⟡ pls note the ai inflicts emotional damage (ᵕ—ᴗ—)
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡎⠋⠋⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣠⠷⠄⠸⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣠⣈⡇⠀⢠⠖⠒⠢⠤⠤⠼⣦⣤⣖⠒⠋⠉⠉⠉⠉⠉⠉⠉⠉⠓⠲⠤⣧⡴⣆⢰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⣤⡀⠀⠀⠀⠀⠀⠀⠈⠉⠳⡤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢴⡇⠸⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀
⠀⠀⠀⠘⢛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⣤⣤⣿⣲⡤⠖⢷⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⣳⣄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣗⠑⣻⡆⠀
⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢰⢃⣤⡾⠋⠉⠉⠹⣆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣷⡀⠀⠉⢢⡀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠈⠻⠾⠛⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⡄⠀⢸⢋⡞⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⡇⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢰⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⢸⡼⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠁⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⡘⠀⠀⠀⠘⡇⢀⣀⠀⠀⢠⢿⠀⠀⠀⠀⠀⠀⠚⠛⠛⠒⣤⠋⠀⢠⠀⠀⢀⡞⠀⢀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠃⠀⠀⠀⠀⡏⠁⠀⠀⠀⠸⡸⡄⢰⡀⠀⠀⠀⢀⣀⣠⡀⢧⣀⣤⡞⠀⠀⣏⠀⢀⡾⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣠⠤⠶⠒⠒⠒⠲⠦⢤⣿⣆⠀⠈⢢⡀⠀⠀⣇⠀⠀⠀⠀⠀⠑⢽⣦⣙⢦⣤⣾⡿⡾⡿⢿⣿⣿⣏⣀⣄⣀⣈⣩⡿⠥⣤⣄⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⠜⠈⠑⠢⢼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⡼⠖⣃⣀⡈⢻⣿⡇⠀⠀⢻⢡⣴⠉⣟⠙⡆⠀⠀⠀⠀⠀⠈⠓⠦⢤⣀⣠⡶⢶⡟⡆⠀
⠀⠀⠀⠀⠀⠀⢀⡴⠒⣦⠀⠀⠀⠀⠸⡄⠀⠀⠀⣀⣳⣶⣿⠽⡆⠀⠀⠀⠀⠀⠸⠀⢷⠋⠙⠇⠉⢻⠏⢸⠀⠀⠈⠏⠁⠀⢸⢠⠃⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⣿⣷⣦⣸⡷⠀
⠀⠀⣴⠛⠓⣦⡾⠀⠀⣸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢹⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠣⣈⣣⣀⡠⢴⠋⠀⢘⡀⠀⠀⠘⡀⢠⠿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣹⣿⠁⠀
