⟡ pls note the ai inflicts emotional damage (ᵕ—ᴗ—)
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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡤⢤⣤⣤⡤⠤⠤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⢚⣛⡿⠛⠒⠋⠉⠁⠀⠀⠉⠙⠳⢦⣬⣉⠛⠳⢶⣤⣄⠀⠀⠀⡤⠚⠁⠀⣸⠍⠁⠙⠛⢻⣶⣤⡀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠞⠿⠿⠋⠩⠼⠃⢀⣴⣾⣶⡦⢤⣀⠀⠀⠀⠀⠀⠀⠙⢿⣶⡂⠬⡛⢿⣦⣼⡤⠤⣄⠐⠁⠀⠀⠀⠀⠀⠈⠙⠳⣄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢁⡀⢤⣀⣴⡄⠐⠀⠀⠈⠀⠉⠀⠀⠉⠙⠻⣶⣄⠀⠀⠀⠀⠀⠈⠙⢦⡀⢄⣸⠏⠀⠀⣿⠦⣄⠀⠀⠀⠀⠀⠀⣄⡀⠈⠳⡄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠖⣡⣾⡿⠟⡿⢻⠋⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀⠀⠀⠀⡖⢆⡙⢧⣹⡦⠤⠖⢻⠀⣾⣳⡶⠒⣲⣤⣄⣈⣏⣓⣢⣜⡆⢸
⠀⠀⠀⢀⣀⡤⠤⠤⣤⣠⠞⡵⢁⣾⡿⠃⠀⡼⠡⠇⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⢀⠘⡄⠑⡄⠙⣷⡀⠀⠘⡄⠾⡝⣿⡟⠋⠉⠉⠉⠚⢧⡈⠉⠾⢈
⠀⢠⡜⢛⠟⠓⠢⣄⣽⢋⠞⣠⡿⠋⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡽⠃⠈⠳⡼⠄⠈⢷⡀⠀⠹⡀⠹⣾⣿⠀⠀⠀⠀⢀⣾⡇⠀⠀⢸
⠀⠸⡾⠁⡆⠀⢀⡾⢁⠎⣠⡟⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡸⣆⢄⠀⠐⣦⠀⠀⠀⠀⠀⠐⢝⣆⠀⠀⠀⠀⠀⠀⠻⣷⠃⠙⣄⠀⢛⣿⣷⣤⡀⣾⣿⠁⠀⠀⢸
⠀⠀⠰⢋⠄⣠⡿⢁⠎⢀⠟⢀⠖⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣶⡀⠀⠈⢦⠀⠀⠀⠀⠀⠨⣿⣆⠀⠀⠀⠀⠀⠀⠹⣧⡀⠈⠳⣾⣿⣿⣿⣧⣿⠃⠀⠀⠀⢸
⠀⢀⡴⢟⡟⣹⢁⠎⠀⠜⠀⣞⡠⠂⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠘⢿⣆⠀⠀⠳⡄⠀⠀⠀⠀⠹⣿⣇⠀⠀⠀⠀⠀⠀⠹⡟⠶⡾⢿⣯⠩⠿⠿⢷⣤⣄⣀⠀⢸
⣴⣋⡴⡟⢱⢃⢞⠂⡼⢀⣼⠏⠁⢠⠋⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠸⠀⡔⣝⣧⣤⣀⣙⣦⡀⠀⠀⠰⡜⢿⡆⠀⠀⠀⠀⠀⠀⠹⣶⠃⠀⣿⣷⣄⠀⠀⠀⠉⠉⠑⢶
⡟⠃⠀⣧⣟⡎⡏⢰⠀⢇⠃⢠⠀⠀⢠⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⡇⡏⠓⠶⣛⢧⡀⠈⢷⣍⠉⠙⠻⡎⣿⡄⠀⠀⠀⠀⠀⠀⢻⢸⣆⢻⣿⡈⠱⣄⠀⠀⠀⠀⢸
⠀⠀⠀⢻⠯⠀⠀⠈⢰⣸⠀⡼⠀⠀⢸⠏⣧⠀⢎⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢷⡇⠀⠀⠀⠉⠚⢷⣤⡻⡷⢤⣀⠘⢸⠇⠀⠀⠀⠀⠀⠀⣎⣿⠈⢼⠘⣧⠀⠈⢳⡀⠀⠀⢸
⠀⠀⣰⣿⠀⠀⠀⠀⢸⡇⠀⢻⠀⠀⢸⣠⣾⡟⢹⡜⢆⠀⠀⠀⠀⠀⠀⠀⠸⣇⢸⡇⠀⠀⢀⣀⣀⡀⢀⣝⠺⣦⣝⠳⢬⣸⠀⠀⠀⠀⠀⠀⠹⢻⣇⣼⢳⡹⡄⠀⠀⢱⣤⡖⢩
