣌⠱⢌⠒ ⠀⠀⠂⠀⣀⣼⣿⣿⡟⠋⣿⡗⠀⢀⡾⢸⠇⣰⡟⢠⣿⢳⠃⠀⠠⠀⠀⢀⠡⢌⠂⠀⢀⣾⡿⢠⠁⠀⠀⣿⠇⠀⠀⠀⠀⠀⢸⠇⡼⣻⡇⣾⠀⠀⠐⠄⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⢍⠀⠂⠀⢸⢸⡇⠀⢸⣷⠀⠀⠀⠀⠀⠀⡀⠐⣿⡄⠸⣿⣇⠀⢻⡄⠘⡇⠀⠀⠄⠈⢧⢻⡎⢷⡸⣿⡄⠹⡇⢹⡤⠎⢹⣧⠙⣜⠂⠻⣷⡌⢈ ⠀⠠⢈⣠⣿⣿⠟⠡⠀⣠⣿⡇⠀⢹⢇⡞⢰⢧⠏⣼⣏⠆⠀⠀⠀⠀⠀⠄⢂⡜⠀⠀⣼⣿⠇⣾⠀⠀⣸⡿⠀⠀⠂⠀⠀⢀⣾⢠⠅⣿⢀⡯⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠄⠀⢸⡛⣿⠀⠀⣿⡆⠀⠀⠐⠂⠀⣘⠀⠀⣷⠀⢻⣿⡄⠘⣷⠀⠀⠀⠄⠀⠐⠈⡄⣿⡚⣧⢹⣷⠀⢻⠈⡇⠠⣿⢐⠫⢌⠳⡀⠹⣿⣄ ⠀⠀⣼⣿⠟⠁⠠⢀⣾⣿⢿⣧⡀⣼⡿⢀⣿⡞⣸⡟⡌⠀⠂⠀⠀⠀⠀⠂⡜⠀⠀⢰⣿⡿⢠⡇⡎⢠⣿⠇⠀⠀⠀⠀⠀⢸⠇⡎⢸⡏⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⢀⠆⢸⠀⠀⠄⠘⡇⣿⡄⠀⢸⣷⠀⡀⠀⠒⠉⠁⠠⢠⣹⣇⠈⣿⣷⠀⢸⣇⠠⠀⠀⠂⠈⢀⠐⢸⣷⢹⡎⣿⣇⠈⣆⣧⣼⢿⡄⡉⢎⡡⢑⡀⠈⢿ ⢀⣼⠟⡁⠠⠐⣰⣿⡿⣋⣾⡿⣿⣿⠇⣸⣽⢁⣿⠞⢁⠂⠀⠀⡀⠄⠁⡘⠀⠀⠀⣼⣿⠇⣼⢱⡇⢸⡿⠀⠀⠀⠠⠀⠀⣾⠂⠀⣾⠇⣾⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣤⠒⣇⢻⡇⠠⠘⣿⡆⠀⢀⢂⠠⠁⢂⠘⣏⣿⠄⣻⣿⣇⠀⢿⡀⠄⠀⠐⠈⠀⠌⠀⢿⣎⣿⣼⣻⡄⠸⣹⡧⢏⣷⠘⡠⢑⠂⡄⠀⠈ ⡟⠁⠀⠀⢂⣴⣿⡟⣵⢫⣿⣟⣿⡟⢀⣿⡏⢸⣏⠏⢠⠀⠂⠁⠀⠀⢄⡉⠀⠀⢠⣿⣿⢠⡏⣾⠃⣿⡇⠀⢌⠐⡀⠐⢈⣿⡀⢰⣿⢡⣿⠀⠀⡀⣼⡀⠀⠀⡀⠀⠐⠦⠤⠖⠃⡈⠀⢼⡆⠉⠀⠠⣿⢸⣿⠐⡄⣿⣇⠈⡀⢸⠀⡈⠄⠂⣿⢹⡇⢸⣯⣿⠀⠸⡅⠠⠀⠂⢁⠈⠄⡑⠸⣷⣚⣧⣟⣇⠀⢷⣯⣛⣼⡇⢱⡈⠥⠐⡀⠀ ⠀⠀⢀⣴⣿⡿⣙⠮⣇⣿⡿⣞⣿⠃⢸⣿⠃⣾⣻⠀⡃⠠⠐⠀⠡⠈⠤⠀⠀⠀⣼⣿⡗⣸⢷⣿⢠⣿⠆⠣⢌⠒⡄⠂⣼⣇⠃⣼⣿⣸⣿⢀⠱⢀⣿⡄⠈⠄⡐⢈⠀⡀⠐⢂⠡⠄⣉⢸⣧⡀⢂⠐⣿⢸⣿⡘⡤⢸⣿⠀⡆⢸⡁⠐⠠⠡⢼⣿⣯⢘⡷⣿⡇⠀⡇⠐⡀⢁⠠⠈⠄⡀⢃⢿⡜⣿⡼⣿⡀⠸⣷⣏⠶⣿⠀⢱⢂⠡⠀⠀ ⠀⢀⣾⣿⡿⡱⢏⣳⢺⣿⣻⣽⡏⠀⣼⡿⢰⣿⠣⡘⢄⠡⢀⠁⠂⢌⠂⢁⠀⡁⣿⣿⡇⣿⣿⡏⣸⣿⡇⡹⢌⡚⢤⠁⣿⡇⡌⣿⢟⣾⣿⢀⣷⠟⣿⠂⠄⣃⠘⡄⠂⡀⠘⡄⢊⡐⢄⢺⠇⠹⣦⠘⣿⢸⣿⡕⣣⢸⣿⢀⡇⢸⡁⢈⠄⡑⢺⣟⣿⢈⡿⣽⣇⠀⢼⠀⠔⠀⠄⡁⠆⡐⢨⢸⣟⡽⣷⣻⡇⠀⣿⡞⣭⢻⣇⠈⣧⠀⡀⠁ ⣰⣿⣿⠟⢠⢯⣙⠦⣿⣿⣽⢾⠃⠀⣿⡇⢾⣯⠃⡜⡀⠆⢠⠈⠰⡈⠆⢀⠂⢀⣿⣿⢧⣻⣿⠇⣿⣿⡧⡱⢎⡜⢲⢠⣿⢳⣘⣿⣾⣿⣽⠿⡱⠆⣽⠃⠰⣀⠧⡘⠠⠄⢘⠄⢣⠐⡌⢜⡂⠱⣌⢻⣿⣼⣿⡗⣱⢸⣿⠂⣿⠠⢇⠌⡰⢈⠵⣺⣿⠆⣿⣹⣿⠀⠈⡄⢂⠁⢂⡐⡐⠨⠰⣈⡿⡼⣿⣽⣧⠀⢸⣏⡷⢫⢿⡄⠘⡧⠐⠀ ⣿⣿⠋⢀⢎⡳⢎⢳⣿⣿⢏⣿⠀⢸⣿⡱⣿⡽⠒⡤⢑⠨⠐⢨⠐⡱⢈⠠⠐⢸⣿⣿⢲⣽⣿⠃⣿⣿⡧⣙⠮⡜⣭⢰⣿⢣⣼⣿⣿⡿⣹⠽⣘⠇⣾⣁⢳⡐⢆⠳⣀⠃⢨⠎⡄⠣⢜⡸⢀⡓⢬⢸⣿⢿⣿⣯⣦⣹⣿⠇⡿⢈⡇⢎⠰⣉⠒⣿⣿⣃⠶⣏⣿⡄⠂⡅⠂⢌⠠⠐⣈⠑⢢⡐⣿⣳⢿⣷⣿⠀⠀⣿⢭⣛⠾⣇⠀⠹⡀⠄ ⣿⡃⠖⡜⣮⠝⣌⣿⣿⡟⣾⡇⠀⣸⣿⠁⣿⡝⡰⢡⠊⠤⠉⠤⢨⡑⡀⠆⢡⢸⣿⡝⢮⣼⡿⡡⡟⣿⡇⡙⠦⣑⣦⣼⣿⣿⢿⡇⣿⡇⢸⡏⣜⠣⣿⢆⢣⡜⢎⡱⢂⡅⢘⠆⡌⠱⢨⠜⡠⠜⢢⢹⣿⣸⠸⣏⠿⣿⣿⣧⣟⡤⠓⡌⠒⠤⡙⢾⣿⡇⢞⡽⣻⡇⠀⣂⠁⠎⡄⠱⠀⢎⠰⡄⢻⣽⣺⣿⣾⠀⠀⢸⡧⣏⣟⣻⡄⠀⠱⠀ ⠧⡉⢾⡹⣬⠓⣼⣿⡟⡼⣿⠃⠀⣿⣟⢸⣟⠧⣘⢡⠊⡔⢡⠂⡱⠂⡄⡃⠄⢸⡷⣏⠲⣽⡷⢱⡇⣿⣧⣵⣾⡿⢟⢻⣿⠐⣺⡅⣿⡇⢸⡗⣌⠳⣿⢎⠲⡜⢪⡑⢣⠄⢸⠐⡈⢅⢊⡝⢠⠉⠦⣹⣿⡿⠀⣏⠰⣹⢹⣻⡿⢿⣷⣬⣕⣢⠡⣿⣿⣯⢘⡷⣻⡇⠀⠤⢁⠚⡄⢃⠉⢆⠱⣊⢽⡶⢯⣿⣾⡃⢰⠀⣿⣳⢮⡽⣇⠀⠀⢣ ⠢⢱⢏⠶⡡⢎⣿⣟⡾⣹⣿⠀⠀⣿⢯⢸⣿⢂⡇⢆⢣⠘⡠⠌⣱⠁⠖⡁⠂⢸⣏⠇⣌⣿⣷⣾⡟⣿⣿⠑⡐⠰⢨⢻⣿⠐⣻⠀⣽⡇⠘⡷⢈⢳⣿⡏⡜⢌⠣⡘⠥⠊⠤⠁⠌⡐⢨⡇⠢⣉⠐⣿⢻⡇⠀⣯⠐⣹⢸⡱⣟⠲⠄⢩⢉⠛⠷⣿⣿⣿⣌⡳⣹⡇⢀⠣⠄⢃⡖⢈⠡⢊⠔⡣⢼⣻⡽⣾⣿⡅⠐⡀⢻⣽⣚⡧⣿⡀⠀⠄ ⢧⡙⣮⠑⣂⢾⣟⢾⣱⣿⡿⠀⢸⣿⡃⣼⣟⢢⠞⡌⢆⠱⢀⠆⣱⠈⡧⡥⠤⢾⡟⡛⠉⣿⡇⣸⠁⣿⣿⠀⢂⠁⠂⣿⣿⠀⣽⠀⢺⠇⠀⣟⠨⢢⣿⡧⠘⡀⠣⠘⣈⠁⠄⠃⡐⠈⣼⡇⠑⠠⢌⡇⣼⠇⠀⣇⠠⢹⢸⣜⣯⠰⠁⠂⠄⡉⢐⣿⡇⣿⢉⡟⣷⡷⠤⢣⢌⡠⢳⠈⢆⢡⠊⡵⢚⡷⣝⡾⣿⡅⠀⡆⠸⣟⣞⣷⣹⡇⠂⢠ ⢧⡙⢆⠱⢠⡿⣹⢮⣽⣿⡇⠀⢸⣷⡃⣿⣻⢌⠞⡰⢊⠔⠡⢊⠴⢈⠖⡐⠀⢸⠇⡇⠈⣿⡇⢸⠀⢹⣿⡀⠀⠀⠐⣸⣿⡄⢸⠀⢸⡇⠀⢹⠐⠠⡿⣧⠁⠀⠀⠁⠀⠂⠐⠀⠀⠁⣾⡇⢈⠐⣸⠃⣾⠀⠀⡇⢠⡟⢸⣾⣿⠀⠁⠈⠄⠐⢸⣿⠃⣯⠸⡜⣼⡧⠀⡇⠠⡐⣏⠐⡊⠤⡙⡼⢩⡿⡼⣹⣿⡇⠀⡆⠀⣿⢻⣼⡚⣷⠀⠰ ⡟⡌⢆⡘⢦⣝⡳⣏⣿⣿⡇⡀⢸⣷⠃⣿⡷⣘⠎⡔⢩⠘⡄⢃⠞⢀⠏⡔⠀⢹⡆⡅⠀⣿⡇⢸⠀⢸⣿⡇⠀⠀⠀⢸⠻⡆⢸⠀⠘⡇⠀⢸⡄⠐⠃⢳⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣿⠂⢀⠀⣽⠀⡟⠀⠀⡇⢠⠇⢸⣿⣿⠀⠀⠀⠀⠀⣾⣿⠀⡗⢸⠰⣹⡇⠐⡅⢂⠱⢬⠑⡌⡱⢰⡹⢸⣷⡙⣧⣿⡇⠀⡇⠀⣹⣻⡖⣯⢻⡆⠁ ⡟⠠⢆⢰⣫⢼⡳⣽⣿⣿⠃⡅⢸⣯⡃⣿⠷⣌⠣⠜⡠⢃⠜⢠⠃⠌⣎⡵⠀⢻⡦⡥⣄⡇⠿⠾⠀⠀⠇⠷⠤⠤⠤⢼⡅⢧⣼⡀⠀⠧⠀⠀⠧⠤⠼⠸⠄⠀⠀⠀⣠⣀⢄⣠⣀⡼⢹⣄⣠⠠⠇⠀⠇⠀⠀⠿⠾⠀⠸⠇⠿⠤⠤⠤⠤⠤⠟⡏⠀⣏⣈⣴⣿⡇⠀⣎⠀⢎⡺⢄⢣⡑⢢⡝⣱⢾⡱⢎⣽⡇⠀⢶⠀⠸⣷⣻⢼⡹⣧⠁ ⠴⢁⠊⣴⢫⡞⣵⣿⣿⣽⠀⠄⢸⡷⡅⣿⡟⢬⣃⠣⡑⡌⡘⢤⡋⠐⢆⣿⠀⢸⣗⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣩⣶⣿⣹⡇⠐⡬⠐⢬⡱⢊⢆⠹⣠⢻⡜⣯⠳⣍⢾⡇⠀⢸⡆⠀⢿⣟⣦⡓⢿⡀ ⡘⠠⢹⡜⣧⢻⣽⣿⡷⡟⠀⠂⢸⡿⡅⣿⡻⣜⠤⢣⠱⡐⡅⢪⡕⢈⠒⣾⡀⢸⠯⢿⣷⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⡿⢿⠂⠠⣗⠈⢦⡹⡌⢎⡱⡐⣷⢺⣽⠳⣜⢸⡇⠀⢸⣧⠀⠘⣿⣶⡹⣺⣇ ⢀⢃⡟⡼⣣⢿⣿⡿⣽⡇⠀⡁⠀⣿⣇⣿⢷⡸⣃⢇⢣⠱⡌⢱⡇⢀⠓⣼⡇⠨⡆⠀⠀⠉⠛⠻⠿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⠿⠟⠛⠉⠀⠀⢸⠀⢸⡇⡈⢦⠳⡜⡡⢖⡡⣟⡼⣯⢳⠸⢸⡇⠀⢸⢹⡆⠀⢻⢻⣧⢳⢿ ⠠⢎⡽⣚⢥⣿⣿⣟⣿⡇⢀⡆⠀⣟⡯⣿⣧⢹⡕⢪⢌⠳⣌⢣⣏⠀⠌⣸⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⡾⠀⣾⠇⡐⢬⢳⢥⢋⢦⠱⣏⣾⣽⢪⡙⢸⡇⠀⢸⠹⣿⡀⠈⣯⢿⣧⢻ ⢨⣛⡼⡱⣺⣿⣿⢾⣿⠀⢸⡇⠀⣯⢽⣿⣮⢳⢞⡥⢪⡑⢦⣘⠾⠀⠂⠐⣿⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿⣿⣿⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣿⠐⡀⡏⣞⢢⡝⢬⢳⣏⡾⣷⠱⡌⢸⠇⠀⢸⢱⣿⢷⡀⠸⣎⢿⣞ ⢮⠵⣚⢥⣿⣿⣯⣿⢻⠀⣸⡇⠀⢼⢫⣿⣞⡱⢾⡐⢧⡘⠖⣬⢻⡀⠡⠈⣿⡆⠘⡆⠀⠀⠀⠀⢀⣀⣤⣤⣶⣿⣿⣿⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⢠⠁⣼⡇⢐⢠⡛⣬⢣⠞⣥⢻⣼⣻⢧⠛⡄⢸⠁⠀⣸⢸⣾⡯⣷⡀⢻⡘⣯ ⣏⢞⡡⣾⣿⡿⣾⡇⣏⠀⣿⡇⠀⢸⡯⣿⣧⣛⢧⡝⢦⡙⡜⡰⣏⡇⠀⡇⢸⣿⠀⢣⣠⣤⣶⣾⣿⣿⣿⣿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣷⣶⣤⣀⡞⢰⣿⠃⠄⣸⠜⣥⢣⣛⠴⣻⡼⣯⠧⡙⠄⢸⠀⠀⣿⡇⣏⣷⣻⣷⡈⢷⡜ ⡞⡬⢰⣿⣿⣽⣿⢣⡇⢸⠻⢧⠀⠈⣗⣿⡷⣎⠷⣎⠳⡜⡰⢣⢟⡴⠀⣿⠈⣿⡇⠸⡍⢴⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⡦⣹⢃⣿⣿⠀⡁⢼⣙⢮⡳⣜⣭⢳⣻⣽⢣⡙⠆⢸⠀⡆⣿⡇⣯⣿⣽⡿⣷⡌⢷ ⡳⢐⣿⣿⣳⣿⡟⣰⠇⣸⠘⢸⠀⠀⣿⢻⡷⣭⢻⣜⢣⠵⣉⢧⢻⣜⠠⢸⡆⢻⣿⡄⢳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⣼⣿⡇⠀⢀⡗⢮⢳⢵⡚⣼⢫⡷⢯⢣⠌⡃⡞⢠⠃⣿⡇⢷⣸⡷⣿⢯⣿⢮ ⠑⣾⣿⣏⣷⣿⢣⣿⠀⡇⡄⢘⡀⠀⢹⣻⣿⣜⡳⢾⣡⢛⡬⢎⣳⠾⡅⢸⡇⢸⣇⣷⣈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢟⡿⢸⠃⢈⢠⠟⣮⢏⡶⣛⡼⣫⡽⡟⣨⠒⠀⡇⢸⢠⣿⣷⢸⠜⣷⣻⡿⡼⣿ ⢱⣿⡿⣜⣿⡟⢦⡟⢸⡇⡇⠆⡇⠀⢸⣿⣿⢰⣏⡟⣦⢋⠶⣉⢾⡹⡇⠨⣗⠘⣿⢸⢷⡸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢫⢿⡇⣿⠀⠂⢸⣋⢶⣫⢞⡵⣫⢷⣹⠇⣒⠩⣆⡇⡆⢸⢯⢸⢸⡪⢽⡷⣟⡷⣹ ⣿⣿⠳⣽⣿⢏⢾⠇⣼⠀⡇⠀⡅⠀⠈⣿⣿⣒⢮⡽⢶⣩⢳⡩⡖⣯⣷⠀⣿⡀⢿⡜⡇⠳⡹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢧⠎⢸⢱⡇⢈⠄⣻⡜⣧⣛⢮⡳⣝⠶⣙⣢⣜⢠⢹⢀⠇⡞⢸⢿⠈⣷⢩⣿⡿⣝⡳ ⣿⢧⣻⢯⡿⣘⣾⢰⣿⠀⡇⠀⢸⠀⠀⢿⣿⣬⠳⣝⣳⢎⢧⠳⣍⢷⣺⡄⢹⣇⠸⣧⣇⠀⠱⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⡏⣼⠃⡌⠀⣿⡜⣧⢻⢼⣱⡾⠛⠉⠀⢻⣾⠸⢸⠀⡇⠸⢹⡃⣿⢂⣿⣿⢿⣱ ⣟⣣⣿⣻⠇⣧⣏⡾⡇⢠⠇⠀⠈⡀⠀⢸⣿⣧⢛⡼⣳⢎⣏⢳⢎⣻⠼⣇⠸⣿⡀⣿⣸⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⣇⣿⠀⡆⣘⣧⣝⣮⣷⠾⢿⢁⣠⡄⠀⡸⢿⡂⡇⢸⠁⢸⢸⡇⢻⣜⢺⣿⣟⣧ ⡳⣼⡷⣏⠞⣼⢿⣳⡇⢸⠀⠀⡄⡇⠐⡀⣿⣿⡸⡜⣧⢻⡼⣙⡞⣼⢫⢿⡄⣿⡇⢸⡟⣆⠀⠀⠀⠉⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⣸⣿⡇⣾⠉⠁⠀⢀⣨⣧⠀⠀⣏⠍⢡⠞⠁⣸⣷⠇⡸⠀⢸⠘⡇⢸⣮⡹⣿⣟⡾ ⢵⡿⣽⢊⡽⣯⡟⣼⠇⢸⠀⠀⢧⢸⠀⢃⢸⣿⣇⠳⣭⢳⡝⣧⢻⡜⣯⢾⡇⢽⣿⠘⣷⣿⣦⡀⠀⠀⠀⠈⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣚⣄⡙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⢀⣼⣿⣿⠀⣿⡆⠀⠀⠉⠉⢸⡿⣟⠻⠿⣿⣿⣿⠁⣾⠀⡇⠀⢸⠀⣿⠸⣧⢳⣻⣿⣿ ⣿⣻⢇⠯⣼⡿⣱⣿⠀⢸⠀⠀⣸⠄⡆⠘⡄⢹⣷⢹⡰⣯⣝⢮⣳⡝⣮⢳⣿⢸⣿⡇⢻⣿⢮⡻⣤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣠⣾⠿⣿⡟⢠⡿⢹⡄⠀⢀⣴⢻⡳⣍⢣⡙⠴⣂⡏⢰⢿⢀⠃⠀⠈⠆⣻⡀⣿⢧⣛⣿⣯ ⣿⡻⣌⣳⡿⣱⢣⣿⠀⢿⠀⠀⠀⠀⢡⠀⢣⠈⣿⣂⢇⡳⣞⣽⡲⣝⢮⡳⣽⡎⣿⣿⠘⣿⡀⠈⠺⢵⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⣠⡾⠟⠁⢰⣿⡇⣸⡗⣸⣿⣿⡿⢣⢽⡱⣊⠦⡙⢦⣱⠇⡎⡎⡸⠀⠀⠀⡇⢸⡇⣿⣹⡽⣞⣿ ⣿⡱⣺⢏⡖⢧⣻⡇⠀⡇⠈⠉⠉⠉⠙⡄⢸⡄⢹⣇⡚⡜⣧⢳⣏⣟⢮⡵⢫⣷⢿⣻⡆⢿⡇⠀⣀⡀⠉⠻⢖⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠉⠀⠀⠀⣼⣻⠄⣿⠇⣿⢢⠧⣝⠢⣏⢖⡡⢎⡱⢆⡿⠰⢀⢇⠇⠀⠀⠀⡇⢸⣇⢹⣞⢷⣫⣿ ⣷⡹⡱⢎⣞⡱⣽⡇⠀⡇⠈⠉⡁⢸⠁⢳⠈⣿⠈⣿⡰⣑⢺⡝⣮⣛⡶⢭⣓⢿⡾⣿⣧⠸⣿⠀⠀⠀⠀⠀⠀⠈⠙⠶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⡿⡏⣸⣿⢸⣯⡙⡞⡬⠱⣭⢢⠑⢦⡑⣾⠃⡅⢸⡎⠀⠀⠀⠀⡇⠘⣿⢸⢺⣽⣳⢿ ⣧⠱⣝⢎⢶⡱⣿⠁⠀⡇⠀⠀⠀⢸⠀⠀⠇⠸⣇⠸⣧⠘⡤⢻⡵⣫⢞⡳⢎⡽⣷⢿⣿⡆⢿⡆⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⢃⣿⡟⣾⡡⢧⡙⠦⣙⠦⡁⠞⢤⢸⡟⡸⠀⣿⠃⠀⠀⠀⠀⡇⠀⣿⡘⣯⢶⣯⢿ ⣏⡳⢎⡞⣬⢓⣿⠀⠀⡇⠀⠀⠀⢸⠀⠀⠘⡀⢻⡄⢿⡘⡰⢙⡞⣧⢛⢮⡝⣲⢻⣻⣿⣿⠘⣧⠀⠀⠀⠀⠘⠟⠛⢦⣀⣠⠖⠁⣠⡿⡏⠐⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠂⠉⡿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢸⣿⢧⣟⡱⢣⡙⢆⡱⠘⠤⣉⡶⣿⢡⠃⢸⡏⠀⠀⠀⠀⠀⡇⠀⣿⡇⡧⣟⣾⣻ ⣿⠸⣝⡼⡸⣭⣿⠀⢈⠃⠀⠀⠀⢸⠀⠀⠀⠱⠘⡝⡈⣧⢁⠣⠞⣽⡹⢲⣍⢧⢫⡗⣯⣿⡇⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⡇⡄⠀⠀⠀⠉⠒⠢⠤⢀⠀⠀⢀⡀⠤⠔⠒⠉⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⣿⣿⣸⡇⡞⣡⠞⢠⠃⡍⢂⣼⢹⢇⠆⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⢱⢚⡷⣯ ⣯⡝⡮⢶⡹⢶⡟⠀⢸⠀⣤⣴⣅⣸⣥⣤⣤⣤⢇⢡⠰⡸⡇⠌⡓⠼⣧⢓⣎⠮⣇⢻⡼⣻⣿⡘⣇⠒⠒⠒⠒⠲⠒⠖⠲⠶⠂⠳⠾⠓⡇⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⡚⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣸⣿⣇⣿⢱⠱⣲⠈⡆⠱⡈⣼⠃⣟⡞⠀⣸⠃⠀⠀⠀⠀⠀⠀⢠⠀⢸⣿⢸⡇⢿⣳ ⣷⢺⣙⠧⡝⣾⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⢳⣹⡄⠙⡔⢻⡼⣌⠷⣊⢷⣹⠽⣿⣧⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠑⢧⡀⠀⢀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⡰⠋⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢡⣿⣿⣻⡇⢮⢃⡇⠜⡠⢃⢰⡏⣸⡟⠀⢠⠃⠂⠀⠀⠀⠀⠀⠀⢸⠀⢸⣿⡎⣿⡘⣷ ⣧⢻⡜⢯⡜⣿⠇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⢣⢻⣤⠘⡡⢷⣊⠷⣙⢦⢻⣝⣻⣿⣆⢧⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠋⠖⠁⠀⠉⢢⠀⣄⠔⠊⠉⠉⠒⢄⣀⡠⠚⠁⠀⠘⠏⠁⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣼⣿⣿⣿⢘⠣⣞⢠⠓⡠⢡⡟⢠⡟⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⡇⣱⠧⣹ ⢮⡳⣝⢣⢞⣿⠀⠀⡀⠀⣀⡴⠿⠟⠀⠀⠀⠀⠀⠀⠈⢷⡀⠳⣧⢳⡑⠎⣆⢻⡘⣎⢧⢻⡼⣿⣿⣾⡄⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠸⢤⣄⡀⠀⢀⣀⡀⠀⠈⠀⣠⣤⣤⣄⣈⣀⣀⣀⣤⠀⠀⣤⢴⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⣿⣿⣷⡏⡜⡱⢎⠰⡈⢔⡟⣀⠎⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣧⢘⣳⡘ ⣯⢳⡝⢦⣻⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠹⣦⢻⡐⢜⢢⡙⢦⡙⡞⣷⣻⣿⣯⢿⡀⠀⠀⠀⠀⡀⣀⣀⠀⡀⠿⠞⣿⠁⠀⢾⣟⢛⠿⣻⡿⣿⣩⣶⡷⣽⣟⡛⣭⣿⠀⠀⠹⠿⠞⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⣿⢹⣿⣽⢢⢱⣙⠆⡱⢈⡾⢾⠏⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣿⢹⠀⡷⣡ ⣽⣣⢟⢢⣿⡇⠀⠀⡇⠶⠲⠴⠒⠶⠶⠶⠖⠖⠒⠒⠒⠒⠒⠳⠀⠙⣦⢹⣆⢣⠘⠦⣙⡜⣹⣷⢻⣿⣯⣧⠉⠉⠉⠉⠉⠉⢠⡊⠀⢀⠐⠀⠀⠀⠀⢈⡽⣿⡿⢧⣻⣿⣿⣥⡿⣝⠻⣅⡀⠀⠀⠀⠀⡀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⣾⣻⠃⣿⣯⢇⡒⢧⡚⢜⡴⢋⠠⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡃⠀⢽⠈⡇⢓⡧ ⣷⡹⢎⡽⣿⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠈⢻⡿⣦⠉⢆⠱⡘⢤⢻⣏⣿⡜⣿⣆⠀⠀⡀⠠⠐⠉⠈⠉⠉⠒⢦⠀⠀⣾⠱⣼⠛⠁⠀⠈⠉⠉⠉⠀⠈⢳⣮⣽⡶⢀⠴⠒⠉⠉⠉⠒⠈⡒⠄⣀⠀⠀⣰⣿⠇⢸⣿⡟⢠⡝⣣⠽⠊⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡆⠂⠘⣼ ⣷⢫⡜⣽⢿⠀⠀⢸⠀⠀⠀⢀⣠⣄⠀⠀⠀⢠⠄⢀⣀⣀⠀⠀⠀⠀⠀⠀⠱⠌⠻⢬⡐⢩⠆⣩⢳⣚⣧⡼⣿⡎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠚⠟⠉⠒⠙⠄⣀⣀⣀⠠⠚⠒⠉⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⣰⣿⠏⢀⣿⡷⢃⢯⠜⠋⠀⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢸⡇⢸⠀⣳ ⣯⠳⣼⡿⢸⠀⠀⢸⠀⠤⠔⠋⠙⠉⠀⠀⠀⡄⠀⠀⠀⠀⠈⠉⠁⠒⠀⠄⢀⣀⣀⠀⠽⠳⣬⡐⡌⢳⡜⣧⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠐⣾⣿⣱⣞⠁⠀⠀⢀⡐⠊⠁⠒⠊⠉⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⡇⠀⡆⢰ ⡷⣙⡾⡇⠈⠀⠀⢚⢀⣀⠀⠀⠤⠄⠤⠤⠤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡤⢶⠀⠀⠅⠉⠳⢮⣜⣹⣦⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⣰⡿⠟⢳⠀⣬⣍⡉⠁⠀⢀⡠⠄⠀⠀⠀⠀⠰⡌⠐⠂⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢁⠘ ⢧⣽⣻⠀⡄⣠⠔⠉⠀⣀⡀⠠⠀⠀⣀⡀⠤⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⢿⠈⡇⠀⡜⠀⠀⠀⠉⠻⢿⣦⠀⠙⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⣰⠋⠁⠀⣚⠀⢿⠀⣧⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⢳⠠⠀⡀⠄⠠⠍⢑⡀⢁⠢⠸⠀⠀⡇⠀⠈⠀ ⡖⣯⣷⣀⠟⠁⢀⠄⠊⠀⢀⠤⠒⠉⢀⢒⣒⣼⣠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⡧⣹⠀⢹⠀⠀⠀⠀⠀⠀⠙⠣⡀⠈⠻⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠟⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⣧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠒⠊⠓⠤⡀⠀⠈⢆⠑⢼⠀⠀⠃⠀⠀⠀ ⣼⠟⠈⢀⡠⠀⣁⡠⠤⠒⠓⠊⠉⠉⠁⠀⠀⣛⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢟⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠸⠬⣿⠀⠉⠉⠉⠀⠀⣀⣀⡀⠤⠮⢬⠆⠀⠀⠀⠈⠒⢄⡀⠣⠈⠢⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡀⡠⠔⠒⠐⠉⠙⣆⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⣮⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠐⠿⠃⠀ ⠀⣄⠀⠀⢸⠀⢀⡀⠀⠸⠀⠘⡃⠠⣳⣖⠀⢀⣦⣀ ⠈⠻⠉⠀⣿⣤⢘⠉⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠙⠀ ⢼⡦⠀⢊⢿⡋⠀⠀⠀⡴⢴⠒⠄⠀⠘⢄⢠⠛⡄⠀ ⠀⠁⠀⠀⠀⠉⢱⠂⠀⠀⠺⠂⠀⠀⠀⠀⢻⣰⠁⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡴⠶⢆⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣳⡄⠀⢠⡗⠀⠀⠀⠀⠀ ⡰⠒⠶⠖⣉⣉⠉⠉⢉⣩⣅⠲⠖⢲⣆ ⠑⠦⠤⢾⣧⡋⠠⠤⠄⢿⣸⠦⠤⠴⠿ ⠀⠀⠀⡰⣿⡏⡿⠿⡏⢹⠁⠀⠀⠀⠀ ⠀⠀⠀⠱⠽⢧⠤⠤⢤⡸⠀smol
