⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀╭––––––––––––––––––––––––––––––––––––––––––––––––––––––––––╮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀.𝚝𝚡𝚝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎯⠀⠀❐⠀⠀⤬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀┞––––––––––––––––––––––––––––––––––––––––––––––––––––––––––┦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀|
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀|⠀⠀⠀𝗕𝗟𝟰𝗖𝗞 𝟬𝗨𝗧 𝗧𝗛𝟯 𝗦𝗞𝗬⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀𝖝.⠀⠀|
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀|⠀⠀⠀⠀⠀⠀⠀ ⠀⠀ 𝖉𝖔𝖓'𝖙 𝖋𝖊𝖆𝖗 𝖉𝖊𝖒𝖎𝖘𝖊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀|

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀╰––––––––––––––––––––––––––––––––––––––––––––––––––––––––––╯

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠃⠀⡼⡇⠀⠀⠀⠀⡇⠀⠹⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣠⡶⢶⠀⢀⡗⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠶⠶⣿⣇⣀⣸⠁⡇⠀⠀⡀⠀⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⡴⢾⣿⠃⠀⠀⠀⠀⣼⠃⣸⠇⣿⡇⠀⠀⠀⢠⡆⠀⠀⣴⡏⠀⢈⡿⢦⣇⠀⣼⠇⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⠁⣠⣿⠏⠀⠀⠀⢀⣼⠏⢰⡟⠀⣿⡇⠀⠀⢀⡾⠁⠀⣼⢟⠃⣴⠏⣀⣴⠟⣿⠃⢠⠀⣧⠀⣷⠀⠀
⡀⠀⠀⠀⠀⣤⠀⢀⡴⢿⡇⠀⢠⣿⡗⠀⠀⠀⣰⣿⡿⢠⡟⠀⠀⣿⡇⠀⠀⣸⡇⠀⣸⠇⢠⣼⣿⣿⣿⣅⣤⣤⣤⣼⣄⡟⠈⣿⠀⠀
⣧⠀⠀⠀⠀⣿⡴⠋⠀⣾⠁⢀⣿⠿⠀⢀⣶⣾⣿⣶⣷⣯⡀⠀⠀⣿⡇⠀⣰⡟⢀⣴⠏⢠⣿⣿⠿⠛⠛⠻⣿⣿⣿⣿⠋⡅⠀⠸⣦⠀
⠘⣧⡀⠀⠀⣿⡇⠀⢸⡇⢀⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⠶⣄⠀⠀⣿⡇⢰⡿⢁⡞⠃⢠⣿⡟⠀⠀⠀⠀⠀⠸⣿⣿⣿⠖⠁⠀⠀⠿⣧
⠀⠹⣷⡀⠀⣿⠁⢸⡿⢀⣾⣿⠿⠛⠋⠉⠉⠉⠉⠙⠻⣦⡈⠀⠀⣿⣡⣿⡥⠞⠀⢀⣾⡿⠀⠀⠀⠀⠀⠀⠀⣿⢿⡿⠀⠀⠀⠀⠀⠹
⠀⠀⠈⢷⡄⣿⢠⣿⣷⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⢸⠿⠟⠁⠀⠀⠀⠈⢻⠇⠀⢰⡆⠀⠀⠀⢀⡟⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⢻⣿⢘⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⣼⠁⢻⣧⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⠉⠛⠶⣌⣷⣀⠀⢀⣀⣠⣶⠋⡻⡎⢹⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⢿⣿⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠬⣉⣙⠓⠦⢭⠒⠲⠤⠉⠙⠻⣿⡟⠧⣌⠓⢭⡒⠊⢿⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠹⣧⡹⣯⣛⠿⠷⠶⢶⣶⣶⠶⠶⡒⢀⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠰⣦⣼⣿⡦⠍⠉⠛⠒⠲⠦⢤⣀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⡀⠀⢸⣷⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠢⢍⡒⠦⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀
⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀
⠀⠀⠀⢶⣙⣯⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠆⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀
⠀⠀⢀⠈⠙⢾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣛⠉⠁⠀⠀⠀⠉⠛⠓⠲⠶⠶⠚⢛⣿⠁⠀⠀⢀⣼⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠘⣦⡀⠀⠙⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣶⣦⣤⣤⣄⣀⣀⣠⣤⣤⣤⡶⢾⡏⠀⠀⢀⡼⢹⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠘⢿⣄⠀⠈⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠉⠉⠀⢀⠀⠀⣀⡀⢤⠄⢀⣠⣾⠇⠀⣠⡞⠁⢸⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⡟⢷⡄⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⢀⣘⡓⠒⠚⠋⠉⠉⠉⠙⠋⠁⠀⣰⡟⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢻⠈⣷⡄⠀⢹⣷⣤⣀⡀⠀⠀⠀⠀⠀⠘⠿⡤⠴⠚⠉⠀⠀⠀⠀⠀⠴⠖⠀⠀⠀⠀⣰⡟⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡆⢸⢿⠀⠈⣷⡈⠛⠿⣷⣶⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋⠀⠀⣰⠏⠀⠀⣠⠄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⡇⢸⢸⠀⠀⢸⡇⠀⠀⠈⠹⣿⣿⣿⣿⣿⣻⠿⠿⠿⠿⣶⠶⠿⠏⠉⠉⠉⠉⠀⠀⠀⠀⣼⠏⠀⢀⣴⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠇⢸⡿⠀⠀⠘⡇⠀⠀⠀⠀⠀⠉⠛⠻⢿⡟⠶⢦⣤⣤⡴⠶⠖⠒⠒⠒⠒⠒⠶⢶⣤⡾⢋⣠⣴⠟⠁⠴⠋⠀⠀⠀⠀