Flan Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠚⠉⠉⠉⠉⠉⠉⠉⠉⠓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠲⠤⣤⣀⣀⣀⣀⣀⣠⡤⠤⠚⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢱⠀⠀⠀⠀⢀⠊⠑⡀⢈⠈⠁⠘⢄⢹⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠤⡎⠀⢀⠀⠀⠀⠀⠀⠀⠀⠣⠂⠀⠀⠀⠀⠉⣧⠤⣤⣀⡀
⠀⠀⠀⠀⣠⠖⢋⠥⠀⠀⠀⠘⣅⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⡄⠄⢍⠙⠲⣄
⠀⠀⠀⠀⢧⣀⠙⠢⠤⠁⠀⠀⠈⠑⠢⠤⣤⣀⣀⣀⣀⣀⣀⣀⣤⠤⠖⣊⠁⢠⠂⠀⡤⠞⢀⣠⠟
⠀⠀⠀⠀⠀⠈⠛⠶⣶⣤⣤⣄⣀⣀⣀⣀⣀⠀⠀⠉⠉⠁⠀⠀⣀⣀⣀⣀⣀⣠⡤⠴⣶⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠑⠒⠛⠛⠩⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠽⠑⠒⠒⠉⠉





⣿⣟⣛⣟⣛⣻⣛⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⢶⣾⣿⣿⣿⣾⣷⣀⣰⣷⣷⣶⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣷⣿⣻⣿⣿⣿⣿⣿⣻⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠿⣿⣤⡙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠝⢻⢿⣷⣶⣶⢿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠻⣷⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡌⠀⠀⣿⡟⠉⠙⣷⣿⠛⠉⠻⠛⣿⣯⣭⠉⢻⣧⠀⠀⢻⣷⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠂⠀⢠⣿⠁⠀⠀⣿⡏⠀⠀⠀⡇⢹⣿⣿⠀⠸⣿⡄⡄⠸⣟⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⢠⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⠀⠀⢱⣾⡟⣿⡄⠀⣿⣧⡇⠀⣿⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢸⡏⠀⠀⢰⣿⡇⠀⠀⠀⢸⣿⡇⣿⡇⠀⢻⣿⠃⠀⢿⡄⠀⣳
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⡇⠀⠀⣾⡇⠀⠀⣸⣿⡇⠀⠀⠀⢸⣿⣿⣿⠃⠀⢸⣿⣿⠀⢸⡇⠀⠀⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣯⠀⠀⠀⡇⠀⢰⣿⡇⠀⢀⢋⣿⡇⠀⠀⠀⢸⣿⣿⣿⡇⠀⢸⣿⣷⠀⠘⡇⠀⠀⣻⣿⣆
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⡈⣿⡇⠀⠀⠻⢿⠁⠀⠀⠀⠸⣿⣿⢿⣇⠀⢸⣿⣿⠀⠀⣧⠀⢸⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣶⣬⠀⠀⢷⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⢰⣿⣿⢸⣿⠀⢸⣿⣿⡇⠀⣭⣶⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣧⣄⣘⣹⠀⠀⠀⢸⣿⠀⠀⠀⠀⢨⣿⣿⣾⣿⠀⠀⣿⣷⣽⣴⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣷⣤⣤⣬⣿⣄⣀⣀⣀⣘⣥⣿⣭⣭⣴⣾⣿⣿⣿⣿⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠴⠶⠶⠶⠶⠶⠶⠦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠛⠛⠉⠁⣿⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠸⡇⠈⠉⠙⠓⠶⣤⣄⡀
⠀⠀⠀⠀⠀⢀⣤⠾⠛⠁⠀⠀⠀⠀⠀⢸⣇⠀⢀⡼⠋⠉⠙⣧⠀⠀⠀⠀⢠⡟⠁⠀⢹⣆⠀⣿⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⡀
⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠛⠋⠀⠀⠀⠀⠸⣧⠀⠀⢀⡾⠁⠀⠀⠀⠙⠛⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⣿⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⠀⠀⠈⠙⠻⠶⢦⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⣤⡶⠾⠛⠁⠀⠀⣀⡼⠋⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣀⡀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⢀⣀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠓⠶⠶⠶⠶⠶⠶⠶⠶⠖⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢮⣍⡛⠳⠶⢦⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⠶⠾⢛⣫⡽⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⢦⣤⣀⣀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⣁⣀⣤⡴⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠓⠶⠶⠶⠶⠶⠶⠶⠶⠚⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⢂⣀⣭⣭⣭⣭⣭⣍⣀⡐⠀⠂⠤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡞⠛⠋⠀⠠⠀⠁⠀⠉⠛⣿⢷⣄⠀⠀⠈⠑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣏⠀⠀⠀⠀⠀⠀⠀⠀⢔⠳⢶⣷⣭⢃⣀⡀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣯⡀⠀⠀⠀⠀⣀⢀⣤⡀⡸⣻⣿⢟⢼⣭⣭⣳⣤⡀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠀⠙⠿⣷⣶⣶⣦⣶⣶⣤⣵⣿⣻⠟⠋⠀⣿⣦⡹⣷⡱⡀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠉⠉⠀⠀⠀⠀⢻⣯⡱⢺⣷⢇⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢰⣻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣼⣿⣷⣿⡿⡸⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⣏⢿⣿⡷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⢟⡴⠁⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠘⢯⡻⢄⠓⠛⠳⣶⣤⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⢯⡏⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠙⠲⢬⣐⡂⠩⢍⠛⣭⣿⣭⣿⠿⣛⣛⣛⣛⣯⡵⠊⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠚⠶⠯⠵⠖⠛⠉⠉⠉⠁⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠒⠶⠶⠶⠶⠶⠶⠒⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⢺⣍⣴⢿⠃⠗⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿⢋⣽⣦⠋⡇⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣧⢸⣿⣌⣦⠑⢦⣄⣑⠤⣤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣯⣙⠛⢍⡣⡙⢿⣿⣦⣤⣈⡳⣴⣬⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠯⠑⡄⠹⠈⠂⠙⠿⣿⣿⣿⢸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⣿⣿⣿⡐⠈⠯⣊⣀⣁⡀⠁⢺⣿⠇⠀⣙⢻⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢈⣿⣿⡛⠉⠒⠀⢤⠤⣄⣈⠁⢻⣻⣿⡃⡊⠙⠿⠿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⡀⢸⣿⡿⢯⠒⠢⠤⠤⠥⢀⣀⣉⣉⠉⠛⠿⣶⣦⡀⢰⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⣿⣿⣜⣀⢻⣷⠀⠙⢂⠤⠠⠤⠤⢤⣀⠈⠉⠓⠤⢈⡙⣿⣿⣿⣿⣿⠛⡒⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⡁⠀⡼⢈⣿⡿⣿⣿⣏⡀⠑⠢⣍⠒⠦⠤⠤⠌⣳⣬⣭⣵⣿⣾⣿⣿⣿⡿⠋⠁⢇⠀⡄⡀⠈⠉⠙⠒⢤⡀
⠀⠀⠀⠀⠀⢀⣠⠤⠔⠒⠋⠠⡀⠈⣸⠁⣸⣿⣿⡿⢿⣻⣿⣿⣿⣿⣿⣿⣴⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠘⡀⠐⠁⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⢀⡞⠉⡠⠚⠁⠀⠀⠀⠀⢰⠋⢠⣿⣿⣿⠀⠀⠈⠉⠙⠛⠿⠿⠿⠿⢿⣿⣿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢳⣶⣶⣤⣀⠀⠀⠀⠀⠀⠙⠢⢄
⠀⢀⡤⠋⠀⠐⢅⠀⠀⠀⠀⢠⣴⠏⠀⣸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠑⡄
⣰⠋⠀⢀⣐⠒⠦⢌⠀⠀⣴⣿⡟⠀⢰⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⡜⠀⠀⠉⠑⠂⠀⣼⣿⣿⠁⠀⣸⡻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈
⠹⡄⠘⠄⠀⠀⠀⠀⢠⣿⣿⣿⡀⠀⣿⣧⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇
⢠⠇⢀⠔⠂⠀⠀⠀⠸⢹⣿⣿⣳⣸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠐
⢾⢀⠘⡄⠀⠀⠀⠀⠀⢯⢿⣿⣿⣟⢻⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣾⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⡀⠀⠀⡄
⠘⢮⡳⢄⠑⠀⣀⣠⠤⠌⠻⣿⣿⣿⣿⣿⣷⡦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠃⣀⣀⣀⡤⠊⠀⡠⢚⡜
⠀⠀⠉⢦⠳⡀⠁⢠⠤⠖⠂⠀⠙⠻⣿⣿⣿⣿⣷⣿⣿⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉⠤⣀⡀⣀⠀⠀⡰⢋⠴⠋
⠀⠀⠀⠀⠳⡙⢄⠈⠀⠀⢀⠤⠒⠀⢀⡉⠛⠿⢿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⡁⠐⠢⢄⣀⠀⠀⠀⣠⠜⣱⠋
⠀⠀⠀⠀⠀⠉⠢⣝⠲⠤⢤⣈⠀⠰⡉⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠈⠓⠂⢀⣀⡤⠔⣊⡥⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⢬⡙⠢⢌⡑⠲⠤⠤⠀⠀⠀⠀⢀⠆⠀⠀⡄⠀⠀⠀⢠⠀⠀⠀⢆⣀⣀⣀⣀⠤⠄⠀⠀⣀⠴⢊⡠⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣌⣉⣓⠒⣒⠒⠒⠤⠌⣁⣀⣀⠁⠀⠀⢀⣈⣉⣠⠤⠄⠠⠤⠤⠤⠤⠖⢒⣋⠥⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠒⠦⠤⣤⣌⣉⣉⣉⣭⡭⠤⠴⠖⠒⠒⠒⠒⠒⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣦⣤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣿⡟⠙⣷⡴⣿⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣷⢿⡿⣿⣿⣤⣼⣷⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⡿⠿⣦⣿⣾⣡⣿⣿⢉⣷⣼⣷⡿⣿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡉⠁⠀⠀⠀⠘⢧⣼⣯⣩⣿⣋⣽⣧⠾⠁⠀⠀⠉⠛⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠛⣿⡿⠳⠶⣤⣤⣄⣀⣀⣀⣀⣀⣉⡁⠀⠀⠀⠀⠀⣠⣾⣿⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⢰⣿⠇⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣿⣿⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⣾⣿⠀⠀⠀⠀⢠⣶⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⢠⣿⡇⠀⠀⠀⢰⣿⠟⠉⣿⣷⠀⠀⠀⢀⣤⣤⣄⠀⠀⢸⣿⡄⠀⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⣸⣿⠁⠀⠀⢠⣿⡟⠀⠀⢹⣿⡄⠀⠀⣾⣿⢻⣿⡀⠀⢸⣿⡇⠀⠀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⣿⡿⠀⠀⢀⣾⡿⠀⠀⠀⠸⣿⡇⠀⢰⣿⡇⠘⣿⣇⠀⣸⣿⠃⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⢠⣿⡇⠀⠀⣼⣿⠃⠀⠀⠀⠀⣿⣿⠀⢸⣿⠃⠀⢻⣿⣶⣿⡟⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⢸⣿⡇⠀⣸⣿⠇⠀⠀⠀⠀⠀⢻⣿⡄⣾⣿⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⣀⣤⣶⡿⢿⣿⡇⠀⢸⣿⣇⣴⣿⠏⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣤⣀⡀
⠀⣰⣾⠟⠋⠁⠀⠸⣿⣧⡀⠈⠿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⠛⠿⢿⣷⣄
⢸⣿⠃⠀⠀⠀⠀⠀⠙⠿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⠟⠁⠀⠀⠀⠀⢙⣿
⠘⣿⣧⣀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣿⡿⠿⠟⠛⠉⠀⢀⣀⣀⣤⣴⣾⣿⠟
⠀⠈⠻⢿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⣰⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣷⣦⣤⣀⣀⣀⣀⣀⣀⣤⣴⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⣀⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣁⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠖⠂⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠠⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⠂⠀⠀⠈⠉⠉⠉⠉⠓⠲⢄⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⣀⣀⣀⠀⠀⠀⢀⣀⣀⣤⠄⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠠⠊⠂⠀⠀⠀⠀⡴⠁⣆⠀⠀⡠⠹⣆
⠀⠀⢀⡠⠴⠒⢊⠃⠀⠀⠀⠦⠔⠁⠀⠀⢰⠄⢀⠔⠁⠀⢸⠀⠀⠀⠀⢹⡍⠛⠲⠦⣤⣀
⢠⠞⠁⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢻⡀⠀⠀⠈⠙⢷⣄
⣯⠀⠀⠀⠀⠀⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡗⠀⠀⠀⠀⢸⣿⠇
⠈⠳⣄⡀⠀⠀⠀⠈⠉⠉⠙⠢⣀⢀⣀⡠⠤⣄⣀⠀⠀⢀⡤⠞⠛⠛⠛⠋⠁⠀⠀⢀⣠⣴⠿⠋
⠀⠀⠀⠉⠙⠲⣦⣤⣄⣀⣀⡀⠈⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⣀⣀⣀⣤⣤⣶⠾⠛⠉
⣀⣀⣀⣀⣀⣀⣀⣉⣉⣛⣛⣛⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣋⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣻⣛⣙⣛⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠛⠿⠿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣾⣿⠟⠁⠀⠀⢺⣿⠆⠀⠀⠀⠀⠀⠀⠸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆
⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣾⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣷⣶⣶⣶⣶⣶⣶⣦⡀
⠀⠀⠀⠀⢿⣿⣯⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣩⣿⣿⠇
⠀⠀⠀⠀⠈⠛⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠉




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⢶⣿⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⢀⠠⡿⠁⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠘⠷⠶⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠶⠟⠛⠛⣷⠀⠀⠀⠀⠀⠀⠀⢰⡿⠶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⠀⢀⣀⣴⠟⠀⠀⠀⠈⠙⠻⢶⣄⡀
⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀
⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿⡀
⢀⡿⠀⠀⠀⠀⠀⢀⣀⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⠛⠳⢦⡀⠀⠀⠀⢠⡾⠛⠻⣆⠀⠀⢸⡇
⢸⡇⠀⠀⠀⣠⡶⠛⠉⠁⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠻⣦⣀⣤⠟⠁⠀⠀⠹⣆⠀⢸⡇
⣿⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢻⡄⠈⣷
⠹⢦⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⢿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⠀⢀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⢸
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟
⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢹
⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⡾⠋⠀⠀⠀⢠
⠀⠹⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⢀⣴⠟
⣀⣀⣈⣉⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣋⣁⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢩⡁⠀⠀⠀⠀⠀⠀⠀⠀⢘⡍⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣶⣮⣥⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠹⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠛⣿⣿⣿⠛⢿⣿⠟⠙⣿⣿⡇⠙⠁⠸⣷⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡜⠀⢸⠹⢿⡇⠀⠀⠁⠀⠀⢸⣷⠃⠀⠀⠀⠈⠛⢧⡀
⠀⠀⠀⠀⠀⠀⣀⡤⠔⠒⠈⠉⢠⣼⠁⠀⠈⠙⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠉⠉⠒⠢⠤⣀
⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠰⣞⡛⢿⣦⣀⠀⠸⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠞⠁⣘⢿⡀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠓⢄⡀⠀⠀⠀⠀⠉⠑⠭⠿⠿⣿⢿⣧⣤⣤⣤⣤⡤⠤⠴⠶⠖⠛⠉⠱⠶⠶⠂⠉⠉⠀⠀⣀⣤⠎
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⣠⣤⣤⣄⣀⣀⣈⣉⣉⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⡀⢀⣠⣤⣤⣶⣶⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠂⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠐⠒⠀⠈⠉





⣿⣿⢛⢿⠛⠟⣿⢟⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠊⣩⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣿⣿⣿⣯⡻⣿⣿⣿⠋⣿⣶⣾⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡴⢛⣧⣸⣿⣿⣿⡿⢛⣷⣮⣭⣄⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀⣿⣿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠳⣼⣏⠻⣿⣿⡏⠻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣦⣬⣙⣳⡶⡿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣶⣦⣤⣤⣤⣄⣀⣀⣀⣀⣀⣠⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉⠀⠀⢠⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣿⣾⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣿⢤⣀⣙⣛⣛⣟⠛⠀⢈⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⡟⠀⢀⣤⡍⠉⠁⠀⠀⢸⡇⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣸⠇⢀⣾⠁⣿⠀⢰⣶⡆⢸⡇⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣿⠀⣼⠃⠀⢸⡇⣿⠈⢿⣼⠇⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⣿⠀⣿⣼⠏⠀⠀⠘⢷⠟⠀⠀⠀⠀⠀⢸⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠻⢦⣍⣁⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠞⠁⠉⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⣀⣈⣉⣙⣛⡛⠛⠛⠛⠛⢋⣿⠷⠶⠶⠾⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠉⠛⠿⠶⠾⠟⠛⠁





⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢊⡯⠯⢯⠯⢿⠏⠋⣿⠉⡱⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢆⡞⢰⠀⡇⠅⢰⢠⠆⠈⣷⠌⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢈⡇⢬⢠⠀⠁⢸⢀⠀⠀⣟⠀⠇⢡
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠤⠒⡎⠇⣘⠃⠇⢸⢐⡄⢸⢸⠀⢰⡇⠁⢸⠘⡆⠤⠤⠤⣀⣀
⠀⠀⢀⠤⠒⠋⠉⠀⠀⠀⠀⢠⣤⢹⠀⢸⠀⠁⠸⠈⠀⢸⢸⠀⢸⢰⠀⡀⣧⢣⠀⠀⠀⠀⠀⠉⠑⠒⠤⡀
⠀⠀⠁⠀⠀⠀⢠⠖⠉⠁⠀⠀⡏⠇⠀⡆⡀⠀⡆⠸⠁⢸⢸⠀⠈⣸⠀⠀⢹⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⢘⠄
⠀⠀⠑⠢⣄⡀⠀⠁⠠⠅⠀⣈⡲⠤⣤⣁⠃⠀⡇⠀⠀⠸⠘⠀⠀⠃⣆⣀⣀⢗⣊⡠⠤⠒⠀⠀⢀⣠⡴⠊
⠀⠀⠀⠀⠀⠉⠛⠶⠶⣦⡤⠤⠌⣀⣀⣀⣈⣉⡉⠁⢈⡉⠉⢉⣉⣉⣁⣀⡀⠠⠤⠤⠔⣒⡲⠝⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠒⠲⠶⢤⣒⣒⣒⣒⣒⣒⣦⠴⠶⠒⠒⠂⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣶⣶⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠙⠛⠻⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿
⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠿⠁⠀⠀⠀⠀⣸⣧⡀⠀⠀⠀⠀⣴⣦⣄⣀⣀⣀⣀⣀⣠⣤⣶⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠓⠶⠶⣶⣶⡶⠶⠟⠛⠅⠀⠀⠀⠀⠀⢀⣿⣿⣷⣤⣰⣿⡿⣿⣏⣿⣿⣟⠛⠻⠿⠿⠿⠿⠛⠋⠁⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣟⠣⣿⢿⡿⢾⣿⣿⣿⣿⣿⣷⡀⠀⠀⢀⣀⣠⣤⣶⣿⡿
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⠟⠻⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠉⠙⠛⠛⠋⠉⠉
⠈⠉⠒⠶⠦⢤⣤⣤⣤⣤⣤⣴⣶⣾⠿⠿⠛⠋⠉⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⢀⠀⣤⣶⡶⣶⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣦⣄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣄⢾⠙⢯⣿⣿⣾⣿⣿⣇⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣀⠀⠀⣸
⠀⠀⠀⠀⠀⠙⢷⣴⣦⣽⣿⣿⣟⣩⠵⠋⠀⠀⠀⠀⠀⠢⣄⣀⡀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣾⣿⣿⣿⠿⠟⢀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⢡⣐⡝⡄⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠿⠿⠿⢿⣿⡿⠿⠿⠋⠀⢀⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠊⠀⣑⢂⡝⠆⠀⠀⠀⠀⠙⠲⢤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠒⠒⠊⠉⠀⠀⠀⢸⣷⡄⠀⠀⢠⣌⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠀⠀⣼⣿⣷⡄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠂⠤⣤⣀⣀⣀⣀⣀⣤⣤⣴⣾⣿⣿⣿⠃⢠⣾⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠿⠛⠋⣀⣴⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠑⠲⢤⣤⣤⣤⣀⣀⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⠟⠋
⣿⣿⠛⠿⢻⠿⡿⢻⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠟⠛⠛⠻⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣨⣿⣀⣀⣀⣀⣀⣀⣿⣅⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠛⠛⠛⠷⣆⠀⠀⠀⢀⣶⠟⠻⢶⡄⠀⠀⠀⣰⡾⠛⠛⠛⠛⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠻⣦⣀⣠⡿⠁⠀⠀⠈⢿⣤⣀⣴⠟⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣸⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣹⣇⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠘⣿⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠃
⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠘⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠃
⠀⠀⠀⠀⠀⠀⠘⣷⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⡖⣱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡲⠇⠀⠉⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⡦⠤⣼⣿⣿⣿⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⢀⠔⠚⠉⠉⠉⠉⠉⠛⢿⣿⣿⣿⡏⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⡰⠁⠀⣠⣶⣾⣿⣿⣿⣿⣶⠟⢿⣿⣇⣀⠀⠀⣸⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⣰⠃⣠⣾⠟⣩⣾⣿⣿⣿⣿⣿⣧⣼⣿⡟⠋⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣦⡀
⠀⢀⣼⣿⣤⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡀⠀⠀⠀⣾⣿⣿⡿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⠟⣀
⠀⣾⣿⣿⡏⢻⣿⣿⣛⣛⣿⣿⡿⠟⣻⠅⡼⡿⠫⠗⣖⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣡⣤⣤⣤⣶⣾⣿⣧
⢸⣿⣿⣿⣿⣾⣟⠛⠛⠋⠋⢙⣀⣤⣵⢿⠇⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣾⠟⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆
⣼⣏⣻⣿⣿⣿⠛⠻⣿⣞⣑⣋⣭⣿⣶⢿⣿⡇⠀⠀⢠⣾⣿⣿⡟⠛⢉⣡⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠈⠙⢺⡻⢋⣩⠅⠤⠯⡝⡄⠀⠸⣿⣿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⢻⣿⣿⣿
⣿⣿⣿⣾⣿⣿⠀⡇⠀⣀⠈⢧⠏⠀⠀⢀⣠⡎⣯⠀⠀⢻⣿⣿⣿⣦⣄⣉⣁⣤⣌⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣾⠿⠭⣤⣤⣿⣆⠈⢿⠲⣞⣽⣚⣧⣬⣦⣀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⡀⢻⣿⣻⣿⣿⣿⣿⣿⣿
⢹⣿⣿⣿⡟⠀⠀⠈⢹⣿⣿⡆⠈⢣⡱⠽⠟⣋⡥⠛⠒⠚⠋⣭⣛⣿⣿⣿⣿⣿⣿⣷⡌⠻⣿⣿⣿⣿⣿⣿⣿
⠘⣿⣿⣿⠿⢶⣤⣤⣾⣿⢃⣾⡤⣠⠛⠒⠉⠁⠀⠀⠀⢠⣾⠟⠛⢿⣿⡿⠿⠿⢿⣿⣿⣶⣬⡛⢿⣿⣾⣿⣿
⠀⠹⣿⡏⠀⠀⠀⢹⢟⣵⣿⣿⢱⠷⣦⣤⡀⠀⠀⠀⣰⡟⠁⠀⠀⠀⢻⣶⣿⣿⣿⣶⣯⣟⠿⠿⠈⣿⣿⣿⠇
⠀⠀⢹⠀⠀⠀⢀⣾⣿⣿⣿⣿⡆⠀⠀⠈⠙⠻⣦⣴⡏⠀⠀⠀⠀⢀⣸⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⢀⠓⠒⡶⠻⣿⣿⣯⡿⢟⣧⣄⡀⠀⠀⠀⣿⣴⣷⣦⣴⣶⡿⠽⠿⢿⣿⣿⣾⣿⣿⣯⣉⣽⣿⣿⠋
⠀⠀⠸⡇⡧⠿⣦⣤⣤⣴⣾⠋⠄⠉⢙⠿⣦⣴⣿⣿⣿⣿⡁⠀⡀⠀⠀⢸⣿⣿⣿⣟⣻⣿⣿⣿⠟⠁
⠀⠀⠀⠈⠁⠀⠉⠻⣿⣿⣯⣄⠀⠀⠀⠀⣼⣿⣿⣷⣿⣿⡿⠷⡦⢤⣥⣾⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠙⠿⣿⣶⣦⣴⣿⣿⣿⢿⣿⡟⠀⠀⠀⠀⠈⢻⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⠉⡿⠻⠿⠿⠿⠿⢿⠁⠀⠀⠀⠀⢀⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⢠⠿⠲⢦⣤⣤⠞⠁⠀⠀⠀⠀⢀⠜⠶⢤⣀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢌⠀⠈⠀⣽⠃
⣤⣤⣤⣤⣤⣤⣤⣬⣿⣶⣿⣥⣤⣤⣤⣤⣤⣤⣤⣬⣽⣷⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣩⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢡⣦⣶⡤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠈⠉⠀⠀⠀⠈⠩⠀⢀⣈⠂⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡄
⠀⠀⠀⠀⢀⡆⠀⠀⣏⡀⡀⠀⠀⣀⢰⡂⠁⢢⠀⣁⠀⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⢹
⠀⠀⠀⠀⢸⣿⣶⠀⡸⠋⠰⠀⢪⠀⠀⢹⣤⡠⠣⡀⠀⡀⠈⢠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⣾
⠀⠀⠀⠀⠀⣍⢰⣤⣦⣀⣤⠀⢀⠐⢶⠋⠘⣆⠀⣿⡀⠉⠑⡋⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⢿⡏⠀⡎⠀⠉⠛⣿⠀⢸⣆⣠⠇⠙⠇⠈⢦⣴⠃⢠⠀⠀⠀⠀⣰⠀⠀⢿⣷⠀⠀⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⢾⠳⣴⠿⢶⢆⣠⡿⠓⢞⠀⠈⢦⣀⡜⢠⡎⢀⠀⠸⣄⠀⠀⢰⣿⠀⠀⠀⠉⠀⠀⠀⣠⢴⣿⠟
⠀⠀⠀⠀⠀⠈⠛⢇⢀⣯⠀⢹⣧⡀⣸⠷⢶⡟⠉⢄⠀⠋⠉⠀⠀⠩⡓⠀⣠⠄⠀⣤⡤⢶⣶⣲⡾⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠙⣏⠳⠞⠈⠉⣿⡄⠀⣧⢀⠌⠉⠀⠀⠀⠀⠀⠈⠻⢭⣙⡿⠿⣻⣏⣽⣿⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠾⢦⣤⠏⠓⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠋⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠄⠤⠀⠀⠀⠠⠤⠆
⣶⣶⣶⣶⠶⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⡶⢶⣶⣶⢶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⣤⣤⣤⣤⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⢋⣼⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢿⡿⠿⠯⠴⠿⢹⡯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠬⣿⢦⡀⣀⡴⣯⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⢰⡛⠺⣿⣿⠓⢹⡄⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠠⣼⢀⣿⣷⡄⢹⡅⢰⣿⣇⢰⣦⠀⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⣀⣶⣽⣿⢉⠹⠛⠿⠿⠻⠉⠸⣿⣧⣆⣀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠠⠛⠀⣹⣿⣰⣈⣉⣽⣏⢉⣠⣂⢿⣅⠈⠻⠈⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡠⡻⢤⡐⠊⠀⠀⠈⢼⣇⠁⠈⠻⢸⠈⠟⠀⠁⣼⡷⠀⠀⠀⠑⢠⡴⡓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢰⠀⠀⠀⠀⠀⢠⠸⠒⠀⣀⢸⠀⡀⠀⠪⠣⠀⠀⠀⠀⠀⠐⡆⠀⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⡘⠲⠕⢠⡟⠘⠐⣻⡀⠻⠖⠃⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡴⢤⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠀⠈⠋⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠃⠀⠀⠑⠒⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⢀⠀⢀⡀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠄⠠⠀⠀⠈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⢄⣄⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠀⣸⣆⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠐⢸⡀⢂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉

⠀⠀⠀⠀⠀⠀⢀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣠
⠀⠀⠀⠀⢀⡤⢊⡉⠈⠢⣄⠀⠀⠀⠀⠀⠀⢸⠷⠉⠉⠉⠺⣿⠀⠀⠀⠀⠀⠀⡠⠼⠿⠿⠿⣄
⠀⢀⠀⢀⡎⠀⠲⢿⡾⠃⠈⢆⠀⢀⠀⠀⢠⠃⣤⢄⣀⡀⣤⡈⢇⠀⠀⠀⢀⣞⠤⡦⡀⢠⡴⢧⣣
⠀⠀⠂⠘⡇⠁⢀⢈⢀⠀⠁⡸⠀⠂⠀⠀⢸⠀⡙⠋⠙⠙⠋⠁⢸⠀⠀⠀⠸⡿⣘⣃⢿⣿⣋⣠⢿⡇
⠀⠀⠀⠀⠘⢦⣈⡊⢊⣀⠔⠁⠀⠀⠀⠀⠀⢳⡁⠐⡘⠘⠀⣱⠃⠀⠀⠑⠂⠱⣄⠰⠠⠰⠀⣠⠎⠀⠁
⠀⠀⠀⠀⠀⠈⠉⠈⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⠓⠒⠒⠻⠁⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣤⡀
⠀⠀⠀⠀⢷⢆⠠⢴⠒⠦⢄⢶⡏⠀⠀⠀⠀⠠⢿⡿⠟⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⣀⣸⣿⣄
⠀⠀⠀⠀⢠⠊⣀⠀⠀⠀⣀⠱⡀⠀⠀⠀⠀⣾⠡⡬⢱⡎⣤⠈⣇⡤⠀⠀⠀⠀⡴⠡⢠⡌⢹⣿⠋⢳⡀⠀⡄
⠀⠀⠀⠀⢘⠀⠿⠞⡤⠳⠟⠀⡇⠀⠀⠀⠰⡏⠒⠒⠙⠓⠒⠊⢸⠇⠀⠀⠀⠀⡇⢡⠍⠛⠏⠁⠙⠀⡇⠒⠃
⠀⠀⠀⠀⠘⠀⠄⡄⢤⢠⠀⠀⠁⠀⠀⠀⠀⢯⠀⠀⢸⡇⠀⠀⡱⡆⠀⠀⠁⠒⠙⢄⠀⠀⠀⠀⣀⢼⠆
⠀⠀⠀⠀⠀⠈⠢⣤⣤⣤⠔⠃⠀⠀⠀⠀⠀⠠⠷⠦⠬⠧⠴⠚⠇⠁⠀⠀⠀⠀⠀⠘⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄
⠀⠀⠀⠀⠀⢀⠀⠀⠀⢶⡿⢛⡀⠀⠀⠀⠀⠀⠀⡤⠛⠒⠒⢎⣧⠂⠀⠀⠀⠀⠀⢀⣠⣖⠉⠁⢉⣢⣀
⠀⠀⠀⠀⠀⠈⠀⠀⢀⡡⢔⡡⠼⡄⠀⠀⠀⠀⢠⠇⠠⠀⠈⠡⠔⠉⣆⠀⠀⠀⠀⣿⣿⣿⣷⢴⣯⣿⣿⣷
⠀⠀⠀⠀⠠⣾⢀⡙⠟⠶⠲⢃⡀⣷⠄⠀⠀⠀⠸⠀⠘⠷⠺⠳⠟⠀⠜⠀⠀⠀⠀⠹⠿⠟⠛⠌⠛⠻⠿⠇
⠀⠀⠀⠀⠁⠘⢏⠁⠒⠒⠰⠈⣹⠁⠀⠀⠀⠀⠀⠴⢄⣀⠀⢀⣠⠶⠄⠀⠀⠀⠀⠀⠀⢥⣀⣀⣀⠤
⠀⠀⠀⠀⠀⠀⠈⠑⠶⠶⠶⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁

⠃⣹⡿⠉⢟⢦⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⠟⣽⡷⠿⣿⣄⣭⡟⠉⡿⣿⠙⢿⡏⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⡏⢸⢷⣶⢿⣦
⢿⠟⠻⢦⣤⣤⡿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⢠⡟⠀⣰⠏⠙⢻⣧⣨⣶⣯⣬⢾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣷⣾⠘⢿⡄⠉
⡾⢧⣄⣀⣉⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣛⣿⡀⣪⠟⢹⡿⠸⣿⣏⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⠷⣦⣽⠶
⣻⣦⣄⡡⠟⠛⠁⠀⠀⢀⣠⠴⠀⠀⠄⠤⣀⠀⠀⠈⠛⠻⠽⢿⣷⣾⣿⣧⣰⠿⠋⠀⠀⠀⢠⡔⢒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠠⣽⡦
⠈⠁⠀⠀⠀⠀⠀⢀⣴⢯⠛⠃⠀⠀⢀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣄⠠⣦⡄⠠⣤⠟⠿⠁⢡⠀⣠⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣴⣿⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠠⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠐⠀⠀⣴⠇⠀⡽⠀⠀⠚⠉⠰⣄
⠀⠀⠀⠀⠀⢠⣯⠀⠐⠶⠦⠀⠻⡟⠓⠧⣤⠀⠰⠟⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡀⣸⣧⠀⣀⠀⠀⠠⣿
⠀⠀⠀⠀⠀⠀⢿⡇⠁⣠⣤⠆⠀⠿⢦⡀⠈⢳⠂⠄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠚⠀⠸⡷⠃⠀⣤⡀⠀⣀⢀⣹⠆
⠀⠀⠀⠀⠀⠀⠸⣷⣤⡤⠀⠠⠆⠀⠀⠙⠒⢴⠗⠉⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢰⡄⠈⠛⠀⢹⡿⠃
⣷⠒⢤⣄⣀⡀⠀⠘⡿⠁⣀⡀⠀⠀⢰⠰⠂⡌⠀⠀⠀⣀⠴⣾⡏⣷⣶⣤⣤⣤⣤⡀⠈⠶⣾⠄⡄⠀⠀⠉⠈⣠⣴⠏⠁⠀⡀⢰⣶⠷⠶
⠋⠙⣿⠟⣩⣟⠀⠀⠀⠈⠙⠳⠄⠂⠉⠓⠀⠀⠠⢲⣾⣦⠞⢻⣦⣿⡿⣍⣿⣿⡟⢿⣦⠀⠀⠉⠛⠖⠿⠶⠾⠛⠁⠀⠀⡜⢻⡿⠛⣁⣲
⣤⣽⠿⣿⣿⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢋⡴⣿⡀⢉⣿⡁⢁⣿⣿⠻⣽⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣠⣿⣰⠞⠛⣻
⣸⣯⣀⣥⣷⣼⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⠇⣰⡿⢻⡏⠈⠻⡟⠙⠟⣧⣼⣯⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡽⠁⣼⡇⣠⣼⠏
⡟⠁⡿⣿⢙⣿⡏⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⠹⣆⣿⠁⢈⣷⣀⣢⣷⣤⣸⣿⡻⠟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠞⣹⡷⠘⣿⣄
⣧⣴⣶⣧⣴⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⣿⠻⣷⣌⡽⠻⣿⠉⢩⢿⢙⣷⣤⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⢠⡟⠀⣰⠏⠘
⣹⡿⠹⣻⣏⣼⡟⠁⠀⠀⢀⠀⠀⠠⡀⢀⡀⠀⠹⣙⣄⣿⠹⣧⠀⢹⣦⡐⣾⣤⣿⠏⠀⠀⠀⠀⣀⣤⣤⣄⣄⠀⠀⠀⠈⣿⣧⣛⣿⣀⣪
⣿⣧⣴⠿⠋⠀⠀⠀⠀⠂⠈⢃⠹⡦⠁⠀⢱⠀⠀⠀⠙⠹⣦⣘⣷⣭⣼⣟⡿⠋⠀⠀⢀⣤⣾⠚⠙⠋⠀⠈⠟⠓⣦⡀⠀⠈⠛⠻⠽⠿⢷
⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⣤⡴⠛⢋⠷⠂⢄⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⣸⠛⠙⠷⠠⣦⠀⢸⠇⠀⠀⠓⣽⣆
⠀⠀⠀⠀⠀⠀⠸⡀⠀⠠⠄⠀⣾⠃⠀⡤⠾⠀⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠇⠀⠠⡀⠘⠂⠀⣀⡀⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢰⡧⠚⠻⠁⠀⠀⠈⠉⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⢀⡶⠞⢹⠁⢠⣄⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠘⣾⢃⡀⠀⠀⡄⠀⣶⠀⠓⠀⠠⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⣁⠂⢠⡞⠁⣠⡎⠁⠀⠀⠀⠰⠃
⣀⣠⣄⡀⠀⠀⠀⠘⣷⣀⣀⠘⠇⠀⠹⠃⣦⡄⢀⣿⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠠⣾⣠⠴⠉⣁⠀⢀⠀⠀⠄
⣻⣉⣿⣿⣦⣄⠀⠀⠀⠹⣷⣄⣠⣥⣤⣴⠿⠛⠙⠁⡀⢰⣶⠷⠶⠾⣷⠒⢤⣤⣀⡄⠀⠀⠀⠀⢣⠐⠠⡘⠓⠀⠏⠀⠀⠀⠀⠀⣠⣴⣿
⣟⡃⠙⣯⣍⣻⣄⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⡾⢻⡿⠛⣉⣲⡶⠋⠙⣿⠟⣩⣟⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠰⣟⢿⣿⣯⢨
⣿⠟⠳⣿⡿⠏⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣠⣿⣴⠞⠛⣻⣧⢬⣽⠿⡿⣿⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣻⣦⣿⡟⠂
⣧⣄⣀⣿⡿⢳⣶⡛⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣜⠁⣼⡇⣀⣴⡏⠀⣸⣷⣀⣵⣷⣼⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⣯⠀⢋⣿⠿
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢹⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⡴⠊⢉⡩⢆⢳⠤⣦⠒⠚⢄⣉⠣⡉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⢢⠖⠉⢉⠊⠀⠀⠀⠇⠈⠀⠈⢢⠔⠢⡈⢅⠙⢴⠢⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡔⠁⠜⡠⠂⠠⠀⢀⢀⠜⠂⠀⠀⠀⣸⠀⠀⠈⢦⡮⡀⠗⠀⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡧⢺⣨⠖⡏⠀⠀⠀⢿⡠⠁⠀⠰⡞⢂⠖⠀⠡⠀⡇⠈⠐⡌⠀⢤⠱⡜⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⠀⡜⠁⠀⡇⠀⠀⠀⠀⢃⠃⡦⢠⠋⠈⠀⠀⠀⠑⠉⢀⢀⠘⠎⢠⠃⠘⡌⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⡇⠀⠀⠠⢁⡠⠀⠀⠀⠑⢤⠃⠀⠀⠀⢀⡄⡀⠀⠀⠉⡘⠄⢄⣄⢦⡦⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠑⠺⣄⠆⠀⠀⠁⠀⠀⠀⢀⠍⠀⣀⢀⢀⠆⢰⠀⢀⣄⢀⠀⠈⣤⠀⠻⡀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢖⠄⠼⠀⠀⠀⢣⠰⠀⢀⠎⠀⠠⠘⢠⠏⠀⠀⢃⣙⠩⠬⡀⢆⠇⢣⢄⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⠺⠀⢣⡀⢠⠋⠁⠒⠎⢠⢠⢀⠗⢢⠀⣀⡄⡀⠀⠀⠀⢣⠈⢀⠈⡌⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣰⡀⡀⠙⣇⠀⡄⡀⠘⡌⢡⠊⠀⡈⢧⠉⢴⡑⣆⣤⢠⠇⠐⡘⡠⠠⡈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠑⠯⣐⠈⠲⢕⢀⠜⠀⠀⢞⠸⣡⠃⠀⠀⢑⠬⠥⠂⣀⡄⡙⠀⡜⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢐⢎⣔⣄⠄⡹⢌⡀⢂⠜⠉⠡⡐⠀⢂⠏⠀⡀⢸⠒⠲⡴⢄⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣀⠁⠂⢰⠀⠉⠉⢄⣰⣣⠋⠉⠉⢢⠥⠥⠎⠢⠀⣳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠘⠉⠚⠀⣤⢀⠋⠉⠂⡀⠆⡈⢀⠀⡈⡆⣲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡄⡔⠈⠚⢆⣀⡄⠌⠀⠈⢮⠤⢊⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⢄⢀⠄⡝⣒⠣⣜⣄⡠⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠒⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣠⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠿⢿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣋⠀⢠⣶⣬⣽⣿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣶⣦⠉⠉⠛⢿⣿⣿⡿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡟⠓⠛⣉⣤⣾⣿⣿⠇⣾⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡇⣾⣿⡿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣡⣾⣿⣿⣿⣿⣦⡹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⠹⣿⣿⣿⣿⣿⣿⠿⠟⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⣴⣿⣿⣿⣿⣿⠏⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⢯⣾⣿⣿⣿⣿⣿⠻⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠈⠙⠛⠛⠉⠉⠉⠉⠃⠛⠘⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣙⣦⣀⣠⡶⢚⡿⢛⣳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠉⣿⠉⢿⣻⠳⣾⣅⣠⠔⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡴⠶⠶⠦⣤⣀⠀⠀⣸⠃⢠⡇⠀⠀⠙⠦⣴⣈⡟⢿⢯⣍⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠋⠉⠀⣸⡅⠀⠀⠀⠀⠉⢳⣤⣏⣠⣼⣧⣀⣀⠀⣀⣀⣉⣉⡛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣦⣤⡶⠛⠉⠙⠶⣤⣤⣤⢴⡿⠉⠙⢧⡀⠀⠈⠙⣿⡉⠁⠀⠈⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⣴⠞⠉⠀⢀⣿⣄⠀⠀⢀⡾⠉⠀⠀⢸⠁⠀⠀⢸⣧⣤⣤⡶⠋⠉⠛⠲⢦⣤⡼⠛⠓⢦⣄
⠀⠀⠀⠀⠀⢀⣸⣇⠀⢀⡶⠋⠁⢩⡿⠒⠺⣇⣀⣀⣀⣼⠷⣤⣴⡟⠀⠀⠀⢷⡄⠀⠀⠀⠀⢈⡇⠀⠀⠀⠙⣧
⠀⠀⠀⠀⢠⡟⠁⠈⠙⣿⠀⠀⢠⡏⠀⠀⠀⣨⠟⠉⢹⡇⠀⠀⠀⣽⣦⡀⠀⢀⡿⠳⠶⢴⡶⠛⠻⠦⣤⣀⣀⡼⢦⣄⡀
⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⠷⠶⢾⣅⠀⠀⣸⠃⠀⠀⠘⢧⣄⣠⣾⠃⠈⠙⠛⣯⠀⠀⠀⠀⢷⡀⠀⠀⠀⠈⢹⡄⠀⠈⠻⣆
⠀⠀⠀⠀⢹⡶⠶⢶⡾⠁⠀⠀⠀⢩⡿⠛⠻⣆⣀⣠⡴⠋⠀⠀⢿⡀⠀⠀⠀⢘⣷⣄⡀⢀⣸⠷⢦⣤⣠⣤⣾⣁⠀⠀⢀⣿
⠀⠀⠀⠀⢸⠃⠀⣾⠁⠀⠀⠀⢠⡟⠀⠀⠀⠀⣹⠹⡇⠀⠀⠀⣸⡷⣤⣤⣶⠋⠀⠈⠉⢻⡇⠀⠀⠀⠀⢻⡀⠉⠛⠒⢻⡅
⠀⠀⠀⠀⢸⡄⠀⠻⢦⣤⡤⢶⡟⠀⠀⠀⠀⢀⡟⠀⠻⣦⣤⠶⡏⠀⠀⠀⣿⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⣸⣇⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠘⣧⡀⣠⡾⠀⠀⢸⡀⠀⠀⣀⣴⠟⠁⠀⢠⡟⠀⠀⢷⣀⣀⣴⠏⠛⠶⣶⠶⠛⠙⠳⢶⠞⠛⠁⠈⠙⠳⡶⠖⠋
⠀⠀⠀⠀⠀⠈⠉⢹⡄⠀⠀⢠⡟⠛⠛⠉⢿⣄⣀⣠⣾⠁⠀⠀⢀⡿⠉⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⣀⣾⠁⠀⠀⠀⠀⣿⠉⠁⣿⠀⠀⢀⣸⡇⠀⠀⠀⠀⣰⢿⡀⠀⠀⠀⣠⠿⣤⣀⣀⣤⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⡄⠀⠀⠀⣰⠇⠀⠀⠈⢻⡞⠛⠁⠻⣤⣤⣤⠾⠋⠀⠻⢦⡴⢾⠋⠀⠀⠉⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡷⠶⠺⣇⡀⠀⠀⣠⡾⠀⠀⠀⠀⢰⠿⣄⠀⠀⠀⣠⡟⠀⠸⣇⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠈⢹⡟⠛⠉⠳⣤⣀⣠⣴⠋⠀⠈⠛⡷⢿⠋⠀⠀⠀⢸⡟⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣼⡄⠀⠀⢀⡼⠋⠀⠘⣧⣀⣀⡼⠃⠘⣇⠀⣀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣾⠁⠀⠀⠀⣸⠟⠉⠀⠀⠀⣸⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣤⡴⢿⣀⠀⣀⣠⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠠⠁
⠀⠀⠀⠀⠀⠀⢠⡊⠄⠐⡁⠄⠀⠁⠂⠄⡰⠀⢠⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⡠⠂⠀⠠⠀⠰⡐⠂⠁⠀⠈⠀⠁⠰⠃⠀⢀⡑⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⡴
⠀⠀⠀⣸⠀⠸⠀⠀⠀⡐⠀⠀⠀⠀⠀⢀⣀⠄⠀⠀⠀⠨⢁⠠⡁⢂⠀⠀⠀⠀⠀⠘⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢀⠏⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠇⠀⠀⠤⠀⠀⠀⡸⢈⠀⠀⠀⠀⠀⠀⠀⠀⣼⠓⣾⢰⢰⡻⠈⣻⠁⡞⢹⠸⣛⡆⡟⣧
⠀⠀⡎⠀⡀⠂⠄⠀⠀⠀⠃⠀⠀⠠⠀⠀⠀⠀⠂⠀⠀⢠⠀⡰⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⢿⣀⢾⣼⢠⣹⠀⣿⠀⡏⢹⠀⡿⡄⣇⡾⠀⠐⠛⠛
⠀⠀⠇⠀⠁⠀⠄⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠶⠶⠀⠀⠁⠀⣀⡀⢁⡀⢀⡀⠀⡀⠀⣀⠀⠈
⠀⠀⢸⠄⠃⠀⠀⠰⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⡄⠀⠀⠀⠃⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⣹⢸⣹⢸⣹⢠⡇⢸⡯
⠀⠀⠀⡄⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠻⠸⠅⠸⠇⠸⠧⠸⠧⠄⠀⠀⠰⣦⡀
⠀⠀⠀⠣⣀⣀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⣀⡞⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠘⣄⠀⣠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠁⠀⣀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠈⠢⣀⠑⢀⡀⠀⠈⠀⠀⠀⢀⡀⠈⣀⣤⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠑⣄⣀⠄⠈⢀⣀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠒⠒⠤⡀⠀⢀⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠐⠒⠈⠘⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⣀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢀⡀
⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠅⠀⠆⠼⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠀⠐⠀⢠⠐⠁⠀⠀⢀⠀⠖⠀⠀⠉⠙⠢⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠸⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢐⠄⠀⠀⠀⠀⠤⠀⠀⠀⡀⠃⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⡘⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⡄⠀⠀⠰⡘⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡇⠀⠀⠀⠈⢳⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⢠⠞⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠈⠲⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⢀⠀⡆⠀⠀⠀⠀⠀⠀⢮⡀⠁⢄⡀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⡠⠀⠈⠁⠠⣀⡴⠃
⠀⠀⠀⠀⠈⠣⢤⠀⠀⠑⠆⠀⠤⠐⠆⠀⠀⠀⠀⠄⠀⠀⠀⢁⠜⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠣⣄⠂⠄⠀⠀⠀⠀⠀⠠⠀⠊⠀⠠⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠓⠄⡀⣈⠦⠀⠀⠀⠀⠓⠂⠠⡤⠠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠈⡠⠆⠤⠀⢀⡀⣀⣠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠒⠠⠤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠛⠦⠤⠬⠤⠊⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠟⠓⠊⠉⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣤⠀⢰⠀⠀⣠⣤⣤⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠘⠷⠟⠉⠀⢠⠀⠀⠈⠉⠉⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣶⡄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠰⠾⠃⠀⠀⠀⡀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⣠⡶⠀⠀⠀⠙⠃⠀⠀⠰⠃⠀⠀⠀⠀⠀⠰⠔⠄⢋⠟⠀⡜⢿⠂⣌⠑⢅⡀⢐⡄
⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠠⠀⠦⠀⠨⠂⢉⡠⠊⠀⠘⠄⠀⠂⢀⢇⠈⢁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠢⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠠⣀⠀⠉⠀⠐⠓⠀⠘⠈⠀⠀⡀⠈⠁⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⢄⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⢉⠀⡰⢤⠀⠀⠠⢴⠀⠈⡏⠀⠠⠣⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠁⠉⠀⢰⠄⠤⠀⠈⠢⠒⠁⠀⣀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⢸⠀⠀⠤⢠⠀⠀⠀⡤⠤⡆⠀⠘⠀⢱⠔
⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠚⠀⠀⢂⡠⢴⠀⠀⠱⠐⡀⡠⢃⠆
⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⣤⣀⠀⢺⡇⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠤⠎⠀⠀⠄⡖⠀⠀⠀⠇⠊
⠀⠀⠀⠀⠘⠀⠀⠀⠠⢤⣝⢿⣇⠸⠃⣾⠟⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⣀⠀⠀⢘⡀
⠀⠀⠀⠀⣤⡇⠀⠠⣶⣶⠶⠀⠠⣶⠄⠀⢶⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠈⠁
⠀⠀⠀⠀⢡⡇⠀⠀⢀⣤⠆⣀⠀⣁⠀⣜⠢⡄
⠀⠀⠀⠀⠘⠷⡄⠀⠈⠀⡾⠋⠀⢨⣆⠘⠃
⠀⠀⠀⠀⠀⢀⠫⢴⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠈⠈⠓⠂⢦⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⣶⣶⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣷⣶⣶⣦⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⡿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠻⠿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠟⠋⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢈⣉⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣶⣤⡀
⠀⠀⠀⣠⣶⣿⠟⠋⢁⣀⡤⠴⠶⢒⣒⣒⣒⣀⣠⠄⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄
⠀⣠⣾⠟⠋⢀⡴⣚⣭⣶⠶⠟⣛⣋⣩⣭⣤⣴⣶⣶⣶⠶⠶⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⢻⣷
⣸⣿⠁⢠⣶⣾⣻⣯⡵⠶⢚⣛⣉⣭⣭⣤⣤⣤⣤⣤⣴⣖⣒⡒⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣝⢷⡄⠀⣿
⣿⡇⠀⣾⡿⢟⣩⣴⣶⠿⠟⣛⣋⣭⣭⣥⠴⠶⠶⠶⠶⠴⠖⠀⠀⠐⠒⠒⠒⠈⠉⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡹⣦⣻⠂⣿
⣿⣇⠀⢻⣿⣿⣻⣭⣶⡾⢿⣛⣫⣥⡴⠶⠶⠶⠶⠶⠶⠶⠂⠉⠉⠀⠀⠀⠀⠶⠶⠤⠄⠀⠠⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡳⣌⡻⣿⣿⢠⢿
⠸⣿⡄⠈⠻⣿⣿⣿⡷⢚⣋⣭⣥⣶⠶⠾⠿⠿⠛⠛⠛⣛⠒⠒⠒⠒⠒⠀⠀⣀⣀⣐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣝⣮⣿⡿⠃⣨⣾
⠀⠹⣿⣄⡀⠈⠙⠿⣿⣿⣯⣭⣶⣶⣾⡿⠿⢛⣛⣛⣋⣉⣉⣉⣉⣉⣉⣉⣀⠀⠠⠉⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣴⣿⣿⠿⠋⢠⣾⣿⠃
⠀⠀⠈⣿⢿⣶⣤⣄⡀⠉⠙⠻⠿⢿⣿⣿⣿⣿⠿⠿⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠠⠤⣤⣤⣄⣀⣀⡀⠀⢀⣀⣠⣾⡿⠿⠋⠁⣀⣴⣿⣿⠃
⠀⠀⠀⢿⡜⣿⣿⡟⢿⣷⣶⣤⣄⣀⡀⠉⠉⠛⠛⠳⠶⢶⣦⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣼⣿⠿⠿⠟⠛⠋⠉⣁⣠⣴⣶⣿⣯⣿⣿⡟
⠀⠀⠀⢸⡇⢻⣿⣿⠸⣿⣿⡛⣿⢻⣿⣷⣶⣤⣄⣀⣀⣀⡀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⡟⣿⣿⡇
⠀⠀⠀⠸⣿⠸⣿⣿⠆⢻⣿⡇⢹⡄⢻⣿⡏⣟⠉⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⢸⣿⢿⡆⣿⣿⠇
⠀⠀⠀⠀⣿⡀⠉⣿⠀⢸⣸⣧⠀⠁⠘⣿⣷⠀⠀⢻⣿⣿⢹⢻⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⢻⣿⣿⣿⡏⣿⣿⣿⣿⠀⡟⣼⣿⢸⢸⣿⣿
⠀⠀⠀⠀⢿⡇⠀⣿⡀⠈⡇⣿⠀⠀⠀⢻⡿⠀⠃⠈⢹⣿⠸⠘⠃⣿⣿⣿⣿⢹⣿⣿⣿⣿⠃⡿⢸⣿⣿⣿⡇⣿⣿⣿⠇⠀⠇⣿⣿⢸⢸⣿⣿
⠀⠀⠀⠀⢸⣧⠇⢹⡇⠀⢷⢹⡄⠀⠀⢸⣧⠀⠀⠀⢸⡟⠀⡄⠀⢸⣿⡿⣿⢸⣿⣿⣿⠉⣾⡇⢸⣿⡇⣿⡇⣿⣻⣿⢰⡇⢸⣿⣿⢸⢸⣿⡇
⠀⠀⠀⠀⠘⣿⢰⢸⣿⠀⠘⢸⡇⠀⠀⠀⣿⡀⠀⠀⢸⣇⠀⡇⠀⢸⣿⡇⣿⢸⡿⣿⣿⢸⣿⣧⢸⣿⡇⢸⢡⡇⣿⣿⢸⡇⢸⣿⡿⣼⢸⣿⡇
⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠃⠀⢸⣿⠃⣿⢸⡇⣿⣿⢸⠉⣿⢸⣿⠇⣸⢸⣇⣿⣿⢸⠃⢸⣿⡇⡇⢸⣿⡇
⠀⠀⠀⠀⠀⣿⡇⠀⠿⠆⠀⢰⡇⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⢸⣿⠀⣿⠸⡇⣿⣿⢸⠀⡟⢸⣿⠀⣿⢸⢸⣿⣿⠈⠀⣸⣿⡇⣇⣼⣿⠃
⠀⠀⠀⠀⠀⢻⣷⣦⣄⣀⠀⠘⠃⠀⠀⠀⢿⠃⠀⠀⢸⡟⠀⠀⠀⢸⣿⢠⣿⠀⣿⣿⡇⢸⠀⡇⣸⣿⢰⡇⣿⢸⣿⣿⢘⣴⣿⣿⣼⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣷⣶⣤⣤⣄⣀⣀⠀⠀⠈⠃⠀⠀⠀⠸⠟⠘⠋⠀⠸⣿⠃⠼⢸⠇⢿⣧⣾⣷⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠿⢿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⠿⠿⠿⠛⠛⠉⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣏⣮⣝⣴⣮⣭⣏⣬⣿⣽⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⠛⢻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⠿⣿⣦⣤⣾⣿⢶⣶⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⣻⣿⠿⣶⣽⣿⣧⣴⡿⢿⣿⠉⠛⢿⣦⡀
⠀⠀⠀⠀⠀⢠⣾⣿⡟⠁⠀⣸⡿⠁⠀⣿⡟⠁⠹⣿⠀⠀⢻⣷⡀⠀⢹⣿⣶⣄
⠀⠀⠀⢀⣤⠀⠀⣿⣧⣀⣠⣿⡃⠀⢰⣿⠁⠀⠀⣿⡇⠀⠀⣿⣇⣀⣼⣿⠉⢻⣷
⠀⠀⠀⢸⣿⢀⣾⡟⠉⣻⡿⠻⣷⣤⣾⣿⣆⣀⣠⣿⣷⣤⣶⣿⣿⠛⠋⢻⣧⠀⣿⡇
⠀⠀⠀⠸⣿⣼⡟⠀⠀⣿⠇⠀⢸⣿⠁⠈⢹⣿⠋⠁⢸⣿⠀⠈⣿⡆⣀⣸⣿⣤⣿⣇⡀
⠀⠀⠀⠀⢿⣿⣿⣤⣬⣿⡄⠀⢸⣿⠀⠀⢸⣿⠀⠀⢸⣿⣠⣾⠟⠿⠟⠛⠋⠉⠛⠛⢿⣦⣤⣄
⠀⠀⠀⠀⣿⡇⢸⣿⠉⠙⢻⣿⠿⠻⣷⣶⠿⢻⣷⡶⠿⢻⣿⠟⠀⠀⠀⠀⠀⣀⠀⠀⠀⠁⠉⣿⡆
⠀⠀⠀⠀⠸⣿⣼⣿⠀⠀⣿⡇⠀⢰⣿⠁⠀⠀⣿⣇⣴⡿⠟⠀⠀⢠⣤⡀⢸⣿⠀⠀⣀⡀⠀⠙⣿⡆
⠀⠀⠀⠀⠀⣿⡟⠻⣷⣶⣿⣧⣀⣸⣿⣄⣀⣠⣿⣿⣿⡄⠀⠀⣀⣀⠙⠋⠀⠉⢠⣾⠟⠁⠀⠈⠛⣿⡄
⠀⠀⠀⠀⠀⠹⣷⣤⣸⣿⠀⢹⣿⠛⠉⣻⡿⠛⠉⢹⣟⠁⠀⠀⠛⠛⢃⡀⠀⠀⠀⣤⣤⣄⠀⠀⠰⣿⠃
⠀⠀⠀⠀⠀⠀⠈⣿⡟⠻⣷⣼⣿⡄⠀⢿⣇⠀⠀⢸⣿⠆⠀⠀⢰⣾⠟⢃⣤⠀⣴⡌⠉⠛⠁⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣀⣿⡟⠿⣶⣾⡿⣷⣶⣿⣿⣷⡀⠀⠀⠀⠀⢾⠟⠀⠘⠿⠀⠀⠀⣀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⡄⠀⣿⡇⠀⠀⣻⡇⠻⣿⣶⣀⣀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⢿⣧⣤⣤⣿⠿⠿⠟⠋⠛⠻⣷⣾⣷⣤⣴⣶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣿⣿⣿⣿⣿⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢶⠛⠉⠉⢉⠟⢻⠒⠤⣀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢋⡔⢡⠃⠀⠀⢀⠎⠀⡎⠀⠀⠀⠑⢖⠋⠀⠀⠀⢀⡠⠴⠚⠀⠀⠈⠉⠉⠉⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡎⠀⡎⠀⠀⠀⡞⠀⢰⠇⠀⠀⠀⠀⠈⢣⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⡜⢀⣠⣇⠀⠀⠰⠀⠀⢰⣀⣄⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⢀⠎⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⡻⠀⠀⠸⠀⣿⣿⣾⡇⠀⡇⠀⠀⢸⣿⣶⡗⠀⠀⠀⠀⢸⠒⠒⠒⠒⠂⠒⠒⠒⠂⠀⠀⣤⠤⠊
⠀⠀⠀⠈⡄⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡇⠀⠀⡇⠀⠈⢹⠉⢀⣴⣷⣶⣦⠸⠏⠋⠁⠀⠀⠀⠀⡸⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⣀⠬⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠘⡀⠘⡿⠿⣿⣿⠀⠇⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠈⠉⠒⠢⠤⢄⣀⣀⣠⠃
⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣥⠀⠀⡇⠀⠀⠀⠇⠀⠹⢤⡿⠃⠀⠘⡄⠀⠀⠀⢀⡎
⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠈⢆⠀⡇⠀⠀⠀⠰⡀⠀⠘⣄⠀⠀⠀⠘⡄⠀⣠⠊
⠀⠀⠘⡄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⠔⠉⠣⣘⡄⠀⠀⠀⠱⡀⠀⠘⢦⡀⠀⢀⡼⠞⠁
⠀⠀⠀⠈⠑⠒⢻⠁⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠈⠙⠲⢤⣄⣀⣘⣄⣀⡀⠵⠚⠉
⠀⠀⠀⠀⠀⠀⠘⣄⠀⢀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁






⡿⠿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣟⣻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠒⠒⠒⠒⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⣯⣥⣼⠁⠀⣀⣀⣀⣀⠀⠈⣧⣬⣽⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⣿⡟⡵⢛⣿⣿⣿⣿⣿⣿⣷⣮⢻⣿⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣏⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⣟⠋⠁⠀⠀⠐⠀⠈⠙⣻⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣮⡳⠤⢌⣁⣀⡠⠤⢞⣵⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠼⠿⠻⢿⢿⣿⡦⠤⠤⠤⠤⢴⣿⡿⡿⠟⠿⠧⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣏⠉⠳⡌⠀⡈⠑⠈⠉⠒⠒⠒⠒⠉⠁⠊⠁⠀⢁⠶⣿⡹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡸⠀⣽⡄⠁⠠⠀⠀⠤⠤⠦⠤⠀⠀⠄⢸⣄⡇⠠⣻⣷⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠈⠀⠡⣀⣿⣇⠀⠀⠀⢀⠀⠰⠀⡀⠀⡀⡀⢸⣿⡇⠀⠹⢻⣇⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠲⣾⣿⠃⠀⠘⢦⣀⣀⣀⣀⣀⣀⡴⠃⣸⣿⣏⠀⠚⣿⣯⡹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⣰⣼⣿⡷⠀⢀⣄⠀⡇⠀⠠⠄⠀⢸⠀⣠⣸⣿⣿⡄⠀⠘⡿⢿⣿⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠰⣮⣿⣿⣿⣟⣤⣿⠿⠃⠰⡰⠌⠡⢆⠆⠐⠿⣿⣿⣿⣷⣄⠀⠐⣻⢿⣷⡹⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⢇⡀⢤⣢⣾⣿⡿⠃⣹⣿⣟⠁⢰⣄⡴⠀⠉⠉⠀⢦⣠⡆⠸⣿⣿⡏⠘⢦⡀⠀⠐⠹⢿⡜⢄⡀
⠀⠀⠀⠀⠀⣀⠤⠞⠉⠑⢮⣾⢟⣵⠷⠒⠋⠁⣩⣿⣶⣦⣤⣤⣤⣤⣤⣤⣤⡴⠶⢚⠋⠉⠉⠙⠒⢾⣶⣄⠀⡴⠊⠉⠳⢤⣀
⠀⠀⠀⠀⡎⢠⣤⠤⠄⢀⣧⣿⠟⠁⣤⣶⣟⣭⣞⣢⣉⣉⣉⣩⣍⡤⡿⠓⠭⡓⢿⣿⣶⣶⣶⣶⣤⣄⣀⣉⣶⣆⠀⠠⠤⣤⡄⢱
⠀⠀⠀⢈⡗⠟⡡⠀⠄⢸⡿⠁⠐⢋⡉⢳⡜⢧⠈⠀⠈⠀⠈⠂⠐⠀⠀⠀⠀⠈⠓⢯⣛⠯⡛⠛⠙⠛⠻⠳⢭⡻⡄⠠⡀⢌⠻⢺⡁
⠀⠀⠰⠶⣦⠚⣠⠎⣠⢋⡴⢒⡩⢤⠐⡖⢻⠘⣧⣀⣦⣠⣰⣄⣸⣶⣿⣴⣶⡄⠀⠀⢉⣯⣞⣆⡄⣆⠀⠀⠈⢷⠙⣄⠱⣄⠓⣴⠶⠆
⠀⠀⠀⠀⠙⠋⠙⢺⣥⣯⣴⡝⣶⢸⣷⢿⣿⣇⣿⡿⠿⠿⠟⣟⣫⠭⠷⠚⠙⢦⡀⠀⣾⣿⣿⢸⣿⣿⣿⣾⣾⣾⣠⣟⣷⡿⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⢿⡇⢿⣘⣛⣽⣏⣠⠴⠖⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠙⢦⣿⣿⠿⠛⠻⠯⢭⣝⡛⢋⣵⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠄⠤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠉⠉⠁⠀⠄⢀⢤⡠⡤⣄⡀⠀⠉⠉⠩⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣠⡄⠀⠀⢰⣾⠃⠀⠀⠀⡙⢶⣄⣰⠀⣆⣀⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣳⣷⣴⣴⢴⣼⢿⣭⣭⡭⡿⣷⣿⣿⣫⣿⣿⢿⡛⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣴⣁⣦⣀⣄⢀⣆⣊⠀⢀⡆⣡⣿⣚⠋⢫⡙⣜⡄⢈⢇⠀⣳⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠥⠒⢹⢫⠗⠉⠈⠉⠀⢈⠉⣉⡿⠯⢖⠻⠖⠉⠓⢻⡾⣶⣋⣴⠏
⠀⠀⠀⠀⠀⠀⢠⠊⠂⠀⠀⣀⡞⠉⠀⠀⠀⠀⠈⠀⠚⠋⠀⠀⠀⠀⠀⠀⠀⠁⠳⣟⣄
⠀⠀⠀⠀⠀⠰⠃⡠⣠⡶⠚⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠃⣼⡼⠋⠀⠀⠀⢱⠀⠀⠀⠀⡎⢀⢤⣠⢤⢤⠠⣤⢤⢄⠋⠀⠀⠀⡈⠀⠀⠀⠀⠀⡔⠚⠋⠉⠁⢀⡠⣬⣉⠉⠃⠀⠂⠲⡄
⠀⠀⠀⠀⠈⡄⡟⠀⠀⠀⠀⢀⣨⣆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⢇⢤⠀⠀⠶⡇⣀⣀⣈⣳⣤⣄⣠⣠⣇⣀
⠀⠀⠀⠀⠀⠙⢮⡙⠒⠉⠉⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⢀⢞⠛⠛⢛⠓⠛⠓⡒⢺⣻⠿⡿⢾⠛⢻⠉⢳⡀
⠀⠀⠀⢀⠠⠀⠄⡙⠲⢶⣖⡀⠀⠀⢙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⢀⢀⠠⢿⢞⠗⠛⠊⠑⠒⢚⣷⢯⠷⡤⠳⠼⣧⣰⣇⡜⠁
⠀⠰⠚⠑⠒⡢⠚⠉⠁⠒⠠⢍⠉⠉⠉⠉⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠀⠀⠀⠔⠁⠀⢀⡜⠃⠀⠀⠀⠈⠐⠊⠁⠀⠀⠀⠀⠀⠳⢯⡉
⠀⠀⠀⠀⠘⠓⠒⠒⠒⠒⠒⠚⠛⠃⠘⠛⠃⠈⠉⠙⠓⠓⠓⠒⠒⠋⠉⠁⠀⠀⠀⠪⢔⡴⠛⠉⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣰⠋⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡒⠄⠐⢀⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣙⠳⠯⣄⣀⣀⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢉⠋⣀⡀⢀⣂⣤⡀⣠⡙⠢⢄⣠⣄⣀⣀⣠⠤⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⡎⠲⠀⠀⠀⠀⢀⢤⣤⠤⠔⠓⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡀⠀⢸⡀⠀⠒⠀⠀⠀⠆⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠰⠀⠀⠁⠀⠈⠁⠤⢴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⢸⣣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠀⣠⡶⠒⠂⠀⠀⠀⡴⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠰⠾⢉⣉⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠉⠁⠀⠀⠀⠀⠘⠛⠉⠉⠁⠁⠀⠈⠉⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⠉⠉⠭⠭⠍⠛⠣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡼⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⢢⠠⠤⠤⠶⠒⠒⠚⠓⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢺⠃⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠒⠒⠒⡂⠈⠭⠉
⠀⠀⠀⠀⠀⢀⠁⡇⠀⢸⡎⢳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢑⣒⣒⠠⠤⠐⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⢜⡼⠁⢠⢾⠇⢸⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠤⢌⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⡀
⠀⠀⠀⠀⣧⠏⢀⡎⢁⡏⢠⡎⡜⢀⣆⠀⠀⠠⡤⣄⡀⣀⡀⣀⣀⣤⣤⣬⣭⠭⠥⠤⠖⠀⠀⠀⠰⢓⣛⣷⢤
⠀⠀⠀⠀⢿⡄⠸⣧⣸⡇⢸⣰⣇⡼⡽⠀⠀⠦⠀⠤⠔⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣠⠿⠩⠔⠊⠀⠀⡀
⠀⠀⠀⠀⠈⠙⠒⠚⠋⠉⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⡓⠀⠀⠀⠀⠀⠀⠒⠁⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠓⢢⡀⠀⡠⠴⠂⠀⡀⠊⢠
⠀⠀⠀⠀⠀⠀⠀⡠⠄⢀⣀⡀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⠀⠀⠀⢀⡗⢺⠃⠀⠀⡀⠹⠆⢰
⠀⠀⠀⠀⠀⢠⠎⠀⠾⠿⠛⠁⠀⣠⠝⠀⢰⠀⠀⠐⠶⠶⠖⠀⠀⢠⡄⠀⠀⠀⢀⠀⠘⣸⡄⠀⠀⠈⠁⢸⠀⠀⠀⡇⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢸⡃⠀⠀⠤⠔⠂⢀⠤⠁⠀⠸⡳⠀⠀⠀⠀⢤⡤⠴⣾⠁⠀⠀⠀⠀⠀⣀⣀⣈⠐⠶⣧⣿⢸⣠⣤⣤⣏⠀⠠⠤⠤⠤⠄⠀⠀⠐⠚⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠒⠒⠂⠒⠀⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⡻⠿⢛⠻⠿⡿⢿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣷⡄
⠀⣰⣶⣶⣤⣴⣦⡀⣿⣿⣿⣿⣿⣦⣀⢶⣾⣿⡷
⠀⢿⣿⣿⣿⣿⣿⣿⣞⣿⣿⠻⣿⣿⢉⣿⡃⠈⠁⠀⠀⠀⣀⣀⣀⡀
⠀⣼⣿⣿⣿⡀⠈⢻⣿⣿⠇⢠⣿⣣⢟⣁⣥⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⣀
⠀⠹⠿⣿⣿⣿⣷⣄⠿⢟⣰⣿⣿⣿⣿⣿⣿⣿⡛⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠙⠛⠿⢿⣿⣿⣦⣄⡀
⢀⣤⣶⣶⣶⡶⠿⠛⠒⠿⣛⣭⣥⣤⣀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣶⣄
⢿⣿⣿⣿⠃⠀⢀⣴⣿⣧⡉⢿⣭⡛⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⣄
⣸⣿⣿⣿⣷⣾⣿⣿⣻⣿⣇⠀⣿⣿⣆⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⡀
⢻⣿⣿⣿⣿⣿⡿⢃⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡄
⠀⠉⠁⣼⣿⡟⠀⢸⣿⣿⣿⣿⣿⡏⠁⢀⣴⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄
⠀⠀⣼⣿⡟⠀⠀⠈⠛⠛⠛⠿⠋⠀⠀⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡄
⠀⢰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧
⠀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⢿⣿⣇⠀⠀⠀⠀⣠⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⡀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠸⣿⣿⡀⠀⠀⠀⠀⠉⠙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠉⠙⠃⠀⠀⠀⠀⠀⣾⣿⡿
⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃
⠀⠀⠈⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏
⠀⠀⠀⠈⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣶⣤⣤⣤⣤⣤⣤⣤⣶⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠏
⠀⠀⠀⠀⠈⠻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣷⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⢀⠔⠀⠀⠐⠀⠐⠀⠀⠀⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⢆⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠳⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠉⠀⠀⠉⠀⠂⠤⡀⠀⠀⠈⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⠠⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⣀⣀⡀⢀⠠⠄⠌⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢀⣀⡀⠀⠀⠀⠀⠈⠉⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣶⣶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠟⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣤⣶⡄⢀⡴⢶⣦⣤⡤⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⠃⠀⠁⠀⠸⠇⠀⠁⠀⠀⣸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠑⠛⣃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣧⡀⠀⠂⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣦⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠈⠛⠻⠛⠋⠁⢿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣏⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠿⠛⠉⠁⣀⣤⣴⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⠟⢌⡳⢤⣀⡀⠀⠀⠀⠀⠀⠀⡠⠚⣁⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⣶⢆⣉⢓⠖⠭⠤⠈⠀⣀⡴⠊⠀⣚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣾⣿⣿⣶⣶⣶⣶⣶⡿⣡⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⣀⣴⠟⠛⠋⠉⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣼⣟⣥⣖⣴⠶⠿⠶⢾⣿⣿⣿⣿⣿⣿⣿⠟⣁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⡟⡭⠀⢀⣤⡤⢒⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡜⣵⠃⢉⡴⣂⣀⢀⠉⠛⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣿⣼⣨⣾⣻⣱⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢙⠿⡿⠿⣿⢿⣟⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠙⠛⠛⠛⠻⠛⠛⠛⢛⠟⠛⠋⠁⢄⠀⠀⠀⠀⠀⠀⠲⣦⣄⠀⠸⡳⣌⣳⢌⣿⡂⣮⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠠⠚⠀⠀⠈⠢⣀⠀⠀⠀⠀⢄⠀⠙⢷⣤⣼⣎⣻⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⢀⣤⠶⠿⠷⠄⢉⣦⣀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⢈⡆⠀⡤⠴⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⡤⠚⠤⣞⣦⣜⣱⢲⣋⡔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠓⠚⠲⠶⠻⣿⠗⠛⠱⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⡤⠒⢲⡀⠀⡴⠁⠀⠀⠙⡆⢰⠃⠀⠙⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡞⠀⠀⠈⠧⠴⠃⠀⠀⠀⠀⠑⠜⠁⠀⠀⠘⢞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⠒⢚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⠑⠲⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡃⠀⠀⠑⠒⠤⢤⣒⣀⣀⣀⣀⣀⣀⣀⣀⣠⠤⠤⠒⠁⡀⠠⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠦⠤⢄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡠⠤⠤⠀⠊⠁






⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣶⡆⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⢾⣷⣹⣿⣷⡇⡿⢸⣿⡇⣿⠀⠀⠀⠀⠀⠀⢸⣆
⠀⠀⠀⠀⠀⠀⠀⡠⡏⣰⡗⠀⣀⠀⠀⠈⠛⠳⠿⠅⢓⣃⣬⡿⠧⠟⠃⠀⠀⠠⠆⢸⣾⣿⡅
⠀⠀⠀⠀⠀⠀⠄⣰⡿⣿⠇⠐⡿⠓⡄⠀⠀⢄⣀⠀⠀⠀⣀⡀⠀⠀⠤⠖⢰⣿⣦⢸⣿⠈⠻⡄
⠀⠀⠀⠀⢀⠀⣴⠟⢠⡏⣰⠀⢱⠀⢠⡿⡆⠀⣏⠀⣤⣦⡈⠇⢠⣾⣦⡀⢸⣿⡀⠂⢻⣧⠀⢿⣆⠀⡀
⠀⠀⢀⣴⣽⣿⠏⢠⣾⡠⠃⠀⣹⡆⢸⠁⢹⠀⡏⣸⣿⢻⣷⠀⣸⡿⣿⣇⠘⣿⣧⣀⢠⢿⣿⡄⠹⣷⡴⣄
⠀⠀⠘⣿⣿⣯⣠⣾⣿⠃⠀⠀⣿⣷⠇⠀⢸⡇⠁⢹⠉⣹⣿⠀⣾⣧⠈⢹⡀⢿⣿⡧⠈⢾⣿⣷⡄⠙⣿⡿⠃
⠀⠀⠀⠈⣿⣥⣿⣿⡇⠀⠀⢠⣿⣿⠀⢀⢻⡇⠀⢸⠀⠀⢿⡇⣿⡿⠀⠀⢇⠸⣿⣧⡀⠸⣿⣿⣷⣷⡞
⠀⠀⠀⠀⠈⠻⣿⣿⡀⠄⠀⣴⣿⡏⠀⠨⣿⣧⠀⢸⠄⣈⣼⡇⣿⣿⠀⠀⢸⡄⣿⣿⣷⣄⣽⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠈⢿⣼⣮⣱⣿⣿⣧⠀⣹⣿⡏⠀⣾⠀⣐⣾⡇⣿⣿⠇⠀⠸⣷⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⣧⣤⣿⣿⡇⠀⡟⢂⣹⣿⣧⣿⣿⣯⣤⣴⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠓⠈⠙⠛⠛⠛⠛⠋⠙⠋⠉




⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣛⣿⣟⣿⣿⣿⣿⣟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠄⠉⠉⠉⠀⠀⠁⠐⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠄⠀⣁⣠⣤⣤⣴⣶⣶⣤⣤⣤⣀⢈⠐⢌⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣡⡴⠟⠛⠛⠍⣄⣨⣾⠟⠛⠛⠋⠈⠆⠀⠀⠉⠆⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⣰⠟⠁⠀⢡⡈⠜⣿⣿⠁⠀⠀⠀⠀⠀⢷⡀⠀⠠⣐
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠘⣯⠀⠀⡀⠴⠞⠿⠟⢛⣇⡀⠀⠈⠀⠀⠀⣉⣶⣾⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠙⢦⡀⠁⠀⠁⠙⠛⠊⠻⠿⢷⣤⡶⢶⡿⠍⢈⡿⠃⠌⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠳⣤⡙⠳⢦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⡴⠞⢋⠀⢊⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢳⣤⣉⠓⠲⢤⣌⣉⣉⣉⣉⣉⡉⠡⠤⠆⠊⣡⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⢾⠙⡟⢶⢦⣤⣤⣀⣀⣀⣤⣤⣤⢶⠶⠟⠉⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣼⡀⡇⢸⠀⢹⠀⢹⠉⢹⠁⠈⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣇⣸⡀⢸⠀⢸⠀⢸⠀⠀⡀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⣀⡴⠞⣋⢏⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠾⢤⣼⣤⣬⣤⡤⠴⠶⠛⠉⠀⠀⠀⠀⠀⣀⡴⠊⠁⠀⣔⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⡁⣠⣤⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣠⡼⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣺⡵⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠘⢛⠖⠀⠤⣀⣠⠖⡡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣋⣉⡖⣰⠇⠀⠀⢹⣯⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣯⡁⠁⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣿⡿⣿⢻⣷⠇⠀⢀⣼⡵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣿⣿⣯⣿⣥⣤⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⠀⠀⠐⠀⠀⠐⠒⠀⠀⠀⠈⠉⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠊⠁⠀⠀⠀⠈⣫⡽
⠀⠀⠀⠀⠀⢀⡠⢤⠁⠀⠂⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠉⠀⠀⠀⡆⠀⠀⠀⣠⣶⠟⠋⡇
⠀⠀⠀⠀⠔⠁⠠⠃⠀⠀⠀⠀⠊⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠆⠀⠀⠀⠀⢠⡎⢁⣠⡶⠟⠋⠀⠀⠀⡇
⠀⠀⢀⠎⠀⠀⠃⠀⠀⠀⠀⠀⠀⢰⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⢄⠀⠀⢀⣠⠞
⠀⠀⡌⢀⡤⠚⢀⡀⠀⠀⠀⠀⢀⠆⠀⢈⠀⠀⠀⠀⢀⡤⠖⠛⠉⠓⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠑⠁⠀⢀⠃⠈⠁⠒⠀⠤⠾⡀⠀⠸⠀⠀⠀⡰⠋⠀⢀⣠⣤⣴⣦⣄⡙⢦⡄⠀⠀⡠⡴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠂⠄⠀⢀⣀⡀⠀⠀⢀⠅⠀⠀⢰⠃⣠⠞⣻⣿⣿⣿⣿⣿⣿⡌⢿⠀⢪⣃⣀⠁⡹⠀⠀⠀⠀⠀⠠⣨⠇⢀⢠⠪⠐⡉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠀⠠⠀⢸⢰⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣸⠀⣼⠁⠀⢹⡀⠀⠀⠀⠀⠀⠀⡃⠀⠀⢘⠣⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣎⢧⣹⣿⣿⣿⣿⣿⣿⣿⢿⡟⡴⠃⠀⠀⡼⠀⠀⠀⠆⢂⠡⢱⠊⢆⣠⢴⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠘⠀⠀⢠⡶⡷⠝⡆⠈⠿⢦⡛⢾⣿⣿⣿⡿⠟⣩⠞⠉⠀⠀⠀⣰⠃⠀⠀⠀⠈⠐⠂⠁⠀⢀⠋⢀⡤⠒⠁
⠀⠀⠀⠀⠀⡔⠉⠁⠀⠀⠠⢄⠀⣿⠯⣠⠚⠉⠛⠲⠼⠭⠷⠲⠯⠴⠒⠋⠀⠀⠀⠀⢠⡜⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠁⠳
⠀⠀⠀⠀⠀⠐⡤⠀⠀⠀⠀⠈⢑⠀⠉⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⢳⠈⢧
⠀⠀⠀⠀⠀⠰⠀⢀⡀⠀⠔⠈⠁⠀⠀⠀⠙⠲⠤⣤⣀⣤⡤⡆⠀⠀⠀⠀⠀⠀⠀⢠⠀⠘⠃⠙⠲⣄⠀⠀⠀⠀⠀⠀⣀⡠⠎
⠀⠀⠀⠀⠀⠐⠂⠁⠙⢤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠪⡠⠀⠀⠀⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡘⠦⣀⠈⠁⠀⠀⣀⣀⣴⡄⠀⠀⠀⣇⣀⠀⠀⠀⢀⠋⠀⠀⢀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠠⢄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣸⠓⠀⠀⠀⡏⠀⠀⠙⡄⠀⠀⠉⠈⢣⠀⠀⠐⠐⠈⢦⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⢀⠌⠀⢬⡀⠈⠑⢢⡀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠙⠦⡀⠀⠱⣄⣀⡠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡠⡀⠀⠈⠛⠦⡀⠀⠈⠐⢄⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⢀⠔⠈⠁⠈⠉⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠳⠦⡈⠀⠀⠈⠛⢄⠉⡢⠑⢦⠀⠀⠀⠀⠀⣼⠉⠀⠀⡼⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠘⢢⢄⠈⠑⣠⣟⠦⡠⣜⠗⠀⠀⠀⠀⠈⠳⠤⠊⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⢘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⠈⢀⠀⡶⣏⣀⠜⠁⡆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠢⣀⡀⠀⣀⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣝⠁⠈⢯⠲⠊⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠃⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠