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣠⠶⠾⠛⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣦⣀⣀⡴⠾⠛⠋⠀⠀⠀⠀⠀⠈⠛⠻⠶⣄⡀⣠⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣇⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣟⣁⡀⠈⣧⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠻⠿⠿⠛⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡿⣏⠉⠁⠀⡀⠀⣻⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠓⠦⣤⣟⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡃⠁⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠙⢷⣄⡀⠀ ⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢀⣀⡤⠤⣄⣀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠈⢻⡄ ⠀⠀⠀⠀⠀⣿⠁⢀⣤⠤⠤⠶⠚⣿⠄⠀⠀⣼⣿⣿⣿⡆⢀⡞⠁⠶⠂⠀⠲⠀⠑⡄⠀⣾⣿⣿⣿⣆⡀⠀⠀⣿⠓⠶⠤⠤⢤⡀⠀⣿ ⠀⠀⠀⠀⠀⠹⣧⢯⡀⠀⠀⠀⠀⣷⠀⡞⠁⠻⣿⣿⠟⠀⠸⣄⠀⠀⠀⠀⠀⠀⢀⡇⠀⠘⢿⣿⣿⠇⠈⡆⢀⡿⠀⠀⠀⠀⢀⡼⣸⠏ ⠀⠀⠀⠀⠀⠀⠙⠷⣽⣲⠦⠤⠤⢾⣧⡱⠤⠤⠃⢀⡄⠀⠀⠈⠁⠀⠀⠀⠒⠒⠉⠀⠀⠀⠀⠘⠦⠤⠔⢁⣾⠷⠤⠤⠴⢖⣫⡾⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠙⠻⢦⣤⣀⡀⠈⠆⠀⠀⡤⠤⣤⣤⣤⢤⣄⠀⠀⠀⠘⢀⣀⣠⡴⠟⠉⠙⠛⠛⠛⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⠟⠉⡋⠉⠁⣿⣠⣼⣿⣧⣅⣽⠀⠛⠛⠛⠻⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⠶⡟⠳⣤⣤⡄⠀⠀⠀⠀⢰⠇⠀⠠⠁⠀⠀⠀⠀⠸⣟⠋⠀⠀⠀⠀⠰⠐⡀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⢷⡶⠛⠛⠻⠿⠟⠳⢦⡀⠀⣿⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣿⠐⣷⣶⣄⣤⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⣀⡀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢿⡄⠈⠀⢠⠀⠀⠀⠀⢰⣤⡆⠀⠀⠀⠀⡄⠀⠀⣠⣿⣤⣿⣧⣟⣱⣪⡍⠉⠿⢧⠀⠀ ⢠⠖⠟⠛⠓⣾⣧⣀⣀⡀⠀⠀⠀⠀⠀⣰⠇⠈⠻⢷⣦⣬⣧⣠⣴⣶⣾⣿⣷⣶⣤⣄⣼⣥⣴⡾⠛⠉⠛⠛⠛⢧⣀⣤⣀⣀⣠⡾⠀⠀ ⢿⣤⣀⣠⣤⡼⠃⠉⠉⠙⠛⠒⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠉⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡾⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡿⠟⢀⣀⢤⡀⠀⠀⠀⠀⠙⢆⡀⠀ ⠀⠀⠀⠀⠀⢀⡄⠈⠀⠀⠀⠀⣠⡼⠟⠛⠛⠓⠙⠚⢡⣀⣀⠀⠀⠀⠀⠉⠃ ⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢫⣍⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢻⡆⠀⠁⠤⣀⠀ ⠀⠀⠀⠀⠀⢀⡶⠛⣶⡼⠃⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠀⣀⣿⠀⠀⠘⠋⠀⣀⠀⠀⠀⠀⠀⠀⣠⡿⠙⣽⣷⣦⡀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⡀⠀⠀⠈⠛⠃⠀⢾⠇⠀⠰⠾⠁⠀⠈⠻⢿⣿⡀ ⠀⠀⠀⡊⠀⢸⣿⣿⣿⣿⣿⡳⡤⢀⡀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⢀⡔⠉ ⠀⠀⠀⡂⠀⢠⣿⣿⣿⣿⣿⣿⣶⣬⣽⣿⣶⣶⣶⣟⠙⠳⣦⡀⠀⠀⠊⠀⠀ ⠀⠀⢸⠀⣰⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣠⠟⢱⡀⠀⠀⠀⠀ ⠀⠀⠀⢰⡏⠉⠉⠉⠉⠉⠛⠛⠻⠿⣽⣿⣿⣿⡛⠛⠉⠀⠀⠠⠉⡉⠉⠉⠉ ⠀⠀⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠃⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀ ⢠⡟⠉⠀⠀⠀⢰⡶⣤⣄⣀⣀⣀⣀⣀⠀⠀⠈⠉⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠛⠒⠒⠒⠒⠛⠛⠀⠈⠉⠉⠉⠙⠓⠒⠲⠶⠖⠒⠓⠀⠀⠀⠀⠀⠀⠀⠀hiiiiiiiii
