╱▔▔▔▔▔▔▔▔▔▔▔╲╱⠀ I⠀N⠀F⠀O ⠀╲╱▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔▔⠀⎯⠀❐⠀⤬⠀|╲

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀𝘏𝘪, 𝘐'𝘮 𝘙𝘪𝘯. 𝘐'𝘮 𝘧𝘳𝘰𝘮 𝘙𝘶𝘴𝘴𝘪𝘢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀𝘈𝘨𝘦: 18
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀𝘉𝘪𝘳𝘵𝘩𝘥𝘢𝘺: 𝘖𝘤𝘵 9
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀𝘊𝘰𝘮𝘮: 𝘌𝘯𝘨 / 𝘙𝘶𝘴

⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡌⢻⣿⣼⣿⣼⢹⣿⡄⣿⣿⣿⠀⣾⠀⠉⣿⠇⠸⡆⡇⢸⡇⣿⠃⠀⢹⢸⡟⡇⢸⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣴⣶⣄⠈⠟⢻⣿⠘⣼⡏⣷⠻⣿⣿⢡⣿⡇⢸⣿⠀⡇⢻⣽⢸⡇⢹⡆⠄⢸⡜⡇⠀⣼⣿⣿⣷⣴
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣫⡆⡇⠟⣿⣿⡇⠀⣿⢳⣶⠟⢰⣿⢰⢿⣿⢸⣿⣷⠀⢿⠀⠟⠈⣿⡼⡇⡌⣷⡄⡇⠇⣿⠀⢸⣿⣿⠱⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⢛⣥⢰⡿⣸⣷⢠⣿⣿⡇⢠⢿⢸⣿⠀⣼⣿⡌⢸⡟⠾⢟⡫⢀⠈⠀⣿⡆⢹⣇⣷⣧⢹⡇⣿⠰⠁⠀⢸⣿⣿⠘⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠛⠋⠉⠀⣿⡇⣾⠇⣿⣿⡄⢻⣿⡇⢸⢸⣿⣿⠀⣿⣿⡇⠋⠇⢚⣩⣾⣿⡆⠀⣿⣿⡀⢿⣘⣿⡼⡇⣿⠀⢰⠀⢸⣿⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⣶⣿⡟⢠⡎⢸⠀⣿⣧⡿⣸⣿⣿⣇⢸⣿⡇⢸⢸⣿⡇⢰⣿⠏⢀⡀⠀⣿⣿⠿⣛⠃⠀⡿⠟⠃⠈⢉⡈⠀⠀⠇⣸⡇⠀⡈⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⣾⠁⠘⠀⣿⢈⠁⣩⣿⣯⣙⠘⣿⡇⣸⢸⣿⠃⣼⠟⢰⣿⣷⠠⢋⠔⠊⢀⣤⣴⡶⣰⣶⠖⠀⣐⣿⡖⢠⣿⣷⣸⣧⣿⡟⠁⢰
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢰⡿⢀⣾⢠⣿⠘⢸⣿⡹⠉⠛⠆⢻⠀⣿⡼⠏⢀⠏⠀⢸⣿⡟⠁⠀⣴⣾⣶⡭⠷⣚⣋⣠⣴⣿⣿⣿⠃⣼⣿⣿⣿⣿⣿⡇⢠⣾
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣼⡇⢨⣿⠘⡿⠀⠿⠿⠷⠄⠀⠰⠘⠀⢸⣇⠀⣼⣇⣰⣿⡌⠃⢠⣼⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⡏⢠⣿⣿⣿⣿⣿⣿⠇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡏⡿⠀⠀⠙⠦⠀⣀⣭⣍⠰⠆⣴⢤⣀⠀⣿⡿⢰⣿⣿⣿⣿⣷⣤⠌⢉⣡⣤⣤⣤⠄⠀⠉⠛⢿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⡄⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠠⣙⠻⠿⢷⡶⠶⣛⣿⠈⠻⢷⣿⣿⣿⣿⣿⡟⠁⣴⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠉⠁⠀⣸⣿⣿⣿⣿⣿⣿⣷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠺⠃⠀⠀⠀⠀⠀⢀⡄⢂⣉⣭⣉⣙⡛⠛⢳⣧⢠⢻⣿⣿⣿⣿⡇⠘⠿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠈⢰⣿⣿⣿⣿⣿⠿⠂⠀⠉⠊⠇⢻⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣶⣶⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣶⣤⣀⣀⡀⢀⣀⣀⣠⣴⣿⣿⣿⣿⡿⣿⣿⣿⠟⣡⢫⡏⢾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠡⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⣴⣿⣿⠋⣰⣗⠞⠀⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⣶⣄⠠⣤⣤⣶⣿⣦⣀