⠑⣾⣿⡇⠀⠀⠀⠀⢸⣇⠀⢸⢀⡴⣿⢉⠎⢱⡀⢿⡄⡅⠀⠀⠀⢠⠀⠀⠀⢻⣜⡇⠀⢴⢟⣩⣶⣟⣿⢿⣷⣾⣿⣍⡲⢹⠀⠀⠀⠀⠀⠀⠀⡟⡛⣧⠀⠳⣿⣄⠀⠀⠋⠀⢸
⡼⠁⢹⡇⠀⠀⠀⠀⠘⣹⣇⣸⡋⠀⣿⡞⠀⠀⠳⣼⡵⡜⣆⡀⠀⠀⠳⣄⠀⠈⣿⡇⠀⢠⣿⡿⣿⠗⠿⢷⣾⣝⠻⣿⣷⣼⣄⠀⠀⡀⠀⠀⠀⠇⣿⡈⣆⠀⠙⣏⠳⣄⠀⠀⢸
⠁⠀⢸⡇⠀⠀⠀⠀⠀⣿⢿⢹⢳⡀⢿⠁⢠⡤⠔⠘⢷⡘⢾⣿⣶⠤⣀⣈⣓⣤⣬⠮⠆⠀⠟⣼⣷⣼⣤⣾⠿⣿⡇⠘⣿⣿⠃⢠⢃⡇⠀⠀⠀⠀⢸⡝⢸⠀⠀⠙⣆⡈⠑⢦⣘
⠀⠀⣸⡇⣇⡀⠀⠀⠀⢹⣮⢸⢸⠹⣼⣾⣿⣿⡿⢿⣿⣿⣕⠙⠧⠉⠒⠚⠂⠀⠀⠀⠀⠀⠀⣿⣭⠈⢧⠟⠀⢨⡿⢀⡟⢸⢀⣎⣼⠁⠀⠀⠀⡄⡆⡿⢰⠀⠀⠀⠹⡏⢦⡀⢸
⠒⠒⢻⣿⠀⢳⠀⠀⠀⠈⣿⣾⣸⣠⣿⣿⠟⢡⡞⠉⡛⢿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣍⠔⢉⣡⣾⣥⡎⢠⢇⡞⣸⣇⡖⠀⠀⢀⠇⡇⣇⣿⢳⡀⠀⠀⢱⡀⠹⣼
⠀⠀⣼⢹⡇⣇⢧⣄⠀⠀⠸⣇⢹⣿⣿⡷⠃⣿⣿⠶⡿⢻⡟⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⠉⡠⢡⠀⣠⣮⣞⣴⢳⡻⡤⠀⡠⡼⠀⡇⡿⠁⢳⢳⡄⠀⠈⡇⠀⢸
⠀⣸⣻⣾⣿⠸⡈⢮⢢⡀⠀⢻⣟⠻⣿⡇⠀⢻⣅⠀⠛⣺⠴⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠇⠽⠚⢻⣟⡆⢸⣘⡝⠀⣴⡱⠁⢸⡇⡇⠀⠀⢳⣿⢦⡀⢰⠀⢸
⢠⣧⢧⣿⣿⡀⢣⠈⢣⡙⢤⡀⠻⣾⡝⠛⢦⡈⠳⢷⣾⠥⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢠⡿⠋⢀⣾⡟⠁⠀⣿⣇⠇⡇⠀⠀⢯⡆⢹⡜⠀⢸
⠘⣨⠎⠸⣿⣇⠀⢧⠀⣗⢄⡙⠶⣬⣧⣀⠀⠁⡝⢠⢠⠄⡆⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⢂⣴⡻⠋⠀⡠⣺⢻⣼⠋⠙⠓⠲⣼⣷⠀⢻⣦⣸
⠰⠃⠀⠀⣿⣿⣆⠀⠳⡘⣄⣏⠑⢿⣟⣿⣙⠒⠡⠎⠈⠀⠀⠀⠀⠀⠀⠲⣾⣁⠔⠊⠉⠉⠺⡆⠀⠀⠀⠀⠀⠀⢀⣠⡾⠷⠝⠉⠀⣠⠞⣠⢫⣿⠃⠀⠀⣀⡴⠃⢹⠂⠈⡇⢹
⠀⠀⠀⢸⡟⠘⢿⡉⠀⠙⠿⣝⢦⠸⡌⠙⣏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡁⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⣀⣴⣚⣉⡀⣀⣠⣶⠟⢡⣾⣿⡿⠁⠀⠳⡊⠁⢀⣴⡏⠀⠀⡇⢸
⠀⠀⠀⣼⠇⠀⠘⣧⢦⠀⠀⠈⠳⣗⣷⡀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠤⣒⠭⠄⠀⠀⠈⠉⠙⠛⠒⠺⢿⡛⠛⠉⠉⠛⠁⠀⠈⠉⠙⠒⠻⣦⡔⠊⠙⢦⢰⠃⢸
⠰⣄⢠⢿⠀⠀⠀⢸⢮⢧⡳⠦⣄⠀⠈⢭⡽⠿⠟⠶⢤⣄⣀⡀⠀⠀⠀⠀⠀⣀⠤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠙⣦⢠⣷⠏⠀⢸
⡀⠈⣙⣶⡇⠀⠀⢸⠈⣻⣿⡶⣄⡉⠁⠀⠈⠙⠲⠤⠤⣴⡿⣛⣉⣉⣩⡽⠛⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠁⠀⠀⠈⠋⡿⠙⠳⡄⠀⢸
⠉⠉⡇⡆⢱⠀⠀⢸⢠⠃⠈⠙⢻⣿⡛⠏⣀⣠⡤⣶⠾⠋⠉⠉⠀⢨⠎⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⣏⡆⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠹⡀⠀⠀⠀⠀⠀⢀⡾⠓⣦⡄⠈⢦⣀