⣿⣿⠿⠿⡿⠻⠿⢿⡿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⣀⣰⣿⡿⠁⣠⠴⠦⠤
⠀⠀⠀⠀⠀⢀⠀⣀⠐⠋⡁⠤⠉⠶⣾⣿⣿⣷⣾⠥⢴⣒⡒⠚⠒⠄
⠀⠀⠀⠀⠀⠘⠋⠟⠛⠏⠀⠀⠀⠀⠀⢸⠉⠡⡀⠐⢦⡀⠉⠙⣶⣄⢅
⠀⠀⠀⠀⣀⣤⠃⠀⢈⠗⣶⣿⣃⠀⢠⡟⠀⠀⢹⣄⠀⠈⣦⡀⠘⡇⠀⢁
⠀⠀⠀⠀⠈⣻⠶⠶⡇⢀⠀⠁⠟⠀⠀⠃⠀⠀⠸⠟⢦⡘⠛⠧⡰⠻⣄⠈
⠀⠀⠀⣀⣰⡇⠀⠀⢻⡧⠴⠿⣆⠀⠚⠀⡜⠛⠧⠀⠀⣽⠀⣤⠇⢠⡏
⠀⠀⠀⠛⠉⢡⣀⣴⠿⠇⠀⠀⠀⣶⣶⡏⠀⠀⠀⣼⠛⠅⢀⡾⠤⢸⣇
⠀⠀⠀⠀⠀⢚⣽⠁⠐⢃⣀⣠⣾⠁⠀⠙⣦⣠⡼⠻⠤⣤⣮⠀⢀⡌⠁
⠀⠀⠀⠀⠰⠋⠿⢦⣴⡟⠛⠹⠛⢀⣀⡼⠛⠿⡃⢀⡼⠋⠉⣸⢹⣆
⠀⠀⠀⠀⠀⠀⠈⢦⠹⣧⠀⠀⣠⣿⡇⣃⠀⠀⡼⠋⢓⣀⣴⢇⡸⠉⠀⠀⢀⡀⠠⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣇⠈⠚⣏⠁⠀⠑⣤⡠⠞⠀⣠⠞⠁⣈⡽⠋⠀⡔⠈⠉⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠻⠒⢻⠀⠀⠐⠛⡻⠶⠚⠉⣽⠩⠁⠀⡴⠊⠁⢠⣤⣄⠀⢰⣧⠀⣠⡆⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⡀⠴⠚⠁⠀⠀⠀⠀⠀⠀⣴⠇⠀⣀⡀⠙⠻⠆⠿⠟⢰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠛⠿⠷⠆⠠⠖⠴⢿⣦⠀⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠀⠀⢀⠔⠆⠀⠑⠤⠞⠋⢾⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⠀⠀⠞⠁⠀⢰⡷⠠⣿⡆⠈⠺⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠀⠀⠀⠀⠀⠘⠇⠀⠙⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢈⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠽⠿⡧⠿⠟⠶⣤⡤⠶⠎⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⠁⠀⠀⠹⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠘⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⡀⠀⠀⠀⣿⣿⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣿⡿⠿⠿⢿⣿⣶⣶⣿⣿⡿⠿⠿⣿⣿⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠟⠋⢻⣿⣷⣿⣿⣶⡈⣿⣿⣯⡀⣠⣾⣿⣷⣿⣿⠟⠛⠻⣿⣷⣄
⠀⠀⠀⠀⣀⣤⣴⣿⡿⠋⠀⠀⢀⣾⣿⠟⠉⠙⣿⣿⣿⠟⢿⣿⣿⡿⠁⠙⢿⣿⣦⠀⠀⠈⠻⣿⣷⣤⡀
⠀⠀⠀⢾⣿⢿⣿⣿⠁⠀⠀⢀⣾⣿⠃⠀⠀⢠⣿⣿⠃⠀⠀⢻⣿⣇⠀⠀⠀⢻⣿⣧⠀⠀⠀⠘⣿⣿⣿⣷⣄
⠀⣀⡀⠀⠀⠸⣿⣿⡀⠀⠀⢸⣿⡏⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢿⣿⡆⠀⠀⢠⣿⣿⠈⢻⣿⣧⡀
⣼⣿⡇⠀⢀⣾⣿⣿⣿⣷⣶⣿⣿⣇⠀⠀⠀⣻⣿⡇⠀⠀⠀⠀⣿⣿⡀⠀⠀⢀⣾⣿⣿⣶⣾⣿⣿⣿⡄⠀⠹⣿⣷
⣿⣿⠀⢠⣿⣿⠃⠀⠈⣿⣿⠏⠻⣿⣷⣶⣾⣿⣿⣷⣄⣀⣀⣴⣿⣿⣿⣶⣶⣿⣿⣿⣯⠉⠉⠀⠘⣿⣿⡀⠀⣿⣿⡆
⣿⣿⡀⣿⣿⠃⠀⠀⣸⣿⡇⠀⠀⠀⣿⣿⠋⠁⠈⠛⣿⣿⡿⠟⠋⠀⢿⣿⡏⠁⠀⢹⣿⣧⠀⠀⠀⢸⣿⣇⡀⣿⣿⡇
⢸⣿⣿⣿⣿⠀⠀⠀⣿⣿⠇⠀⠀⢸⣿⡟⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⢸⣿⣇⠀⢀⣠⣿⣿⣤⣴⣶⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⣿⣿⣿⣿⣷⣤⣤⣿⣿⣇⠀⠀⠸⣿⣷⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⢸⣿⣇⣰⣿⡿⠛⠻⠿⠛⠛⠛⠃⠀⠈⠛⠛⠙⢻⣿⣷⣶⣦⡀
⠀⣿⣿⠃⠈⣿⣿⠿⠛⠻⣿⣷⣶⣾⣿⣿⣷⣤⣤⣾⣿⣿⣷⣦⣤⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠙⢿⣿⡆
⠀⣿⣿⡀⢸⣿⡟⠀⠀⠀⣸⣿⡟⠉⠁⠈⣿⣿⠟⠛⠁⠈⣿⣿⡟⠛⠉⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡄
⠀⠘⢿⣿⣾⣿⣷⠀⠀⠀⣿⣿⠁⠀⠀⢰⣿⣿⠀⠀⠀⠀⢸⣿⡇⣠⣾⣿⠿⠟⠀⠀⠀⠀⣴⣦⡀⠀⠀⣿⣿⠀⠀⠀⢀⣀⠀⠀⠀⠉⣿⣿
⠀⠀⣾⣿⡿⣿⣿⣦⣀⣀⣿⣿⡄⠀⠀⠸⣿⣿⠀⠀⠀⠀⣸⣿⡇⣿⣿⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⡆⠀⠻⠟⠀⣀⣴⣿⡿⠂⠀⠀⠐⣿⣿⣷
⠀⠀⢹⣿⡇⠀⠙⢿⣿⣿⠿⢿⣿⣦⣤⣴⣿⣿⣷⣤⣤⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⢠⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⢿⠿⠋⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠈⢿⣿⣦⣄⣘⣿⣿⠀⠀⢹⣿⡟⠛⠉⠈⣻⣿⡟⠋⠉⠀⢹⣿⡟⠁⠀⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣀⠀⠀⠀⠀⢾⣿
⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣧⡀⢸⣿⣇⠀⠀⠀⣿⣿⠁⠀⠀⠀⠸⣿⣷⣄⠀⠀⠀⠀⠀⣠⣴⣿⣿⠀⠀⠀⠀⢀⡈⠛⠻⠿⡿⠇⠀⠀⢀⣼⣿
⠀⠀⠀⠀⠀⠸⣿⣿⡀⠙⢿⣿⣿⣿⣿⣄⠀⠀⢻⣿⣇⠀⠀⠀⣰⣿⣿⡏⠀⠀⠀⠀⠸⠿⠟⠉⠀⣼⣿⡇⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⢺⣿⣯
⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⡀⢸⣿⣿⠻⣿⣿⣾⣿⣿⣿⣷⣶⣾⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⠀⠈⢿⡿⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⡄⠀⠉⢹⣿⡟⠀⠉⠉⠉⣿⣿⡍⣿⣿⣤⣤⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣄⠀⢸⣿⡇⠀⠀⠀⠀⣸⣿⡇⠈⢛⣿⣿⣿⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣄⣀⣀⣠⣿⣿⣿⣿⣿⡿⠟⠛⠿⢿⣿⣷⣶⣿⣷⣄⣀⣴⣶⣶⣿⡿⠋⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣈⣛⣿⣿⣿⣿⣛⣁⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣙⣻⣿⣿⣿⢛⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡞⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠁⠀⡆⠈⠀⠘⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣲⡏⠩⠁⣿⡀⠀⢇⠀⠀⣰⣖⠀⠉⢉⣲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣋⣡⠤⠖⡉⠁⢀⠗⠈⠁⠻⡅⠀⠀⠐⠤⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠉⢠⠁⢀⠾⠁⢉⡿⢠⡏⠈⢳⡅⢀⠄⠴⠀⢀⠸⡈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢠⡆⢠⠋⠁⠀⢸⠇⠘⠁⠀⠀⢻⠘⡧⡀⠀⠸⡄⢽⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠸⠀⣼⠃⠀⠀⣸⠀⠀⠀⠀⠀⣸⠀⢹⠁⠀⠀⠁⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢨⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠘⣇⠎⠀⠀⠀⠀⡄⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠁⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠈⣇⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠊⠀⡼⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠛⠒⠢⡄⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⢀⣀⣤⠼⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⢤⡀⠀⠙⠛⠛⠲⠦⠴⢥⣀⣀⣀⣀⣀⣠⡤⠤⠶⡶⠶⠖⢉⣁⣠⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡠⠤⠒⠢⣤⠀⠀⠈⠁⠛⡉⠉⠀⠀⠀⠀⠀⠀⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠚⠉⠁⠀⠉⠒⠤⠄⠐⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡜⢀⡿⠀⠀⠀⠀⠀⣾⠀⠀⢰⡇⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣁⡾⠃⣿⠀⢀⡞⢈⡟⢰⡇⣸⡇⣿⢸⡄⢺⢆⡾⠁⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠋⠀⠀⢿⡠⠘⣧⠼⡇⢹⣤⢿⡇⣿⢸⡇⢺⠘⣧⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠼⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢀⠀⠀⠀⢀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⢀⠀⠀⡀⢀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⠶⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠳⡷⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣠⣯⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣼⣯⣹⣿⣹⣏⠟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⢿⢸⣿⣏⣺⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣧⣄⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣤⣽⣿⣟⡼⣿⣿⢃⣾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡟⢱⣾⣾⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣶⣯⣿⣿⣿⡿⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢘⣍⣽⠻⣯⣟⣿⡿⠿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉⠀⢛⣃⣝⠻⣾⢇⣸⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠰⡿⠻⣩⠟⡔⡶⡌⠐⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠑⠫⣿⠀⠡⠟⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⣧⡿⠀⢰⢆⣾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣿⠇⠀⠐⢏⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣷⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⠀⠀⠀⢸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠛⠁⠀⠀⠻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢿⣿⣿⣶⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⣾⠿⢭⣭⡿⠦⣽⡷⢲⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣴⣬⣮⣩⣻⣓⢶⣤⡀⠀⠀⠀⠀⠐⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢁⣾⣡⡶⠶⣯⣀⣲⣿⣼⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣤⡽⠟⠋⠉⡩⠽⠂⠀⠀⠐⣡⠃
⠀⠀⠀⠀⠀⠀⠀⠠⣹⠋⣽⠇⣀⡾⠋⢸⣯⣀⣽⣧⣿⣿⡄⠀⠀⠀⠀⢀⠤⠎⣉⣤⡿⠋⠀⣀⡴⠈⠀⠀⠀⠀⡀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠞⣿⠗⢻⣧⣤⡿⠉⡿⡿⠹⣿⣹⣇⠀⠀⠀⢠⣯⠴⠚⠋⢁⣤⣶⠟⣿⠇⠀⠀⠀⡠⠊⠉⠙⡀⣀⣀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢰⡏⣀⡾⠁⣹⣷⣴⣾⣧⡾⣿⡿⠃⠀⠀⠀⠟⠁⠀⠀⠀⣿⡿⠍⢼⣇⡀⠀⢀⡜⠁⠀⣠⣷⠘⡿⠻⣿⠿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣡⡽⣧⣴⢊⣼⡏⢘⣿⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⡿⣼⣃⣰⣿⣿⣾⣷⣏⠀⢠⣶⢷⡎⣿⣤⡿⢫⣿⣿⣮⣿⡇
⠀⠀⠀⠀⠀⠀⡀⢀⣀⠀⠈⠉⠉⠛⠛⠟⠛⠛⠉⠀⠀⣠⣶⡦⠀⠀⠀⠀⣼⣹⢂⣿⣰⣿⣇⣴⡟⢻⣿⣄⢾⣧⣼⣿⣄⣹⣿⣶⣯⣥⣿⢻⣷
⠀⠀⠀⠤⠐⠂⢀⠀⠁⡄⠀⠦⠤⡀⠀⠀⠀⠰⠶⣦⡄⠉⢩⣤⠀⠀⠀⠀⢿⢻⣥⢿⣿⣿⠋⢹⣷⣿⣯⣿⡀⣘⣿⡀⢹⣿⣅⣿⠋⢹⣿⣿⠇
⠀⠀⡤⠀⠈⠳⣌⢀⣸⠃⢀⣴⠆⠉⠀⠀⠀⠀⠀⠀⣀⡀⠀⠁⠀⠀⠀⠀⢄⡼⠿⣟⢉⣽⣦⣿⣏⣸⣿⣾⠁⠫⣿⡙⢻⣇⡸⢿⠿⢿⣧⠟
⠀⢀⠀⠀⠀⣀⠀⠎⣹⠀⠀⠀⠀⠛⠀⠀⠀⠀⣐⡒⠐⠌⣢⣤⠤⠰⠀⠀⠈⣿⣶⣿⠚⣿⣆⣾⣿⣹⡿⠋⠀⠀⠀⠁⠉⠛⠭⠿⠒⠟⠁
⠀⠀⠃⠐⠛⡩⠀⠀⠀⠠⣄⠀⠀⡐⠀⠀⠼⠀⠉⠛⣀⡟⠁⢸⡀⠘⣠⠾⢀⠈⠋⠹⠾⠻⠧⠛⠛⠋
⠀⠀⠡⠤⠄⠀⠀⠀⠻⠀⢈⠓⠀⠃⠀⠈⠀⠀⠀⠀⣻⠃⢀⡏⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠄⠴⠓⠀⠐⠊⠁⠀⠀⠀⠰⠀⠀⡤⠄⢸⣆⡞⠙⡀⠐⠂⠀⠩⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⠶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠉⢠⠀⠹⣦⠀⢶⣶⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣎⣉⣠⡁⣴⡡⢈⣍⠉⠛⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣴⡀⡀⠀⠘⠇⠀⣀⣀⣾⠏⠀⠀⠀⠀⠄⠀⠀⠀⠚⠛⠿⠭⢿⣽⣿⠶⠿⠖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⣤⣶⣄⣤⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠙⢄⠀⠀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠄⠑⠒⠊⡁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠶⢟⡒⠂⠀⠀⠀⣀⢀⠀⠀⠈⠢⠤⠄⡶⠂⠀⠀⠀⠀⠀⣴⠀⠀⠀⡠⠋⢇⠀⠀⣀⣠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⡀⠀⠈⠱⡄⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢀⠜⠙⣄⢀⠔⠁⡄⠈⠉⢉⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠐⡀⠀⠀⠀⣯⠤⠤⣀⠀⢀⠎⠀⠀⠈⠁⠀⠠⠄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠷⢄⣀⠀⠀⢠⠞⠒⢲⣰⠁⠀⠀⠈⢣⡯⠔⠦⣀⠄⠀⠁⠀⢀⡈⠴⠾⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣑⠾⢄⣀⡴⠛⢆⣀⢀⣠⠞⢇⡀⣀⠧⡀⠀⠀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠁⠀⠈⠳⡦⣵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⢀⣠⢤⡀⠀⠀⠀⠀⢀⡠⠤⡀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣀⡠⠔⠉⠀⠀⠈⠦⣀⣀⠔⠉⠀⠀⠘⢆⠀⢀⠤⠤⡀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⣉⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠉⠁⠀⠀⠈⠑⠒⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠰⡷⠀⠀⠈⠉⠀⠀⠀⣠⡀⠀⠘⠃⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠈⠀⠀⡀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢀⣤⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠈⠁⠀⠀⠀⠙⠀⠀⢀⣀⠈⠋⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⢾⠆⠀⠀⠀⠀⠁⠀⠀⠀⢠⡄⠀⡇
⠀⠀⠀⠀⠀⠐⡟⠛⠓⠑⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠓⢰⡄
⠀⠀⠀⠀⠀⠀⠙⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠒⠒⠒⠒⠒⠒⠂⠈⠉

⠀⠀⠀⠀⠢⡀
⠀⠀⠪⡡
⠀⠀⠀⠀⢂⠀⠀⠀⢀⠀⠀⠀⠀⠡⠀⢠
⠀⠀⠀⠀⠀⠡⠐⠀⠀⠑⠀⠀⠀⠀⠙⢄⠈⠐⠂
⠀⠀⠀⠀⢀⠁⠁⠀⠀⠀⠀⠐⠄⠀⠀⠀⠑⠄⡀⠀⠀⠁
⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠄⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣀⠠⠐⠈⠁⠀⠔⠒
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠰⣆⣠⠀⢢⠀⡀⠀⠀⠀⠀⠀⠀⠐⠂⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠐⠡⠀⠀⠀⠀⠆⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠐⢆⠀⡀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠢⣈⠁
⠀⠀⠀⠀⠀⠈⢌⠀⠧⠤⠀⠀⠀⠈⠀⠀⠀⢀⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠈
⠀⠀⠀⠀⠀⠅⠀⠀⡄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠅⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⠈⢕⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⢈⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠖⠉⠄⠀⠀⠈⠐⠈⠐⡁⠀⢀⠀⠄⠂⠀⠀⠈⠄⠀⠀⠀⠈⠂⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠈⠈⠀⠀⠀⠀⠀⢀⠔⠒⠒⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⢀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠁⠘
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⣼⣿⣿⣿⣿⣿⣿⣿⡎⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⡏⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢳⣴⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠶⣾⣿⡷⠶⣶⣾⣶⣾⣯⣭⣭⣿⣯⣴⣾⣿⢷⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣶⠧⣴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣉⣿⣿⣿⣿⣿⡀⠀⢙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠻⣠⡿⣧⣤⡀⣤⣍⡉⠉⠉⠛⠛⠛⠛⠛⠛⢋⣻⣇⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⣿⣏⡠⣀⠘⠢⣀⠀⠈⠀⠀⢀⣉⡉⠉⠙⠟⠛⠛⢻⣶⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠸⡟⣿⣟⣆⠀⠀⠙⠢⠀⠀⠀⢠⣼⠏⠀⣶⣶⠾⢻⣿⡽⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢈⣿⣧⡄⠀⠀⠀⠀⣶⡰⠊⠀⣶⣴⣿⠃⠀⣼⡏⠰⠎⢹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⢀⠰⣧⣈⣿⢸⣧⠠⠄⠀⣶⣿⣧⡀⠶⣤⡿⠋⠀⣴⣿⡏⠱⠶⠋⢩⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠀⠀⠀⣄⣿⣽⣿⡿⠄⠠⠀⠀⠘⠉⣿⣿⣿⡃⠘⣿⣿⣾⣿⣾⣿⣦⠄⠀⢨⡿⢛⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠷⠀⠀⠀⢠⡈⣻⣿⣯⠀⠀⠀⠀⢰⡆⠠⠉⠉⠉⠁⠀⠀⡜⠋⠉⢿⣜⠃⠀⠀⠀⠀⠈⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠘⣿⣿⣿⠀⣀⣀⡀⠈⣷⡀⠱⡄⠀⠀⠀⠀⠑⠚⠀⣿⣿⡄⢰⣡⡄⠀⠈⠁⠰⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡁⠀⠀⠀⣀⠻⣿⣿⣿⣦⣿⣿⣧⣤⣼⣷⡤⣿⣶⣤⣀⣤⣄⣠⣠⣿⠛⠿⣿⡿⠀⠀⠀⠀⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠁⡰⢦⣀⢙⣿⠏⢿⣟⣿⠟⠛⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣧⡀⠀⢨⣧⠀⠀⠀⠀⠺⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⡈⠙⢿⡿⠀⡞⠛⢻⣧⣠⣿⣭⡿⠉⣿⠷⠶⠾⣷⣾⣾⣿⣿⣴⠇⠀⣼⠛⠃⠁⢰⠃⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠀⠀⢀⠹⣿⠁⢰⣿⣛⠀⢉⣿⣿⡿⠀⠐⣿⠓⠺⠻⢿⣿⣿⣿⣿⣷⡄⠀⣍⠀⠀⠐⠻⣴⡿⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡆⠀⣥⠀⢙⣿⠃⠀⢠⣿⡋⢡⣾⠻⠯⠄⠀⠀⠉⣀⢀⣤⣤⣿⣿⣿⣿⡿⠁⢀⠛⠳⢦⣤⣤⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣄⣸⣥⣠⣿⡟⠀⠀⢸⣏⡁⢸⣿⣡⣤⣤⣤⣤⣤⣤⣤⣤⣌⣿⣘⣿⠿⣇⡰⠇⣠⡆⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠉⠉⣿⡇⠀⠀⢘⣿⣿⠿⠿⠿⢿⣿⣷⣾⣯⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠋⢀⡈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠈⢠⣶⣶⠶⢦⣿⠃⠀⠀⢸⣉⡉⠀⠀⠐⠒⠿⢿⣿⣦⣾⣿⣿⣿⣵⠾⢿⣿⣿⡆⠰⣠⣾⣵⠟
⠀⠀⠀⠀⠀⠀⠀⠄⠀⣾⣿⡟⣀⠀⣽⠀⠀⠀⣼⡛⠋⠁⠀⠐⠀⢀⣼⣿⢿⡿⠛⠛⠁⠀⠀⠀⢴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠁⣿⣸⡇⠀⡄⠀⣿⠤⠀⠀⠠⠄⠀⠀⣹⣿⡄⠸⠂⠀⠀⠀⠛⠛⠻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡀⣿⠋⠀⣤⠀⠀⠲⠀⠀⠀⠀⠀⠀⣀⠉⣿⡇⣾⡆⠀⠀⠀⠀⠉⠑⢻⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠳⠋⠀⢀⠀⠀⠀⣸⣀⣈⣙⠀⠀⠠⢤⣤⣿⡇⠙⠷⠤⠀⠀⣀⣀⣈⣹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠛⠛⠻⠿⠿⣿⣿⣿⠁⠀⣶⡿⠛⠛⠋⠉⠉⠭⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠀⢠⠒⠲⠶⠀⠀⢀⣈⣽⣿⠀⠀⣿⡇⠀⠀⠐⠒⠒⠶⠾⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣀⡀⠀⠀⠀⠰⣿⣿⠀⠀⢘⠁⠛⠛⠋⠀⠀⢶⣶⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠉⠀⣀⠀⠒⠛⢿⣿⣏⠀⢠⡟⠓⠶⣶⣶⠒⡢⢤⣤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⣀⣈⣤⣤⣴⣾⣿⣿⠀⢸⡇⠀⠀⠓⠂⢉⣡⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠉⠉⠽⣿⣿⣋⡀⠃⠀⠀⠀⣀⢠⣼⡿⠃⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠰⢿⣿⡿⠛⠂⠀⠀⠀⣨⣾⠛⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣄⣤⡀⠰⣾⣿⡇⠀⠀⢰⣾⣿⣭⠋⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠄⠀⠀⠀⣹⣿⣿⠀⣤⣀⣸⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⠚⠛⠿⣿⣿⠻⣿⣿⠟⠃⠀⠀⠸⠆⠀⠀⠀⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣄⠀⢀⣠⣾⣿⠀⠸⣇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠈⠻⢿⣿⣄⠀⢻⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣄⡀⠀⣀⣼⠆⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⠟⠀⠀⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⠟⠋⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⡀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡤⠊⠉⠛⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⣀⣠⠶⣀⠀⠀⠀⠀⣀⠞⠀⠀⠀⠀⢀⡼⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠉⠁⠀⠈⠉⢻⠀⠻⢁⠖⣁⣠⠖⠲⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠦⣄⠀⠒⠒⠾⣷⡞⠛⣯⣤⣖⠛⠒⠶⠖⠋⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⢳⡤⠤⢾⣁⣹⠉⢻⠶⢭⡉⠓⠀⠀⠀⢀⡴⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠉⠉⠛⠋⠀⠀⠹⡤⢶⡒⠒⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⣠⣦⠀⠀⡞⢳⠀⢠⠶⡄⠠⡟⡆⠀⠀⡟⡆⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⡼⠁⡇⠀⢸⠃⠘⠶⠋⠀⢳⣀⡇⢹⡀⠀⡇⠱⣄⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠋⠈⠀⡇⢀⠏⠀⠀⠀⠀⠂⠀⠉⠀⠀⠳⣠⠇⠀⠌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠑⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠒⠲⠶⠶⠶⠖⠒⠒⠚⠉⠉



⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⣲⣾⣿⣿⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠐⠲⠮⢍⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠙⢿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠀⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⢷⣀⢀⡉⠛⠿⠿⣿⣿⡿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⣀⢀
⠀⠀⠀⠀⡠⢒⡬⠟⢛⣿⣿⡏⠰⢸⣿⣤⡉⢻⣷⡢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⡩⠀⠀⡩⠧⣶⠄⠈⡧⢀⠈⡫⡀⠢⡀
⠀⠀⠀⣸⢴⠏⠀⣠⠏⠀⢸⣧⣴⣿⠃⢸⣿⣮⣽⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣎⢥⠎⠀⢀⠊⠀⠀⢏⠀⡌⠀⠀⠑⡀⠈⢢⣈⡆
⠀⠀⡔⠁⣸⣶⣾⣿⠀⡄⣾⠏⠹⣿⣠⣤⣿⡿⠛⣿⣄⣿⣧⠀⠀⠀⠀⠀⠀⠜⠀⠸⡄⠤⢖⢠⡄⢠⠊⠉⢃⠀⠀⡆⡓⠒⠪⡱⠈⢢
⠀⡴⣧⣡⡟⠀⠈⢿⣷⣿⡏⠀⠀⣽⣿⣿⣿⠃⠀⢻⣿⣿⣿⣄⠀⠀⠀⢀⡔⢇⣁⠎⠀⠀⠈⢤⡠⡆⠀⢀⡀⢱⠤⠔⠀⠀⠀⢰⠤⠔⢄
⢸⣴⠋⢸⣇⠐⠀⣸⠋⣙⣷⣄⣘⣻⡟⢀⠹⣷⣾⣿⣿⠉⣿⣿⡆⠀⠀⢜⡠⠊⠀⡄⠰⠀⠠⠃⡀⢂⠀⠘⢁⠎⢀⠈⢂⠘⠂⣰⣷⠡⡈
⢀⡅⠀⣼⠛⡷⣾⡃⢠⡙⣨⣿⠛⣿⡄⢸⣷⣿⣿⢻⣿⣴⣿⣿⡅⠀⠀⢠⢅⠐⡠⠉⠢⢴⠁⣤⠉⢀⠹⠉⠩⠀⠹⠆⠶⠓⠘⡘⠃⢠⡘
⡌⣧⣰⡇⢠⣿⣽⣷⣬⣷⣿⠇⠀⣹⣷⣾⣿⣿⡟⣸⣿⣿⣿⣿⡇⠀⠀⠆⢆⢀⠁⠠⠀⠀⢆⡈⠀⣠⠁⠀⠀⠣⡀⠛⢀⠃⠀⠑⣄⣈⠜
⢧⣿⡙⣧⣾⣿⠿⣿⡏⠙⠻⣆⠸⢟⣿⡿⠛⣿⣠⣿⣿⣿⣿⣿⠇⠀⠀⢎⡸⡉⢆⣮⠈⠒⠀⣵⠇⠘⡀⠸⠋⢀⠌⠉⢃⢠⡘⣺⠌⠐⣀
⠀⣿⠹⠎⣿⡷⣾⡿⠀⣤⠷⢹⣿⣿⡏⢠⣿⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⣇⠻⠆⠙⠄⠐⡊⠉⣌⠷⠈⡖⠐⠊⠀⠀⠈⢪⠥⠎⣀⠀⡇
⠀⢻⣿⣿⣿⢠⣽⣷⢠⡍⣾⣸⣿⣿⣷⣾⢿⢿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢋⠗⡒⢺⢠⡀⢁⢠⡉⣷⢀⠃⠀⢴⡔⠃⠀⡐⠀⢣⡋⢴⠃
⠀⠀⠉⢿⣿⣯⣿⣿⣷⣯⣴⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠈⡻⣌⢌⠓⠂⡗⠥⠄⢂⢸⣦⢘⠠⡤⡚⠡⢋⠜⡖⠁
⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣉⡹⣀⠲⢀⡌⠒⠥⡫⡞⠰⢻⢆⡡⠊
⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⠥⣜⣅⠡⣌⡢⠨⢋⢕⣀⡡⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⢿⣟⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⢠⣤⣀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠿⣟⣛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣦⣤⣴
⠀⣰⣿⣿⣿⣅⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣰⣿⣿⣿⣿⣿⣴⣿⣿⣾⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠻⠿⣿
⢿⣿⣿⣿⣿⣿⣇⢈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠋⠉⠉⠉⠉⠙⠁⠙⠋⠙⠛⠉⠉
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⣀⡼⠋
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⡿⠛⠈⠉
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠙⠿⣿⡿⠿⠛⠛⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⡿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠿⠿⠛⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣿⣿⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠛⠻⢶⣤⠀⠀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣷⣄⡀⠀⠀⢹⣧⣼⠟⠉⠀⣩⣿⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡶⠿⠛⠛⠋⠉⠛⠿⠶⠶⠿⠿⠶⠾⠟⠋⠉⠛⠛⠻⠿⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠉⠙⠛⠷⢶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⠶⠾⠟⠛⠉⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⡿⠁⢀⣤⣶⣦⡀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣻⣿⠶⣶⣦⣤⣀⣀
⠀⠀⢀⣠⣴⠾⠟⠋⠉⠀⣰⡿⠿⠶⠟⠋⠀⠹⣷⡀⣠⡾⠟⠛⠻⣦⠀⠀⠀⠀⣠⡾⠛⠙⠻⢷⣄⠀⠀⠀⣀⣴⠟⣿⡄⠀⠀⠉⠉⠛⠿⢶⣦⣄⡀
⢀⣴⠟⠋⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠙⢷⣤⣤⡾⠋⠀⠀⠀⠀⠀⠙⠻⠿⠟⠛⠁⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣄
⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿
⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿
⠀⠛⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠷⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣶⣶⡶⠶⠿⠿⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠋
⠀⠀⠀⠉⠛⠷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⠾⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠷⢶⣶⣤⣤⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣴⣶⠶⠾⠟⠛⠋⠉⠁

⠀⠀⠀⠀⢀⣠⣴⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣀⣀⣀
⠀⠀⠀⡰⢋⡵⢒⠒⢌⠙⡌⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⠶⣺⢟⡿⠋⢉⡟⣩⠏⠁⢀⡴⣫⠟⠉⠙⢦⡀⠀⠀⠀⢀⣀
⠀⠀⢠⠃⣾⢰⡯⣹⢀⡆⡩⠘⣦⣤⣄⡀⠀⠀⠀⠀⠀⣰⠛⣽⣫⠏⠀⣰⣣⣎⣀⣤⣯⡴⠷⠶⠖⣿⡿⠿⣖⡓⢶⡼⠃⠀⠀⠀⠎⠀⠛⠑⠖⠢⣀⣀
⠀⠀⠸⠀⠘⢦⣑⣒⣫⢴⡗⣋⣭⡭⢍⡙⢷⡄⠀⠀⠀⠈⠛⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠙⠶⠶⠞⠛⠉⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣸⣿⠗⠎⠣⢱⡀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠰⠶⣤⣀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠺⡷⠭⢜⡴⢸⢇⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠊⠠⠂⡛⡄
⠀⠀⠀⢸⡀⠀⠀⠀⠀⠙⠦⣀⣈⣉⣴⠷⠋⢀⠆⠀⠀⠀⠀⠀⣀⡠⠤⠖⣒⣉⡭⠭⠛⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⣏⠛⠓⠒⠒⠒⠒⠒⠚⠋⠁⢀⡠⠊⠀⠀⠀⢀⡴⠋⠓⢞⠉⠁⠀⠀⢆⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡆⡀⢀⠀⡼⠁
⠀⠀⠀⠀⠘⠶⠦⠤⣤⣤⣤⣤⠤⠶⠚⠉⠀⠀⠀⠀⠀⠸⡀⠀⠀⠘⡀⢀⣀⣠⠼⡖⠒⠂⠈⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠻⢧⣥⣯⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠤⠔⠒⢻⠉⠁⠀⠀⢳⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⣾⡁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠈⣆⣀⡤⠤⠺⡗⢋⣉⣁⣷⡆⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣀⡀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠀⠀⠀⠀⠀⢳⠒⠊⠉⠹⣀⠖⠲⣄⠜⠁⠀⠀⠈⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⠀⠘⠀⠀⠀⠀⠠⠊⠉⠒⠚⠋⠁⠀⠀⢀⡤⠤⠔⠒⠠⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠛⠲⢤⣀⠀⠀⠀⡆⠀⠀⠀⢀⣀⣠⠤⠤⠖⠋⠉⠉⠁⠀⠀⠀⠀⠀⢙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠈⠑⠢⣄⠇⠀⠀⠀⠀⠀⢘⡄⠀⠀⠀⡀⢠⡀⣀⠰⠐⠀⠧⠘⡹⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠔⠈⠠⠤⣍⠂⡀
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⣷⠄⠖⠓⠉⠈⠁⠀⠀⠀⠀⠀⠀⢇⠂⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⡔⢀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⡌⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠰⠋⡀
⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠛⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠤⠤⠴⠖⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⡠⠚⠁
⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠌⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⡇⠀⠀⠀⠂⠄⡀⣀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⢀⠀⠀⠀⢁
⠀⠀⠀⠇⠀⠀⠀⠀⠄⠐⠏⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⣴⠖⠚⠋⠉⠀⠑⠆⡇⠈⣦⡔⠁⠀⠀⠀⠀⡇
⠀⠀⠀⢀⠀⠀⠈⠁⠒⠐⠋⠀⠀⠀⠀⡠⠤⣤⣀⡀⢀⡞⢉⢹⠀⢰⠆⠀⠀⠀⠨⠗⠀⠀⠇⢃⠀⢻⡇⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⢹⡇⠈⢸⠀⠀⠀⢀⢄⠀⠀⠀⠀⠀⢸⠘⡄⢸⡟⠁⠒⠒⠠⠤⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠈⣷⠀⠏⡆⠀⠀⠀⠉⠀⠀⠀⠪⠂⢀⣣⠵⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⣀⢽⣄⣰⣐⡙⢁⣀⠠⠴⠗⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠔⠒⠉⠀⠀⠈⠁⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠲⢶⠟⠖⠚⠉⠈⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⡆⠀⠀⣠⣄⣀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡶⠟⠁⠀⣹⠀⠀⠙⠛⠋⠀⠀⠀⡆
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢰⣤⣄⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣤⡶⠀⠀⠀⠀⠀⠉⠛⠁⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⣠⡄⠀⠀⠀⢶⠄⠀⠀⢠⠎⠀⠀⠀⠀⠀⢠⣀⣀⠴⢲⠤⣀⣿⢇⡀⠶⣖⠀⠀⢀
⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⢸⠟⠁⠀⠀⠀⠀⠀⠀⢀⠅⠀⠀⠀⢀⠀⡄⠀⠠⡄⢰⠃⡠⠏⠀⡇⠈⢃⠀⢱⡒⠚⡃
⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠈⠀⡈⠀⠀⠁⠸⠋⠀⡤⡄⠈⠤⠆⠀⠃⠑⠦⠓⢌⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⡀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⢀⢀⠔⠓⠈⠳⠂⢐⡀⠀⠀⢀⠀⡀⠈⢢⠔⢄⢨⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠰⢠⠎⠉⡁⠀⠨⠉⢇⢀⣸⠀⠀⠁⠈⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢻⠃⠀⠀⠀⠠⠋⠛⠃⠀⢀⠋⠀⣄⠠⡇⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⣀⣀⠘⠘⡃⠀⠀⡘⠉⢹⡀⣀⠀⢀⡌⡅
⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠃⠈⠀⠀⢀⠖⠛⠃⠀⡠⠁⠹⠠⠎⡼⠁
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠰⣶⣤⡀⣿⠀⣠⣶⠆⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠓⢻⠀⠀⠈⠹⣁⠀⠀⠘⠉
⠀⠀⠀⠀⠈⡆⠀⠀⠀⠛⠶⠍⠻⠇⠛⠰⠟⢁⣀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢠⡄⠀⣠⠦
⠀⠀⠀⠀⡶⡇⠀⠀⠻⠿⠛⠃⠀⢸⠟⠀⡘⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉
⠀⠀⠀⠀⢂⣿⠀⠀⠀⣶⠞⣠⡄⠠⣄⠰⣌⠳⠆
⠀⠀⠀⠀⠘⠛⣧⠀⠀⠀⠼⠋⠀⠀⣾⡆⠈
⠀⠀⠀⠀⠀⢀⠙⡺⡆⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠈⠁⠙⢒⣲⣄⠀⣀⣀⡀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡿⣿⡿⣷⣾⣷⣶⢿⣿⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣿⢿⣷⣬⣾⣿⣬⣵⣿⣷⣥⣾⡿⣿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣶⣾⣧⣍⣵⣿⣙⣣⣿⣮⣩⣼⣷⣴⣿⡇⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣙⣽⣏⠻⢋⣿⠻⠟⣿⡝⠟⣹⣯⣉⣼⡇⠀⠀⠀⣠⣶⣿⣿⢿⣿⣷⣦⡀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡙⢟⣿⢻⡟⣿⢿⡿⣿⢻⡟⣿⠻⢋⡿⠁⠀⢀⣼⣿⣿⣿⡐⡦⣹⣿⣿⣿⠆⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣷⣾⣿⣶⣶⣿⣷⣾⣿⣿⠟⠁⠀⠀⣼⣿⡇⢶⡌⢿⣶⣿⣿⡿⢋⣾⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢮⣥⣿⣌⣡⣿⣬⠵⠛⠁⠀⠀⠀⠀⣿⣿⡿⢶⣶⣾⣿⣿⠟⣵⣿⣿⡿⠿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡐⣒⣨⣿⣿⣷⣾⣿⣿⣧⣐⢓⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⠀⠀⣀⣤⣶⣶⣶⣦⣄⠀⠀⠘⣿⣿⡿⢛⡉⣿⡿⢿⣿⠰⣭⡙⣿⡟⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⡃⣾⣿⣿⣿⢩⡝⣿⣿⣷⡄⠀⠘⢿⣷⣬⣴⣿⡇⠧⣹⣷⣬⡵⢛⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣌⢿⣿⣿⣨⣴⢟⡛⢿⣿⡄⠀⠈⠙⠛⠿⠿⣿⣿⣿⡭⠥⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢟⠻⣿⣿⣿⣎⢻⣿⣿⣃⣛⣋⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣜⣫⣴⣿⣿⣿⣮⣿⣿⡿⢛⡛⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⢩⣶⢂⣿⡿⣿⣿⠻⢷⣮⣥⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣴⣿⠫⡆⣹⣿⡸⢂⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⣶⣿⣿⣿⣿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀
⠀⠀⡤⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠶⠶⠾⠷
⠀⢠⠿⠄⡘⢳⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⡰⠊⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠆⠴⠒⠚⠂⠀⣐⣒⠛⠁⠂
⠀⣸⣢⣄⣈⡻⡇⠀⠀⠀⠀⠰⣷⣯⡭⠭⠟⠦⠀⠀⠀⠀⠀⣸⣀⠀⠀⠀⣠⡄⠀⠀⠀⠐⠒⠛⠫⠭⠁⣠⡶⡀
⠀⠘⠿⣬⡙⣿⠃⠀⠀⠀⠀⠀⣿⣦⠁⠄⠀⠀⠀⡄⠀⠀⠐⠬⣿⢓⠂⠈⠈⠀⠠⠒⠶⠖⣢⣶⣾⣩⠿⠟⢋⡔
⠀⠀⠀⠁⡏⠁⠀⠀⠀⠀⠀⠃⢣⠘⣄⣸⠸⠀⠀⠁⠀⠀⠈⠀⠑⠊⠁⠀⠀⠈⠁⠐⠂⠀⠩⠤⠤⠤⠤⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢂⠈⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠺⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠠⠐⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡷⠆⠀⠀⠀⠀⠀⣀⠀⠀⠤⠀⠒⠀⠀⠀⠀⠀⠀⠀⣄⠤⡁⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠐⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⢐⠒⣋⠄
⠀⠀⠀⠀⡀⠀⠀⠀⠐⣿⣦⠷⡀⠀⢀⡸⠀⠀⠀⠀⠀⠀⠀⢰⠤⠄⢤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠙⢿⠿⠍⠁⡴
⠀⠀⠀⡄⠁⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⢲⣄⡀⠀⠀⠀⠈⠁⠀⠀⠱⣰
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⢄⡃⢜⠤⡀⠀⠀⠀⠀⠀⢀⡗⠠
⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠈⢏⠉⠇⠀⠈⠑⢷⡀⠀⠀⠀⠀⠀⣾⢧⣀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢠⡀⢯⠲⡀⠁⢄⡑⢅⣠⠈⢷⢦⠀⠠⢤⠀⢷⠀⣹⡖⡁⠀⠀⠀⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣾⠀⠈⢄⠡⡄⠀⡆⠀⠙⠧⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣠⢴⡀⢆⡀
⠀⠀⠀⢀⣠⠀⢐⢙⡀⠲⢄⠀⠉⠁⠓⠺⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⢙⣆⠣⠆⣭⣄
⠀⠀⢠⡎⠉⠀⠀⠀⠀⠐⠈⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⣠⠀⠀⠀⠀⠀⠀⡜⢏⠻⢦⠈⠑⢾⠧⣡⣵
⠀⠀⢸⠀⠀⠁⠀⠀⠀⠀⢰⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠢⢍⣿⣽⠀⠀⠀⠀⠀⠀⠛⠮⠑⠦⢾⠿⠎⠁⠿⠉
⠀⠀⠀⢲⣤⠀⠀⢠⠠⣸⣿⡏⠀⠀⠀⠀⢸⣦⡀⣘⣿⣿⣥⣮⠽⠃⡀⣐⡦⡾⠀⠀⣜⠂⠀⠉⠉⠉⠩⠤⢖⡥
⠀⠀⠒⠂⢈⠛⠿⢾⣿⠟⠫⠃⠀⠀⠀⠀⠀⠈⠻⠶⠋⠉⠛⠡⠀⠸⣿⡿⠃⠀⠀⠀⠙⠅⠀⠀⠀⠀⠀⣶⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠐⠈⠁
⣿⣿⠿⢿⢻⠿⡿⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢦⠀⣠⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢛⢾⣯⡼⣶⠙⣎⠉⠒⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⢒⡟⢳⠃⣯⠜⠃⢯⡬⠿⣩⠗⢀⠎⣹⡶⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⡠⠚⠉⠀⣀⣤⠞⠀⡞⠀⡡⠒⠲⡍⠑⠒⠀⠀⠀⠀⢇⢸⣀⠀⠀⠉⠓⢄
⠀⠀⠀⠀⢠⠎⠀⠀⠀⡞⠁⡎⠀⢠⠁⡼⠁⠀⠀⡇⠀⠀⢠⠋⠈⠲⠚⠀⡏⠉⠑⡄⠀⠀⠱⡄
⠀⠀⠀⠀⡏⠀⠀⠀⢸⠁⠈⢧⣠⠃⣰⠁⠀⠀⢰⠁⠀⢀⠏⠀⠀⠀⠀⢀⡇⠀⠀⡇⠀⠀⠀⢹
⠀⠀⠀⠀⡇⠀⠀⠀⠘⢆⠀⠀⠙⠲⠧⣤⣀⠀⡼⠀⠀⡼⠀⠀⣀⡤⠞⠉⠀⠀⢸⠁⠀⠀⠀⢸
⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠈⠉⠛⠒⠒⠛⠚⠉⠁⠀⠀⠀⣠⠖⠉⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠉⠉⠉⠒⠤⠤⣀⠀⠀⠀⠀⢀⣀⡴⠒⠈⠁⠀⠀⠀⠀⣀⡞⠁
⠀⠀⠀⠀⠀⠀⠙⠮⣒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢭⣐⡢⠤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⣔⣒⠽⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠲⠶⠶⠮⠽⠒⠋⠉⠉⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⢰⡆⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⣿⡄⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⠀⠀⠀⠀⠘⣟⢦⡀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢾⡀⠀⠀⠀⠀⠈⠳⣝⡢⣄⡈⠙⠦⣄⡀
⠀⠀⠀⠀⠀⡠⠋⣴⠀⠀⠀⠀⠀⠈⠻⣶⣤⣀⡀⠀⠀⠀⠉⠓⠿⠷⠦⢤⠉⠒⠤⣀
⠀⠀⠀⢀⡞⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠻⠭⣗⣒⣲⠤⠤⣄⣀⣀⠀⠀⠀⠀⠉⠲⢤⣄⣀
⠀⣠⢴⠏⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠒⠻⠿⣶⣤⡀⠀⠀⠀⠈⠙⢿⡲⢤⡀
⡜⠁⡞⠀⠀⠀⠀⠀⠈⠻⣗⡦⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣆⠀⠀⠀⠀⠀⠙⢆⠙
⡿⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠾⠯⠭⠭⠭⠭⠭⠭⠿⠿⠿⠷⢶⣤⣀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⢸⡾
⡇⠀⠙⠲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠄⠀⠀⠀⢀⣀⡤⠴⠚⠁
⣧⠀⠀⠀⠀⠀⠈⠉⠙⠒⠒⠲⠦⠤⠤⠤⠤⣤⣄⣀⣀⣀⣠⣤⣤⠤⠤⠤⠤⠶⠒⠒⠛⠉⠉⠀⠀⠀⠀⠀⢠
⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎
⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⢶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡀⠀⠈⠉⠙⠓⠒⠒⠒⠒⠒⠒⠛⠉⠉⠀⠀⣨⠇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣙⣓⣒⣶⣤⣤⣤⣤⣤⣤⣤⣴⣖⣒⣛⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣄⣀⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠶⠛⠛⠛⠋⣉⣍⣀⡀⠀⠀⠈⢠⣈⠑⠌⠙⢷⠶⠦⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣠⡾⢋⠤⣢⣶⠶⠚⠛⠋⠉⠁⠂⠀⠀⠀⠀⠁⠀⠙⠲⢞⠀⠀⣄⠀⠙⣷⣄
⠀⠀⠀⠀⢠⡾⠟⢹⠀⢩⠘⠁⡀⠒⠋⢉⣉⣭⢗⡄⠀⠀⠀⠠⢦⠾⠞⠀⠀⠀⠄⠀⠹⡇⢈⡟⣷⣄
⠀⠀⠀⢀⣿⠀⠀⠸⡄⠸⣍⠀⠉⠈⢒⣒⠒⢲⠍⠊⢀⡀⠐⠢⡄⠀⢤⣀⣰⣶⠆⣠⠜⡣⢞⠴⡱⣹⡄
⠀⠀⠀⠘⣿⢤⠀⠀⡀⠀⠀⠑⠺⢷⣄⣀⡁⠀⠀⠀⠈⠉⠀⠚⠁⠀⢀⣀⣀⣠⣽⠒⠉⣀⠴⣊⣴⣿⠁
⠀⠀⠀⠀⠙⢿⣆⠀⡈⢦⡈⠢⣈⠢⡀⠀⠈⠉⠛⠛⠛⠓⠋⢍⣉⣛⣉⢉⣀⣀⣒⣪⠭⢖⣋⣵⡾⠁
⠀⠀⠀⠀⠀⠀⠻⣦⣈⢦⡉⠳⣌⡳⢬⡂⠀⠂⠐⠢⢤⣀⡀⠀⠈⠉⠭⠭⣭⠤⠶⢒⣻⣽⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⠲⢬⣭⣶⢭⣝⣲⣬⣝⣒⣲⠮⠤⠴⣶⣒⠶⠛⠛⣉⣉⡿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡹⣗⠲⡦⢤⣤⣀⣀⣍⣁⣀⣉⣩⣭⣭⣥⠤⡴⠒⡻⢉⠌⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡍⡄⢹⡄⣇⣀⢹⠉⠉⠁⡃⢀⡏⢠⠇⢰⠀⡰⢁⢊⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡌⡆⢣⠘⡰⠸⠀⠀⢀⠃⢴⠃⡼⢠⠇⡰⢁⢢⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠸⠘⡄⢷⠀⣇⠀⢴⠀⢨⢠⠃⡞⢠⠃⢆⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣬⣼⣆⣧⡂⢸⠄⣋⣸⣰⣁⣾⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⡿⠟⠛⠛⠛⠿⢿⣷⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣷⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢿⣷⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠙⠻⠿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⠿⠛⠋⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠉⠙⠻⠿⣿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⠿⠛⠋⠁⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣶⣦⣤⣤⣤⣴⣾⣿⠿⠛⠋⠁⠀⠀⠀⠀⢀⣤⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿
⠀⠀⠀⠀⢠⣶⣿⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⣄⡀
⠀⠀⠀⣰⣿⠟⠁⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⠿⢿⣷⣄⡀
⠀⠀⠀⣿⡿⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⠀⠀⠙⢿⣿⣆
⠀⠀⠀⣿⣧⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠹⣿⣇
⠀⠀⠀⠹⣿⣦⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⢸⣿⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠙⢿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣷⣄⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⢀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣶⣶⣾⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣃⠀⠀⠀⠀⠈⠉⡉⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⣤⣴⣶⣶⣾⣭⣉⠂⢈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡾⠀⠀⠀⠀⠀⠀⠀⡼⢳⣿⠋⢙⣿⣿⣿⣿⣿⠟⢻⣦⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢾⠀⠀⠀⠀⠀⠀⣀⣠⠃⣿⣿⠀⢸⣿⣿⣿⣿⣿⣇⣸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⠀⠘⢧⠀⠀⠀⡼⢿⢻⣿⡇⣿⣿⠀⢸⣿⣿⣿⣿⣿⡟⢹⣿⡇⣿⠋⠓⢷⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢩⡿⠷⠾⠗⠀⠀⠃⠈⢸⣿⡇⢿⣿⣀⣼⣿⣿⣿⣿⣿⣷⣾⣿⠱⣿⣄⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⢰⡇⠀⢰⢢⣠⣾⡟⠛⢀⡹⢿⣿⣿⣿⣿⣿⣿⠿⠛⣡⡶⠻⢿⣷⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣼⡇⠀⣸⣾⣿⢏⣰⣧⣀⠑⠦⣠⣤⡉⠀⣀⡤⠔⠚⠁⢠⠾⠢⠄⣙⠻⠿⢦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⣿⡇⢠⣍⣛⣡⡾⠹⣇⣹⡿⠒⠤⢼⣷⣾⣋⣠⣤⣴⠊⢰⠀⠀⠀⠀⠑⠀⠚⠛⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠈⣻⣿⠉⠉⠉⠉⠀⠀⠍⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠃⠀⠀⣠⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⢸⠀⠀⠘⣷⡄⠀⠀⠀⠀⠹⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠛⣀⢠⣾⣟⣿⠇⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣠⣤⠄⢤⣀⡤⠄⣀⠀⠀⠈⠀⠀⢀⡿⠇⠀⠀⠀⠀⠀⢌⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣾⡟⢀⡀⡀⠀⢠⣰⣿⠁⢄⠀⠀⡇⢀⠀⡶⠤⢶⠀⢸⠀⠀⠀⠀⠀⠈⣿⣦⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⢠⡾⢿⢿⡷⠞⢻⣿⡀⢻⠃⠠⡇⠨⠀⣟⡛⢳⠀⠰⠀⢴⣦⠀⣠⣸⣇⡿⠙⣶⠰⠶⢦⡶⠿⢷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢘⡁⠀⢰⡟⠁⢸⠀⢀⡇⠴⢀⣏⣉⣻⠀⢀⠁⠀⠀⠀⢀⣹⡇⣸⣾⣝⠛⠲⢶⣄⣀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢸⣧⠀⠀⠀⠀⠙⢦⣤⣿⣭⣏⣀⣤⠄⠀⠀⠀⠀⢸⣷⡟⠀⠈⠀⠀⠀⠉⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠐⣿⡿⠀⣄⡀⠀⠀⢸⡠⠀⠈⠋⠀⠀⠀⠀⡄⠀⣀⣼⡿⠃⠀⠀⢀⡀⢀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣼⡏⣿⠀⠀⣸⡇⠀⠀⠀⠀⠀⠒⠛⣧⣤⠾⠿⢆⣠⠀⣄⠀⣽⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣛⣿⣷⣷⣶⠞⣳⣶⣶⣦⣴⣦⣀⣠⣆⢁⣠⣤⠀⠈⢻⣷⡄⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣛⣿⣿⣿⣿⣋⣹⣷⣾⠛⠛⢿⣿⣿⡿⣴⣷⡏⠉⠉⢀⠰⠄⢙⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣻⣿⣿⡾⢿⣿⣿⣿⡟⠙⠀⠉⠀⠀⠸⣿⣿⣦⣁⣤⣤⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢹⣍⠻⣬⣉⠋⠘⠀⠀⠀⠀⠀⢀⡿⠉⠉⠛⣹⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠁⠀⠀⠙⠶⣤⠇⠀⠀⠀⠀⣿⠀⢀⡶⣿⡄⢴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠈⠰⢧⣀⣀⡼⢧⣴⠋⠀⠈⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⢀⣠⡟⠉⢻⡟⠃⠀⠀⠈⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠀⠀⠀⠀⠀⣿⠁⠀⠀⠈⠙⠀⠀⠀⠀⠈⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠄⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⡄⠀⠀⠀⠀⡀⠒⠀⠀⠀⠀⠀⢠⠓⠂⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠘⢂⣀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡜⢠⠏⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠛⠀⡏⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠰⣤⡤⠈⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠘⠀⠀⢀⠼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠎⠀⠀⠀⠀⠀⠀⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡦⠀⠀⠰⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢷⣿⣿⣿⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣷⣾⣿⡿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠶⠿⠗⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⠈⠿⣿⡷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⠀⠀⢀⣀⢳⣤⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡘⠟⠣⠄⠀⠤⠘⠛⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣄⠉⠀⠀⠁⢠⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⣧⣄⠀⠀⠚⡃⢀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠦⠤⠤⠤⠶⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⣀⣀⣀⡀⠀⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠉⠉⠉⠙⠻⣷⣦⡀⠀⠀⠐⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠠⡶⠮⣾⣟⢂⡀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢹⣧⡀⠀⠀⠀⠀⢤⣤⢠⣿⣿⣯⢾⣭⣽⣦⡀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠀⠙⠿⢶⣷⣦⣷⣷⣾⣿⡿⠟⠁⠘⣷⣎⠻⣜⡄⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠈⠀⠀⠀⣿⣶⢩⣿⢧⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⢏⡌⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠹⣽⣟⠙⣷⢤⣀⣀⠀⠀⠀⣀⣀⣠⣴⣿⣿⣿⡿⣻⠋⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠈⠳⣅⡂⠈⠙⣛⢿⣻⣟⣿⣿⡿⠿⢿⣿⣛⡯⠃⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠈⠙⠒⠶⠾⠭⢭⡭⠖⠛⠛⠋⠉⠁⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠓⠒⠚⠛⠚⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⠿⠟⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠻⠿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠘⠿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⠃⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠈⠙⠿⢷⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⡾⠿⠋⠁⠀⠀⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠀⠀⣀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⣷⣶⣶⣶⣶⣶⣶⡶⠿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣦⣀
⠀⠀⠀⠀⣠⣾⠟⠋⢰⣿⢿⣷⣾⠿⣿⡄⠀⠀⠀⣀⡀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣴⡿⠿⣷⣼⣿⣿⡆⠙⠻⣷⣄
⠀⠀⢠⣾⠟⠁⠀⢀⣿⡏⠀⠉⠁⠀⢿⣇⠀⣠⣿⠿⣿⡀⠀⠀⣾⡟⠻⣷⣄⠀⣰⣿⠋⢹⣷⡀⢀⣾⡟⢿⣇⠀⠀⢸⣿⠀⠀⠙⠛⠁⢹⣿⡀⠀⠈⠻⣷⡄
⠀⢠⣿⠋⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠈⠿⡿⠟⠁⠀⣿⡇⠀⢀⣿⠇⠀⠈⠛⠿⠛⠁⠀⠀⠻⠿⠿⠋⠀⢸⣿⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠙⣿⡄
⠀⣾⡏⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣤⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣴⡿⠃⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢹⣷
⠀⣿⡇⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⢸⣿
⠀⠸⣿⡄⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠹⣿⣄⠀⠀⠀⠀⠈⠙⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠋⠀⠀⠀⠀⠀⣠⣿⠏
⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠈⠙⠿⢷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⠿⠋⠁⠀⠀⠀⠀⢀⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠈⠛⢿⣶⣤⣀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣷⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⣀⣤⣶⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣶⣶⣦⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣴⣶⣶⠿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠁

⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢀⠀⣀⡀⠀⢀⠀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⠀⣴⣾⣷⣦⠀⠀⠀⡟⡟⡇⠀⠀⠿⢾⠾⢟⠗⠿⡶⠺⢻⠅⠀⣴⡾⣿⣿⠿⠿⠿⠿⠿⣿⣿⣷⣶⡄⠀⠠⠐⣨⣤⣦⡼⡤⣍⠓⠢
⠀⠀⣾⣿⣿⣿⣿⣷⡀⠀⡇⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠒⠁⢸⣿⣇⡇⡇⣿⠀⠑⠊
⠀⠀⣿⢻⠛⡟⡿⣻⠀⠀⢷⣿⠃⠀⣰⣦⣤⣤⣤⣤⣴⣤⣤⣤⣀⡀⠀⠤⠶⠿⠿⠛⠻⠿⢿⠆⠀⣀⡏⢙⣀⠀⠀⢸⣿⡇⡇⡇⡟
⠀⠀⠘⡄⠀⣇⠃⠎⠀⠀⢸⡿⠀⠀⠀⠙⠋⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⢀⣠⢀⣤⠀⣀⡀⠀⠀⣾⣿⣿⣿⣿⣷⠀⠘⠉⠇⠇⠇⠃
⠀⠀⠀⠁⠀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⣤⠴⡄⠀⠀⣼⣿⢿⡿⣿⣿⣷⡾⠆⠈⠉⠉⠉⠉⠉
⠀⠀⣤⣴⡖⣲⠒⣒⢲⣦⣤⠀⠀⠀⠀⠀⠀⠀⢸⠉⣹⢦⠾⣴⢯⠉⣳⠈⠀⠀⠀⠀⠀⠉⠀⢀⡀⢀⣀⣀⣀⣤⣤⠀⢰⣶⣾⣶⡆
⠀⠀⠉⢹⡏⡏⣿⢹⢹⡏⠉⠀⠀⠀⠀⠀⠀⠀⣨⠖⢻⡈⠉⢁⡼⠿⢇⠀⠀⠀⠀⠀⠀⠀⢴⡾⢻⣿⡿⠟⠋⠉⢀⣠⣴⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠸⡇⡇⣿⢸⢸⠃⠀⠀⢀⣀⠀⠀⠀⠀⠙⠲⠤⠬⠟⠯⠤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠐⠿⠻⠃⠀⠀⠀⢰⣿⣿⣿⣟⣿⣻⣿⢿⣿⡆
⠀⠀⠀⠀⠇⡇⠋⢸⢸⠀⠀⢰⣿⣿⣷⠀⠀⣠⣤⣀⣤⣠⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⣴⣶⣿⡿⠿⠿⠿⠿⣿⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⣴⣶⣴⡂⠉⠈⠉⠒⢄⠀⠀⠀⣾⣷⠤⠤⠤⠤⠤⠤⠤⠆⠀⠀⡇⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠵⠒⠀⠀⠒⠎⠀⡄
⠀⠀⠀⢺⣿⣿⣿⠟⠀⠀⠀⠀⠀⢱⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣧⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠺⢿⠗⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⠀⢀⣴⣾⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠁⠀⡞⢿⠙⠋⠋⢘⠉⡏⢹⢻⠂⠀⡀
⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⡠⠊⠀⣠⣴⡶⠶⠖⠒⠒⠲⠶⣶⣤⣄⠀⠀⠀⠀⠀⠳⡈⠂⠁⠀⠘⠐⠀⠂⡼⠁⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠌⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣷
⠀⠀⠀⣠⣤⣤⣄⣀⣠⣄⣀⠀⠀⠘⣿⣿⣦⣤⣤⣤⣤⣀⣠⣤⣾⣿⡿⢀⣴⣶⠿⠿⠿⠿⠿⠿⠿⡿⢿⣶⣄⠀⠀⣀⣴⣤⣶⣤⣦⣀
⠀⠀⣰⣿⣿⣿⡟⠀⠀⠀⠀⠉⠢⡀⠈⠙⠛⠛⠿⠿⠿⠟⠛⠛⠛⠉⠀⠘⣿⣿⣶⣦⣤⣀⣀⣀⣤⣴⣶⣿⠟⠀⣾⠛⠉⠁⠀⠀⠉⠛⣷
⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠉⠋⠉⠛⠉⠉⠛⠁⢸⠃⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠹⣿⢿⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⣤⠶⠟⠛⠛⠛⠛⠛⠛⠿⢷⣦⠀⢀⣀⡤⠴⠤⠤⠤⠴⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⡠⠃⠀⢿⣄⡀⠀⢀⣤⣤⣄⠀⢀⣠⣿⠂⣾⣀⡀⢀⡀⠀⣀⣀⠀⢀⣀⣉⡷⠀⠑⠄⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⢠⠊⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠘⢿⣾⡧⡞⠙⡣⢼⡋⢣⢜⣽⠏⠀⠀⠀⠐⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⠒⠒⠋⠉⠁