⣦⣝⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⣡⣾⣿⣿⡿⢁⣾⣿⣿⠰⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣿⡿⣻⣿⣿⣿⣿⡗⢌⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⡩⢆⣴⣾⣿⣿⣿⠟⡀⣼⣿⣿⠟⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡆⠈⠠⣻⣿⣿⠛⠉⠁⠀⢻⣶⣍⡛⢿⡿⠿⠿⠿⢿⣛⣛⣉⣁⠤⢐⣡⣶⣿⣿⣿⣿⣿⠏⠀⢰⣿⠟⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⠁⠀⢸⣿⣿⡝⠀⠁⠀⣄⠈⢿⣿⣿⣷⣬⡛⠷⣶⣤⣭⣭⣉⣒⣚⣽⣿⣿⣿⣿⣿⡿⠃⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣟⢿⣿⣿⣿⣶⣝⢿⣿⣄⣴⣿⣿⣷⡈⢿⣿⣿⣿⣿⡐⣬⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣦⡻⠿⠿⢋⣽⣧⢈⣿⣿⣿⣿⣿⠟⠈⢻⡏⠙⠛⠳⠘⢟⢷⣌⠻⢿⣿⣿⣿⣿⡿⠛⣁⣠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣏⠐⢒⣬⣙⣣⠙⢿⣿⡟⠠⣦⣦⣈⠳⡀⣁⣦⣧⠘⢠⣿⣷⡀⢭⣙⣋⠉⣴⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⣿⡔⡆⠹⣷⣐⣿⣿⣿⣧⢻⣿⣿⣿⡠⣿⣿⣿⡇⠸⣿⣿⡄⠘⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⡄⢸
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣏⠡⢊⢠⣿⡧⠁⡰⠹⣿⣿⣡⣶⣦⡁⢿⣿⣿⡇⠿⣛⣛⠇⢸⣿⣶⠇⣠⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⢠⠰⠃⡇⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠁⠐⠂⠈⠇⠀⢮⣗⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣾⠃⠀⠀⠀⣠⠀⠀⡄⠈⠻⠱⠀⠀⠈⡙⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠅⠀⢠⠾⠃⢀⠀⢠⠀⡀⢆⡀⢀⣷⣷⠀⠀⠉⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠂⠀⢀⠥⠂⣸⠯⠋⠃⣀⡁⠈⠀⡸⠛⠛⢀⠀⡀⠀⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⢬⡆⠀⠐⠸⡆⢈⠓⠁⠩⠐⠠⢀⢈⠑⠀⢺⣄⠀⠲⡥⠈⣑⠀⠘⡧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⢸⣦⠨⢦⡀⡆⡀⠀⢀⣞⡠⠀⠀⠀⢬⠆⠉⠀⡖⣰⣿⠦⠀⢀⠀⣴⡆⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠻⠀⠄⠀⢆⡃⠀⠀⢱⠃⠄⠈⢻⠳⢈⠠⢠⠄⠠⡟⠀⠀⠛⣴⡛⢨⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠅⠐⠐⠿⣅⡀⠈⡓⠇⠸⡭⠄⢿⣳⡄⠀⢰⠧⠀⢄⡿⠏⠀⠂⢄⣧⠲⠊⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠡⠙⢙⣀⢄⢦⠠⠀⠀⠙⠿⣄⠰⠣⠘⠁⠀⠀⠈⠋⠠⠀⠀⠁⠀⠀⠀⠀⠀⡀⠀⢤⠷⣢⡠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠥⠈⠀⠂⠀⠀⢀⠀⠀⠀⠀⡄⠀⢠⠀⢶⡐⠀⠀⢀⠈⠉⢭⡲⢢⣖⡄⠍⡁⠀⠉⠑⠀⢤⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⠂⠀⠀⠀⣀⠀⠀⠀⢠⢀⠀⢀⣴⡶⡘⠁⠀⠀⠃⢄⠂⠐⡻⠫⠀⢂⠀⠀⠄⠠⠀⠀⠄⠀⠀⠀⠴⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⡁⠄⡐⢊⠈⠀⠀⠁⡀⠀⠀⠘⢁⠰⡠⠂⠐⠁⠦⠣⠀⠀⠐⠀⠀⠀⠀⠀⠀⠑⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⢰⠃⡄⠀⠀⠀⠘⣧⠈⠐⠀⠀⠀⠂⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠈⠀⠀⠑⠧⠃⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