⠀⠀⠙⢧⠀⠈⠃⠀⢠⡏⠀⠀⠀⠀⢰⠇⣀⣰⠟⣦⡭⡇⢠⣴⠀⠀⠀⠀⠀⠀⠀⢠⢶⡄⢀⢃⡔⣦⠀⢈⠁⠀⠀⠀⢳⢿⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⡟⠀⠀
⠀⠀⠀⠀⠙⠦⣄⣀⡞⠀⠀⠀⠀⢀⡞⠘⣦⡌⠀⢛⡇⡿⣼⡏⠀⠀⠀⠀⠀⠀⠀⢘⡚⠇⡾⡜⠜⠁⠀⣸⠀⠀⠀⠀⢸⠀⠙⠻⠶⠦⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣤⠾⢷⡜⢇⣼⡶⢻⠁⢱⡀⠀⠐⢦⣴⣶⡶⠖⢛⡿⠃⠀⠀⠀⠀⢀⣰⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀
⢦⣄⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⠁⠀⠀⠀⣠⢞⡀⡎⠀⠀⠑⢤⡀⠀⠙⠛⠛⠛⠉⠀⠀⠀⠀⢀⡴⡿⠃⠀⠀⠀⠀⣠⡿⠲⣤⠤⢄⡀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢸⠙⠦⠤⠔
⠀⠈⢩⢷⡶⣶⠒⠋⠉⠁⠀⠀⠀⠀⢀⣾⡿⠃⡼⡴⠀⠀⠀⣇⡟⠲⣄⠀⠀⠀⠀⠀⣀⡤⠚⢁⣾⠖⠀⠀⠀⢀⡜⠻⠃⠀⠈⠳⣖⡷⠤⠤⠤⠤⠤⠼⢤⡤⢤⢄⣈⣧⣀⠀⠀
⠀⠀⢎⣀⠀⣉⠇⠀⠀⠀⠀⠀⠀⢠⣿⡹⠁⢠⡟⡇⠀⠀⠀⡟⠀⠀⠈⠳⣀⣠⠴⠚⣅⠀⠀⣿⢹⠀⠀⠀⡴⡹⠁⡼⠀⠀⠀⠀⡇⡏⡗⠒⠒⠒⠒⢲⠞⢒⠳⢤⡔⠛⢿⠷⣒
⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⢠⡇⠀⠸⣇⢧⠀⠀⠀⡇⠀⠀⠀⠀⠹⣧⠀⠀⠈⣧⡀⢻⣾⡀⠀⢰⡳⠁⣰⠃⠀⠀⠀⠀⡷⠁⡇⠀⠀⠀⡴⠭⠭⢍⣲⠏⠀⠀⢈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⠳⠀⠀⠻⣿⡦⠀⠀⢧⠀⠀⠀⠀⠀⠙⡆⢀⡰⢿⡑⡄⠳⣅⠀⢾⠁⢠⠇⠀⠀⠀⠀⠀⡇⢠⠃⠀⠀⡸⢉⣯⠒⡶⠃⠀⠀⡰⠋⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠈⠙⠦⣄⠈⢆⠀⠀⠀⢀⡠⣾⢟⡇⢸⠱⣿⡉⠙⢦⣼⣤⣯⣀⠀⠀⠀⠀⢀⡇⢸⠀⠀⢰⢃⣿⠁⣰⠁⠀⠀⡜⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠈⣻⢮⣆⢠⢴⠿⠊⠀⢸⠀⢸⠀⠘⡇⠀⢀⡽⣿⠢⣼⣷⣤⡀⠀⢸⠃⡏⠀⠀⢸⢸⡇⢠⡇⠀⠀⣰⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢺⠁⠀⠀⠀⠀⠀⠀⡿⢆⠀⠀⢀⡴⠃⢸⣿⣧⢋⠀⠀⠀⡾⢀⣾⡀⠀⢹⣓⡾⠀⣸⡆⠙⣿⠁⢩⠶⣼⢀⠃⢠⠀⠘⡜⣹⠈⡆⠀⢠⠃⠀⠀⠀⠀⠀
⠀⠀⣠⢦⣄⣀⣀⣠⡇⠘⣦⠄⠀⠀⠀⠀⣠⠇⠘⣆⣴⣎⡠⠴⠋⡟⣧⠸⡀⠀⠀⣧⢿⢹⣿⢶⣄⣿⣇⣴⣿⡇⠀⠸⣦⣾⣤⡇⣸⠀⠈⢆⠀⡇⡟⡄⡇⠀⡎⠀⠀⠀⠀⠀⠀
⠀⠀⠛⢾⡇⣀⢀⠀⢣⡀⠀⠑⠒⠴⠒⠋⠁⠀⢠⠋⠀⢏⠀⠀⢸⡽⢱⢇⣷⠀⢐⣫⣼⣾⣿⣿⣿⣿⣿⣹⠟⠀⠀⢠⠯⣹⡷⢁⠇⠀⠀⠸⣆⢠⢰⢇⢹⢸⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢸⡇⠰⠊⠀⠀⣹⠦⠄⠀⠀⠀⠀⠀⠀⣾⠀⠀⢮⣢⣤⣼⣧⢏⣞⢻⡆⠘⣏⢉⠉⣹⡿⢿⣿⡿⠁⠀⠀⣠⡞⢻⡿⢁⡎⠀⠀⠀⠀⠙⣼⡿⣚⣺⡿⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠉⡇⠀⠀⡠⠊⠀⠀⠀⠀⠀⣀⣠⡴⠚⠈⢦⠀⠀⠈⠻⡀⠘⣾⠹⣦⢷⠀⠙⠿⢻⣽⡁⢸⡟⠀⠀⣠⢾⠿⣥⡛⢁⡞⠀⠀⠀⠀⠀⠀⠘⢷⡲⠭⢧⠙⢦⡀⠀⠀⠀⠀
⠀⠀⠀⠀⣇⢀⡞⠀⣠⣒⠬⠟⠛⠋⠉⠁⠀⠀⠀⠀⠙⠲⣄⠀⢱⠊⢈⣷⡈⠿⡆⠀⠀⠀⣯⣧⣸⡇⣠⡎⠙⣷⠃⠹⣿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠷⣤⡵⣄⠀⠀⠀
⠀⠀⠀⣀⣿⣾⣠⣾⣋⣁⣀⣀⠠⠤⠤⠤⢤⡄⠠⠤⠤⠔⠚⣇⣮⣴⠋⠀⢻⢦⣧⠀⠀⢰⣿⠇⣿⢱⣏⠹⣶⡙⣧⣴⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⡄⠀
⠀⠀⠀⢙⣿⡿⠛⣻⠟⠛⠚⠒⠒⠂⠀⠀⠸⣄⠀⠀⠀⠐⠚⣻⢻⠃⠀⠀⠈⣇⢹⠀⠀⠘⠛⠶⠟⢳⣻⠓⣲⡛⠉⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