⠀⢸⢱⡇⠀⠃⠀⢸⣾⡀⠀⠀⠀⠁⣹⣷⣶⠟⠛⠥⠴⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣿⣧⠀⣀⡀⠻⡷⠀⠀⡐⠉⠠⠏⠴⠂⢹⠆⠀⠀⢳⠀⠀⠀⢀⣠⡯⣔⣊⣁⣤⣤⣤⢽
⠀⠸⣾⢰⣄⠀⠀⠀⣿⢆⠀⠀⣠⠞⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⢼⡟⠋⣻⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⢠⣤⣶⠛⣠⠴⠛⠉⠀⠀⢳⣾⢸
⠀⠀⢻⡆⠹⣏⠓⠢⠟⠻⣷⣄⠈⢦⣼⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠴⣚⠏⠉⣳⠀⠀⠈⠑⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢰⠀⣿⣷⠟⢁⣠⡤⠚⠓⢦⡀⣿⢸
⠀⠀⠀⠻⢦⣈⣻⣦⣄⢀⣈⣉⣹⠯⠞⢷⡋⠉⠉⠉⠐⠒⡆⡸⡄⠀⢇⡀⠠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠳⢤⡉⠲⣅⣀⣿⠵⠚⠉⠁⣀⠜⠁⠀⠀⢸⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣂⣉⣤⣐⣋⡈⣡⡈⠉⠘⠱⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⢤⣤⠔⠁⢀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠈⠹⣦⣤⠤⣀⡀⠀⠀⠀⠀
⠀⠀⠰⠩⠁⣰⣿⠃⠀⢠⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⣟⣦⡀⠈⣷⠀⠀⠀
⠀⠀⠀⢗⣠⡿⠁⠀⢀⡃⠀⣈⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⢢⠰⠀⠈⣾⣧⢰⢸⠀⠀⠀
⠀⠀⠀⠘⣿⠁⡘⠀⡌⡇⠀⡿⠸⠀⠀⠀⠈⡕⡄⠀⠐⡀⠈⠀⢃⠀⠸⡾⠧⠂⠀⠀⠀
⠀⠀⠀⢀⠇⡇⠃⢠⠀⠶⡀⡇⢃⠡⡀⠀⠀⠡⠈⢂⡀⢁⠀⡁⠸⠀⡆⢟⡀⠀⠀⠀⠀
⠀⠀⠀⠸⠀⢸⠀⠘⡜⠀⣑⢴⣀⠑⠯⡂⠄⣀⣣⢀⣈⢺⡜⢣⠀⡆⡇⠘⣧⠀⠀⠀⠀
⠀⠀⠀⡇⠀⢸⠀⡗⣰⣿⣻⡿⡳⡅⠀⠀⠀⠀⠈⡵⣿⣿⡻⣷⡡⡇⡇⠀⣿⣇⠀⠀⠀
⠀⠀⣸⠀⠀⡆⡄⣧⡏⢸⣧⣿⣼⠁⠀⠀⠀⠀⠐⢙⣿⣻⢡⠘⣇⡇⠃⠀⠸⣽⡄⠀⠀
⠀⢠⠟⠀⠀⢰⢁⡇⠇⠰⣉⢉⡜⠀⠀⠀⠄⠀⠀⠘⣉⣉⠌⠀⠃⠰⠀⠀⠀⢻⡰⠀⠀
⠀⡛⠀⠀⠀⠀⢊⣤⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⢸⠃⠀⠀⠀⠀⢱⠃⠀
⣨⠁⢀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⢸⠸⠀
⠛⠸⠘⡀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠒⠋⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⢠⢸⠀⡇
⠀⠇⢆⢃⠀⠀⠀⠀⠀⡏⢲⢤⢀⡀⠀⠀⠀⠀⠀⢀⣠⠄⡚⠀⠀⠀⠀⠀⠀⣾⢸⠀⠀
⣶⠈⢌⢎⢆⠀⠀⠀⠀⠁⣌⠆⡰⡁⠉⠉⠀⠉⠁⡱⡘⡼⠇⠀⠀⠀⠀⢀⢬⠃⢸⠀⡆
⠈⢣⡀⠑⢵⣧⡀⠀⠀⡿⠳⠂⠉⠀⠀⠀⠀⠀⠀⠀⠁⢺⡀⠀⠀⢀⢠⣮⠃⢀⡞⡰⠀
⠀⠀⠑⠕⣆⡙⡭⠢⢀⡀⠀⠁⠄⣀⣀⠀⢀⣀⣀⣀⡠⠂⢃⡀⠔⠱⡞⢁⠆⣁⠔⠁⠀
⠀⠀⠀⠀⠀⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