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢸⣿⣿⢹⡿⣟⣿⣿⣻⣑⣿⣼⣿⣿⣽⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣯⣭⣟⣛⣿⣿⣿⣿⣿⣿⢿⣻⣿⠟⠀⣾⣟⠏⠾⠙⠛⠉⠉⣻⢧⡼⠛⣇⠀⠘⣯⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⠿⠿⣿⣿⣿⣿⣿⣿⡽⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⢀⣇⠀⡙⠀⠀⣹⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣶⣾⣯⣽⣿⡿⠿⠿⠶⢶⣶⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⢰⢈⢇⢀⠃⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡰⠆⣿⣿⣿⣿⣿⣿⡇⠀⠀⣀⣠⣴⠾⠛⠉⠀⠀⠀⠀⠀⢀⡀⠀⣣⡠⠋⠔⢢⢤⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠃⠀⣿⣿⣿⣿⣿⣿⡏⢰⠾⠛⠉⠀⠀⡀⠀⠀⠀⠀⠀⠎⠰⠞⠓⠁⠪⡹⢂⡀⣘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⣿⣿⣿⣿⣿⣿⡇⠀⢠⠒⠒⡄⠘⠹⢁⣀⡠⡀⠀⠀⠀⠀⠀⠀⠐⢍⣉⡞⣲⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣧⣀⡐⠜⠣⠂⠀⠐⠣⣄⡠⠃⠤⠤⠒⠉⠈⠁⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⢀⣾⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠁⠊⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⡿⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢝⢷⣦⣤⣀⣀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⢠⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣻⣿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣼⣿⠛⠉⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⢸⣿⣿⢿⣿⠀⠸⣿⣿⣿⡷⡟⠏⠙⠉⠸⡏⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⠏⠛⢿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀ ⠈⣿⣿⠀⢿⡄⠀⠹⣿⠟⠁⠀⠀⠀⠀⠈⣟⣠⠤⠶⠂⠺⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠊⠀⠀⠀⠈⠙⠛⢿⢷⣆⢸⣿⣿⣿⣿⢿⣻⢻⡝⢯⡻⣝⣻⣷⠀⠀⠀ ⠀⠘⢿⡀⠀⠙⠂⣴⠋⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡖⠤⣀⠀⠀⣠⠄⠒⠒⠂⠈⠁⣴⣿⢿⣿⣿⣿⣯⣷⣯⣾⣽⣷⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⠀⠀⠀⠀⢰⠙⢿⣟⢿⣿⣝⠿⣦⣀⡀⠈⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠿⠛⠛⠋⢹⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⠥⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠒⠚⠛⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡏⢹⠉⢹⠩⠴⠀⠀⠀⠘⠄⠀⢰⢲⢸⢲⡀⠀ ⠀⠀⠀⢀⣾⠁⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠈⡆⠀⠀⠀⠐⠵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢣⠂⠠⠀⢟⣌⣋⡁⡄⠤⠈⠀⠀⠈⣸⡾⡄⠀ ⠀⠀⣠⣾⠡⠀⣀⡄⣶⣒⢱⡤⣠⢤⢠⡄⣀⠸⡇⠀⣀⣀⡀⡇⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠬⠒⠉⠁⢀⠴⣣⠁⠇⠀⠀⠀⡆⡟⠈⠹⠀ ⠀⠀⣾⡁⠊⠀⢹⣤⠻⠛⢊⡍⢆⡴⠊⢔⠂⢸⣷⠈⠁⠀⠀⣧⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⡼⠁⠀⣠⢔⡊⠁⠀⠑⠚⢠⠁⠀⠀⠁⢘⠶⠙⡆ ⠀⣸⠃⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠹⣄⡄⡰⠋⡧⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂⢠⣞⣃⡠⠷⠒⠒⠉⠉⠁⣰⠀⠀⠰⠘⡄⠔⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⡏⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡸⠟⢹⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠘⣇⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⣷⣠⣿⣤⣤⣦⠀⠀⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣶⠆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⣷⣄⠀⠀⠀ ⠀⢸⠟⢁⣴⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⡈⠙⠀⠀⠀ ⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠿⣿⠿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣸⢃⠜⠋⣁⣤⣤⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢿⡿⠿⠻⠿⣿⣿⣿⣿⣿⣿ ⡇⣠⣰⣿⣿⣿⣿⣧⠈⣿⣿⣿⣿⣿⡿⠋⣴⢾⣿⠀⣴⣾⣿⣷⡌⢻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠀⢿⣿⣿⡿⢋⠁⣾⠁⢀⡍⢸⣿⣿⣿⣿⣿⡀⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠻⢋⣴⣿⣄⠋⣰⣿⠇⢠⣶⣆⢹⣿⣿⡇⢠⡈⢿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣰⣿⣿⣿⣿⣧⡙⠉⠰⢠⣿⠏⣸⣿⣿⣷⣿⣿⡌⢻ ⣿⣿⣿⣿⣿⣿⣿⣿⡏⣼⣿⣿⣿⣿⣿⣿⡇⢾⣷⡿⠏⣰⣿⣿⣿⣿⣿⣿⣿⡈ ⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣷⣌⣩⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣟⠀⠀⢻⠟⢸⣿⡍⠘⠛⣻⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣦⣴⣿⡘⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⣿⣿⣿⡿⢷⣶⣤⣉⠻⣿⣿⣿⣿⣿⣿⣿⡿⢁ ⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⠙⢿⣿⣿⣿⣿⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣾ ⣿⣿⡿⠿⠟⠋⢁⣠⠆⣈⠳⠤⠙⠻⠿⣿⣿⣿⣦⣿⣿⣿⣿⣿⠿⠟⠁⡄⢇⢻ ⣀⠀⣤⡀⠂⡴⢈⡛⠆⡇⢸⣿⣼⢱⣶⣤⣤⣭⣉⢉⣉⣩⠀⣤⣶⣿⣃⡇⣸⣆ ⢋⣴⣿⣷⠘⣡⣾⣿⡄⣇⣔⡗⣿⢸⣿⡇⣿⠿⢟⡂⣿⣿⣿⢢⣶⡆⠟⠡⢰⣾ ⣼⣿⣿⣿⡇⢸⡿⠿⠃⣨⣼⣿⡏⢸⣿⣷⡔⢾⣿⣷⡘⢿⣿⣶⠄⣢⢡⡌⢸⣿ ⣿⣿⡿⠿⠗⢠⡔⣶⣾⣏⣸⣿⢷⢸⣿⣿⣏⠾⢿⣿⡿⢸⠟⣵⣿⡿⢨⣀⡼⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢆⢻⢿⣅⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣤⡘⠁⠀⠸⢨⢻⣧⣤⣄⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡋⢿⣟⡄⠀⠀⠀⠀⠀⠉⠉⠁⠈⠉⠽⠿⢷⣖⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⡏⣧⣌⡤⠀⠀⠀⠀⡀⠀⣠⠀⣀⣠⣄⣀⣤⡽⠟⢯⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⢙⣴⣿⣿⣿⣿⣿⣿⣯⡻⠓⠴⠺⠿⣦⣼⣿⣿⣿⣿⣿⣿⣧⣾⣿⣠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣐⣶⠶⠶⠴⣍⣿⡟⠋⠀⠀⠛⣿⣿⣿⣿⣇⣴⠀⣴⣿⡟⠉⠀⠈⠻⣿⣿⣿⣿⣿⣿⠶⠶⠶⣂⡀⡀⠀ ⢀⡜⣯⡿⠋⡉⡇⣿⡟⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡏⠀⣿⡇⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣻⠻⢍⠹⢭⢿⣦⡀ ⢸⡟⣿⠡⠈⠈⡇⣿⣷⣄⣀⣀⣀⣼⡿⠻⢻⣿⣿⡟⠁⣿⣧⣄⣀⣀⣰⣾⠿⠟⢻⣿⣿⡛⡑⠀⠓⠈⢻⢿⡇ ⢸⡿⣿⣀⠀⠀⣧⠟⣿⣿⣷⣿⣿⡏⠀⠀⠀⣸⣿⠇⡀⢿⣿⣿⣶⣿⣿⠇⠀⠀⢰⣿⡻⣕⣿⣠⠶⣠⢾⣸⡇ ⠀⠠⠯⣝⣳⣐⣙⣆⠙⢿⣿⣿⣿⣷⣠⣤⣶⡿⢃⣸⣷⡀⠻⣿⣿⣿⣿⣇⣠⣤⣼⠛⠃⣻⢙⣃⣙⣭⡿⠏⠁ ⠀⠀⠀⠈⠉⠉⢿⠀⠀⠈⠉⠻⢿⡿⠟⠛⠉⠡⣭⡿⡿⠿⢀⣈⡙⠿⠿⠿⠗⠊⢁⣠⣴⣿⠟⠉⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠶⢶⡶⣀⠑⢽⣀⠀⣆⠤⢾⣅⠱⣦⠤⢿⡯⠶⠖⠀⣛⣉⡴⠞⢩⡿⡯⢴⢶⣤⡀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠋⣯⣝⣗⣮⡍⣛⢛⣡⠸⠉⠒⠋⠀⠺⢻⣦⣯⡴⣞⣫⣷⠟⣳⡟⢋⣧⣤⣭⠟⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⠿⣾⣟⡟⠉⠀⠀⠀⠀⠀⠀⠀⠳⣺⠾⠋⢁⣤⢺⣳⣴⣿⠏⢀⡿⡄⣾⣧⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⠀⠀⢀⡠⡬⡂⠀⠀⠀⢹⣅⢠⠿⢟⢾⣿⠟⠁⢀⣘⣏⠇⠙⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢛⣇⠀⠰⠟⠋⠉⠉⠃⠀⠀⠏⠁⣤⣬⣿⠟⠁⠀⠀⠘⢇⣯⣤⣴⣽⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠄⠘⠱⠷⠶⠓⠈⠀⢠⡾⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣶⣶⢶⡆⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣠⠀⣠⣿⠀⢐⣓⣄⣠⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠋⠀⠀⠙⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⡀⡀⡀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠄⠒⠁⠁⠀⠀⠀⠀⠀⠀⠀⠑⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢂⠀⠀⠀⠀⠀ ⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀ ⠀⠆⠀⠀⠀⠐⠀⠀⠀⢰⠃⠀⠀⠈⠙⡄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀ ⢘⠀⠀⠀⠀⠀⠀⠀⠀⠹⣉⠉⠉⠉⣉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀ ⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀ ⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀ ⠆⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀ ⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀ ⡃⠀⠀⠀⠀⠀⠀⠀⠀⡤⠔⠃⠀⢸⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅ ⡂⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⠒⠒⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂ ⡂⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂ ⠐⠀⠀⠀⠀⠀⢐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅ ⠈⡀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆ ⠀⠂⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⡃ ⠀⠨⡀⢰⠦⡇⠹⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢄⡵⣆⡀⠀⠀⠀⠀⠀⡇ ⠤⠄⠥⠬⠇⠄⠤⠾⠅⠄⠄⠄⡀⡀⡀⠀⠀⠀⠀⠸⡀⠈⠀⠀⡹⠀⠀⠀⢀⡸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠁⠁⠒⠑⠂⡂⡲⠂⠒⠒⠊⠉⠀⠀
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