⠰⠒⠒⠒⠂⠀⠖⠐⠒⠒⠒⠒⡄⢀⠄⠤⠠⠀⡀⠀⠀⠀⡀⠄⢤⠀⠐⠒⠒⠒⠀⠀⠀⡀⡀⢀⡀⢀⡀⡄⡀⠀⠀⠐⠒⠂⠒⢐⠀⡀⠀⠀⠀⠀⠠
⢰⠀⠀⡰⡂⠀⠆⠀⠀⡄⠀⠠⡇⠿⠀⢀⡀⠀⠄⢉⡆⠨⡀⠀⡰⠀⠀⠀⠀⠀⠈⠈⠻⠽⠇⠣⠧⠸⠃⠀⢇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠉⠁⠈⠉
⠠⣄⠀⣠⣂⠀⣤⢀⢠⡆⢀⠠⠁⢀⣀⣀⣀⠈⠉⠩⠀⢀⣨⣭⣤⣤⣤⣌⣁⠀⠀⠀⡀⠄⡀⠀⠀⢀⠈⢬⠉⡀⠉⢁⣀⡀⠉⠈⠀⢰⣿⣽⣿⣿⣶
⠀⣀⡀⢀⣤⣴⣶⣶⣤⣄⠀⠀⠀⣿⣿⣿⣿⣿⣆⠂⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⢠⠋⠠⣄⡈⠓⠀⣨⠑⠊⠐⠂⡄⠈⢁⠐⠉⢂⠀⢸⣿⣿⣿⣿⡗
⢈⠠⢨⣽⣿⣿⣿⣿⣿⣷⠁⠀⢀⣿⣿⣿⣿⣿⡏⠀⢸⠇⣿⠏⡿⢹⣯⠹⠇⢿⠈⠂⠤⣉⠈⠑⡮⢦⠅⠛⡄⠀⠘⠤⢀⣀⣥⠎⠀⢸⣿⣿⣿⣿⠃
⠀⢠⣁⣧⠙⠻⠿⠿⠛⢁⠣⠀⠘⠿⡿⣿⣿⣿⠃⠀⡙⢄⡀⠀⠀⠘⠃⠀⡀⠜⠁⠀⠀⠀⠉⠐⠠⠬⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠿⠿⠫⡇
⠀⠠⡀⠈⠑⠀⠀⠀⠺⠃⢀⠀⠀⠀⠀⠈⠉⠀⡰⡄⠈⠐⠀⠂⠠⡄⠀⠁⠀⢁⠄⡀⠀⠀⣀⣀⢀⣄⣀⡀⠀⠀⣀⡤⠲⠰⢙⡝⠲⡄⠀⠒⠒⠈
⠀⠀⠈⠂⠠⠀⢀⠀⠠⠔⢀⠤⠒⠉⠉⠉⠦⢰⡰⠀⠀⠀⠀⢀⣠⢣⣀⠀⠀⢜⣊⠯⠱⠄⣱⠂⠀⠀⠲⢆⠀⠇⠠⡤⠔⠈⠁⢀⠠⠀⢠⢒⡂⠲⢄
⠀⡆⡀⣀⣰⡀⠀⠀⢀⠔⠁⡤⠀⠁⡠⢐⡵⡌⢀⠉⡉⠢⡀⠃⠀⠤⢀⣃⣀⣀⣀⠀⠀⢸⠀⠀⠘⠀⠀⠀⡆⠒⠨⠥⠄⠐⠈⠀⢀⠀⢣⡀⠠⠐⠟
⠀⢀⡤⠀⠀⠀⠀⠀⡦⠨⠤⠄⠐⡉⠴⢏⠀⡇⢨⠀⠠⠀⠱⠀⢠⣾⣿⣿⠿⢿⣿⣿⡀⢸⡀⠀⠆⣐⠒⠀⡇⠀⣠⠤⢤⡀⠀⡎⡄⡛⠢⡈⠉⠁⡀
⠀⠤⣸⠀⢀⠀⠀⣴⣶⣄⠀⠀⡐⠁⠀⢀⢞⢃⠌⡆⠀⡀⠈⠀⠸⣿⣿⣿⣿⠿⠿⡫⠃⢸⡀⣈⡛⠥⠐⠀⡇⠸⠃⠐⡀⢴⠀⢁⠠⢉⢊⡛⡬⠁⣬
⠀⠀⠱⠀⠘⠀⢸⠛⠛⢋⡅⠰⠀⠀⠀⠈⢟⠹⡀⠑⢆⠠⢠⠀⠀⠁⠀⠀⠒⠒⠈⠀⠀⠀⠊⠡⠬⠈⠠⠞⠁⣀⠵⠂⠐⠋⠀⠈⠑⠎⠳⠄⠈⠥⠞
⠀⠀⣸⠀⠀⠀⠀⠁⣨⡅⠀⢠⠀⠀⠀⡀⠸⡀⢇⠈⡄⠱⢏⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣄⡀⢀⠁⠀⠈⠀⠀⠀⠀⢠⡴⢀⠀⠠⢀
⠀⠘⡍⠄⠀⠀⠰⢿⣿⣿⡆⠀⠳⣠⠔⠃⡈⢷⢘⢇⠃⢀⣿⠵⢏⣋⠉⡶⣉⠴⢏⢶⢉⠽⠏⡙⣆⣎⢸⣿⡄⠁⠒⠈⢠⡄⠀⠀⠫⢀⠂⠍⡒⠄⢵
⠀⡄⠀⠤⢠⡀⠈⠊⠀⠁⠃⡀⠀⠀⠀⠀⠈⠊⠤⠃⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢀⡳⠀⠄⠀⡇⠀⠈⠀⠂⢈⠎
⠀⠁⠀⠀⡈⢠⣦⠤⠭⠭⠴⠖⠆⠬⠥⠒⠄⡀⠀⢀⡀⢀⡙⠻⢿⣿⣿⣷⣾⣴⣿⣶⣾⣦⣿⣿⣿⡿⠟⢋⠠⠄⠒⠛⣥⡍⠁⢰⣈⠀⢤⠀⢀⠌
⠀⠀⠘⠚⢦⠚⠒⠖⠖⢐⠒⠒⠂⠒⠓⠊⣴⠧⠒⡁⠄⡌⠀⠀⣀⢀⡉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⣆⡀⠀⢀⠀⢀⡅⠀⡂⠀⠀⠃⠀⡖
⠀⠀⡠⠐⠘⡤⢀⡀⠀⠀⠀⠀⠀⢀⣠⠼⠁⠂⠀⣀⠔⢡⢖⡳⣌⡅⣷⢛⡿⠂⠀⠀⣠⣾⣿⣶⡄⠀⠀⢀⡘⣩⢈⣄⣀⠇⠀⠘⠢⠄⠀⠴⠁
⠀⠾⠀⠤⠅⠤⠠⠐⠉⠪⢈⡉⠙⠉⠐⠲⡂⠀⣉⠀⠀⠘⠤⠀⣈⠉⠉⣀⢤⠂⠀⢀⢿⡿⢻⣿⣿⠀⠀⣸⣧⣿⣿⠿⢻⠀⠀⡤⠀⠤⠀⠠⠄⠠
⠀⣠⠄⣠⡄⠀⣤⠀⢤⡄⠠⡄⢉⣁⣁⠈⠓⠎⠸⠀⠀⠰⠄⠀⠀⠀⢀⡀⢠⠀⠀⢸⠸⡇⠉⣹⡇⠀⠀⢸⡛⠉⣁⣤⡞⠀⠀⣳⠀⠒⠂⠒⠃⠘
⠀⠀⠀⠀⠀⠀⡂⠀⢸⠀⠀⠰⠈⢄⠀⠈⢙⡬⣠⠀⡀⢀⠇⠀⠀⠁⠀⠁⠀⢆⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠁⠀⠀⠈⡄⠀⠀⠀⣀⣠⣇
⠀⠚⠀⠐⠂⠀⠓⠤⡘⠂⠀⠋⠀⠀⠘⠽⣛⣖⣩⠓⢣⠙⠒⠀⠀⠀⠀⠐⠂⠈⠀⠀⠑⠒⠒⠂⠀⠀⠀⠀⡈⠍⡀⢎⡀⠀⠀⠀⢠⣴⡶⢿⣛⣩⣿
⠀⠒⡖⠒⠂⠀⠺⡐⣗⠂⠐⠐⠂⠒⠒⠆⠀⢠⣒⢺⡅⠀⢠⣊⣡⣤⣤⣉⣢⠀⠀⠀⠀⠨⠄⡀⠀⠀⠀⢀⡁⠨⣉⠊⠁⠀⠀⠀⢸⣿⣷⠿⠛⠋⠉
⠀⠀⡇⢀⣁⡈⠀⠣⡌⠢⡀⢠⠀⠀⠀⡇⢀⠜⠀⠀⠣⡀⢰⠈⠉⠉⠉⠉⠸⠀⠈⠀⢀⣠⣮⣵⣦⣄⢠⠋⠑⠄⣀⠳⠤⡀⠀⡀⢘⠉
⠀⠀⡇⠁⠘⠣⠒⠀⠚⡄⢆⢀⡀⠀⠀⡀⠀⣴⣶⣶⣦⡅⠀⠀⠂⠒⠂⠒⢻⢀⠔⢰⣿⣿⣿⠿⡟⠻⣄⠑⠢⡉⠈⢰⠀⠘⡆⠈⠛⠀⠀⠀⠐⠂
⠀⠉⠉⠉⠉⠀⠀⠀⠀⠃⠈⠏⠉⠉⠉⠀⠐⡶⣴⠀⡖⠀⠀⢣⡀⠀⢀⡠⠋⠁⢠⠚⢅⡀⠉⠁⠐⠘⣁⠜⠀⠀⠑⠺⠀⣂⡀⣀⣤⠀⠠⠶⡀⠐⢄
⠀⣠⠠⢪⡍⠲⢢⠀⢰⠢⠖⠉⠲⠒⡆⠀⢠⣤⣭⣤⣥⡆⠀⣀⣈⢉⣉⢀⣀⢀⣀⣁⣐⣒⣂⠀⠈⠁⠀⡀⣔⢢⠀⠀⠘⠁⢠⠌⠲⣵⠀⠙⠾⠉⢈
⠀⠘⠊⠂⠐⠉⠊⠀⠘⠊⠓⠀⠊⠁⠃⠀⠸⠿⠿⠿⠿⠃⠀⠮⠿⠦⠿⠦⠿⠧⠽⠧⠹⠧⠽⠀⠀⠀⠐⠐⠃⠨⠂⠀⠈⠢⠽⠄⠀⠀⠀⠐⠂⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠶⠾⢛⢹⡿⠀⢻⡿⣦⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⣀⡴⠂⣠⡟⢸⠇⠀⠘⠃⢹⣧⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡴⠞⠋⢀⡴⠋⢠⡟⠀⢠⡶⠟⠛⠛⠻⣦⣼⣏⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢀⣠⡴⠋⠁⣠⠟⠀⢠⡟⠀⠀⠀⠀⠰⣾⣯⠉⠉⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠋⠁⠀⣠⠞⠉⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠙⣷⣤⠴⠆⠀⠀⠀⣠⡾⠃⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢶⡄
⠀⠀⠀⠀⠀⠀⠀⣾⢣⣄⠀⠀⠈⠙⠶⣦⣄⣀⣛⣁⣤⣶⣀⣹⣷⣤⣀⡀⠀⠀⠀⢀⣴⠟⠁⠈⣿
⠀⠀⠀⠀⠀⠀⢰⡏⠀⠉⠛⠷⠶⣤⣤⣤⣈⣉⣉⣉⣉⠉⠉⠁⠀⠀⠉⠙⠻⣿⣛⣫⣥⡴⠟⠀⢹⡇
⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠃⠈⠛⠛⠋⠉⠉⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⣸⠇⠀⠀⣀⡀⠀⠀⠀⣠⣶⡄⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠻⣦⡀⠀⢻⡆
⠀⠀⠀⢠⡿⠀⢀⡾⠋⣷⠀⠀⢠⡟⠈⣿⠀⠀⠀⢀⣾⠋⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⣷⡀⣸⣧
⠀⠀⠀⣸⡇⣠⡾⠁⠀⠻⣦⡶⠟⠀⠀⢿⡀⠀⢀⣾⠃⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠈⠛⠋⢿⡀
⠀⠀⢀⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⣀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠘⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠟
⠀⠀⠀⠉⠙⠛⠳⠶⢶⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⠴⠶⠞⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢖⣹⡭⢦⢶⢑⡄
⠀⠀⠀⠀⠀⠀⠀⣆⣱⡄⢒⠉⣧⠵⡜⣏⣣⠘⣄
⠀⠀⠀⠀⠀⠀⢰⠻⣆⠴⡊⣣⠬⢖⠙⣉⣦⠷⡘⣆
⠀⠀⠀⠀⠀⠀⠸⢸⡟⣆⠙⣤⢷⠚⣯⡽⡞⢏⣁⠼⡆⠀⠀⠀⠀⢀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⢰⠂⠇⡏⣧⡨⢖⢫⣈⢥⠚⡏⣿⠀⠇⠀⠀⠀⣴⣑⠖⡶⣬⣉⡒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠳⡀⢃⢻⢹⠒⠃⠃⢸⠀⠇⠟⣠⠀⠀⠀⡴⢠⢏⡝⡲⢧⣜⢉⠏⠠⢉⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢌⠸⢸⠀⡆⠇⢘⡤⠶⠛⠁⠀⢀⡞⣰⠓⡼⣸⢉⠞⢤⣍⡰⠇⡜⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠼⠴⠒⠉⠁⠀⠀⠀⠀⠀⢸⢦⣉⡛⠶⢥⣟⢑⠦⣴⠉⡖⡇⡇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⢈⢹⠒⠮⣀⠋⠖⣠⢾⢡⠹⢃⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣘⠊⢸⠈⠀⠃⠙⢰⢹⢸⠘⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⡀⠇⢸⢸⠘⢈⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠾⠗⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⠀⢠⣬⣿⡟⢁⡤⠒⠂⠀⡀
⠀⠀⠀⠀⠀⣀⣠⣄⣉⡀⠄⠀⠙⠾⢿⣿⡿⠿⠲⠶⢍⣁⡉⠂
⠀⠀⠀⠀⠀⠈⠙⠉⣙⠀⢀⡠⠀⠀⢠⠁⠀⣄⠈⠲⡄⠀⠙⣷⠔
⠀⠀⠀⠀⢴⣞⠀⣀⠞⠹⠿⢧⡄⠰⡟⠀⠀⢸⣦⠀⢸⣶⡀⢸⡀⠀⡄
⠀⠀⠀⠀⢠⠟⠙⢻⣠⠀⣀⡜⠀⢀⡀⢀⣠⡌⠉⠳⣎⠈⠳⠊⢳⠄
⠀⠀⠀⣴⠾⠀⠀⣠⣿⠊⠉⠛⢀⢈⡠⠊⠀⠙⢀⣠⠏⠐⡋⠀⣾
⠀⠀⠀⠀⠀⡴⡾⠋⣉⠀⠀⢀⡞⠛⢧⡀⠀⢠⣟⠀⢀⡼⠋⠁⠿
⠀⠀⠀⠀⣀⢾⣇⠀⣠⡶⠶⣿⠄⠀⢠⢿⣾⡇⠈⢱⡟⠇⡠⢾
⠀⠀⠀⠀⠀⠈⢩⡻⣿⠀⠀⠀⣰⡖⠋⠀⠉⢰⠶⡇⠀⣠⠇⡻⠂⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢱⠘⠃⣤⠞⠉⠱⡘⠀⡠⠋⢀⡼⠒⢛⣾⠅⢀⡠⠤⠊⠀⠀⠈⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠻⠶⡤⢼⡆⠀⠀⠿⢿⣤⡤⠛⡠⠖⠛⢁⡠⠜⠀⣀⡀⠀⢀⣦⠀⠀⡀⠀⠀⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠴⠇⠀⠀⠀⠁⠀⠀⣸⠀⠀⠀⠹⢿⡆⢸⣿⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠸⠿⣶⣦⠀⡤⢤⣶⣄⠀⠤⠖⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⡀⠄⠀⠐⢤⡼⠛⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⣇⠀⠀⠰⠓⠀⠀⣶⠀⣶⡆⠘⠽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠇⠀⠙⠇⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⣰⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠧⠼⠟⠳⣤⠤⠶⠏⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠚⣩⢽⣻⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢀⢞⡵⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⢮⡞⢙⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⢄⣸⣸⣇⣿⣿⣿⣿⣿⡿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⣿⡻⢿⣿⣿⣿⣯⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⠤⣈⣑⠂⣀⣴⠞⣫⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⢍⡑⠢⠭⠭⠍⠀⣚⠥⠊⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡇⠀⠀⡝⠉⢛⣻⣷⠿⠗⠛⠛⣼⠙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡇⠀⠀⡇⠀⢸⢹⠀⠀⠀⠀⠀⣷⡀⠀⠀⠉⢲⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⡇⠀⠀⡆⡇⠀⠀⠀⣀⣸⡋⠒⠤⠤⣯⣞⢀⣽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⢱⠀⠀⢧⡷⠶⠚⠛⠉⠀⠳⡀⠀⠀⠀⠈⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣒⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣤⣽⠂⠀⠀⢀⠏⠉⠲⡄⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢟⠀⠀⠀⠘⠀⠀⠀⢣⣀⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡆⠀⠀⠀⢸⠉⠉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⠤⢼⠃⠀⠀⠀⠨⡆⠀⠘⠓⠒⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣸⢀⣀⡤⠴⠞⠓⠒⠈⠉⠉⠉⠉⠉⠉⠙⣖⠒⠒⠠⠤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣠⠔⠋⠁⠀⠀⠀⠀⢀⠤⠒⣉⣉⣉⡉⠒⢤⡀⠈⢆⠀⠀⠀⠀⠀⠈⠉⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣄⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⡴⢃⡴⠋⠁⠀⠀⠈⠑⢦⠙⢆⠈⡆⠀⠀⠀⠀⠀⠀⢀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠋⢉⣁⡤⠔⢺⠋⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⡎⠀⠀⠀⠀⠀⠀⠀⠀⢁⠘⡆⢸⠀⠀⠀⠀⢀⠔⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠓⠒⠶⣌⡉⠁⠀⠀⠀⠈⠓⢂⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡇⠘⡀⠀⠠⠐⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠘⢄⠀⠀⠀⠀⠀⠀⡠⠃⡼⠀⢀⠃⢀⡴⠋
⠀⠀⠀⠀⠀⣀⣀⣀⡤⢶⠚⣻⣉⡦⠤⠐⠒⢚⡶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢌⠙⠒⠤⠤⠒⢋⡠⠞⠁⢀⡸⠖⠉
⠀⢀⠴⠊⣉⠴⣒⠶⢷⣞⣋⣉⣠⢤⠴⠒⠋⠁⠈⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠋⠉⣀⠤⠒⠉
⡰⠃⠀⠾⢅⣤⣱⠲⢾⣇⣧⡤⠗⠰⠇⠀⠀⠀⠀⢀⠤⠜⠓⠲⠤⢬⣀⡀⣒⡀⠀⠀⠀⣀⣀⣀⡤⠤⠖⠚⠉
⠉⠑⠒⠠⠤⠔⠒⠉⠁⠀⠀⠀⠀⡜⠀⠀⠀⠀⢀⣳⣄⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠴⠒⠋⠉⣉⡡⠔⠊⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣵⣦⣶⣦⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⢎⠉⠉⠐⠂⠄⢀⠌⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⢀⠄⠈⡁⠀⠠⡂⠤⠒⠀⠠⠒⠘⠀⠴⠅⣈⠁⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⢀⣤
⠀⠀⠀⢠⠃⢸⠆⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢘⠈⢄⠢⡀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⡟⠀⠆⠀⠀⠀⠈⠀⠄⠀⠀⡃⠈⠉⢱⠀⠀⢀⡄⠀⠀⠂⢁⢘⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⢰⢠⡄⡶⡆⢲⡖⢠⠖⣦⠲⢲⢠⠶⡄
⠀⠀⡼⠀⠀⠱⠄⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠐⠢⠐⠀⠀⢀⠀⢤⠁⠈⢢⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⣸⣇⡹⡆⢸⡇⢸⠗⣿⢸⢯⢸⠁⡇⠀⠰⠶⠶
⠀⠀⣧⠀⠈⠀⢀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠡⠀⠂⠈⠀⠀⠀⠀⣠⣄⡀⠈⠛⠈⠋⠀⠛⠁⠈⠁⠘⠀⠁⠘⠈⠈⠛⠁
⠀⠀⢱⡀⡆⠀⠈⢀⠀⠀⠀⠀⠰⠀⠁⠀⠀⢀⠐⠀⠄⡀⠀⠀⠀⠖⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢻⡦⡟⡆⡟⡆⣼⠀⣼⣃
⠀⠀⠈⡁⠀⢄⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⢈⠀⠀⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢹⡇⡟⠁⣿⠁⣿⠀⣿⡁⠀⠀⠀⣠⣀
⠀⠀⠀⢇⠀⠈⡁⠀⠠⠠⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠁⠀⠀⠁⠀⠉⠀⠈⠁⠈⠉⠀⠀⠀⠈⠙
⠀⠀⠀⠈⠱⡂⠇⠀⠠⠑⠒⢃⠀⠀⠈⠀⠄⠐⠠⠀⠀⠀⡘⠒⢃⡞⠁⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠱⣄⠙⠅⡀⠀⠀⠁⢶⠀⠀⠀⠀⠀⠆⠐⡊⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠈⠓⠲⡎⠒⠢⡁⠀⠀⢁⠔⢚⠀⡴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠜⠒⠊⠃⠐⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠎⠉⠀⠁⠈⠑⠀⠠⠒⣉⡑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠁⢠⠀⠀⠈⠓⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠑⠀⡀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠈⠀⠐⣄
⠀⠀⠀⢠⠏⠀⠀⠀⠄⢀⡀⠀⠀⠀⠀⢢⠔⠂⡈⠐⠃⢀⠢⠤⣄⣀⠀⠀⠀⠀⠀⢀⠞⡁⠀⠀⠀⠀⠀⠀⠀⠤⠐⠒⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⡼
⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠀⢀⠄⠈⠁⠀⠀⠀⠀⠑⣄⠀⠀⠀⢨⡀⠀⠀⠀⠀⠀⡀⠊⠀⠀⡀⠀⠣⠔⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⣠⠃⠀⠀⠀⠀⠐⠀⠀⠀⢠⠋⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠈⠂⠀⠀⠈⢁⠀⠂⠀⠀⠄⠀⠀⠀⠀⠁⣈⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠺⠤⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠠⡆⠀⠀⠘⢦⣂⠀⢀⠁⠀⠀⠀⠀⢠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⠇⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠐
⠀⠀⢠⠿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⢲⠋⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡜
⠀⠀⠀⠓⢤⡀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣁⠀⡀⢠⠇⠀⠀⠀⠀⠀⠀⠸⣀⠀⢢⡄⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⢀⠄⠈⠀⠀⠦⣠⠞
⠀⠀⠀⠀⠀⠑⠶⡄⠀⠈⠒⠀⠂⠀⠓⠄⠀⠀⠀⠀⠂⠀⠀⡈⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢤⡁⠀⢀⡀⢀⠠⠀⠀⠒⠐⠁⠀⠄⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⢀⡔⠀⠀⠀⠀⠈⠑⠀⣠⠆⠠⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠈⢅⠐⠂⠂⠀⣠⢀⣀⡤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠒⠤⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠤⠾⠥⠔⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⠈⠉⠓⠲⡆⠀⠀⠀⠀⡠⠄⠠⠔⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⠢⢄⠙⡆⠘⢢⡾⣥⠂⠀⠀⠀⢉⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠙⠦⠒⠚⡟⠒⢿⣀⣸⠋⠢⠔⠶⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠳⠤⠞⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢀⡤⡀⠀⢠⡞⠉⡆⢀⣀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡇⠀⡞⠀⡇⠀⡼⠀⠀⠙⠊⠈⡆⢸⠁⡄⡘⠈⠇⠀⢀⡀⠀⠀⡞⣧⢹⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⣀⣇⡰⠁⢰⠄⠀⡇⠀⠀⠀⠀⠀⠃⢸⠀⠈⠁⠀⢺⠀⣿⢹⡄⠀⣳⢸⡎⡦⣄⡈⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⢀⡴⠊⠁⠈⡇⠀⣸⠀⢸⠃⠀⠀⠀⠀⢰⡄⢸⠀⠀⠀⠀⠘⠦⠟⠀⡇⠀⢹⠈⣿⠃⠀⠉⠳⣄⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⢀⡴⠁⠀⠀⠀⢸⡇⠀⣿⠀⡾⠀⠀⠀⠀⠀⠸⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⣸⠀⣿⠀⠀⠀⠀⠀⠙⢄⠀⠙⣆
⠀⠀⠀⠀⠀⠀⡸⠁⠀⢠⠏⠀⠀⠀⠀⠀⢸⠀⠀⠙⠚⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⢹⠀⠀⠀⠀⠀⠀⠈⢧⠀⠈⣆
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠞⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢣⢀⡀⠸⡄⠀⠀⠀⠀⠀⠀⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠘⢦⠳⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⠦⢤⣤⣤⣀⣀⣀⣀⣤⣤⣤⠤⠶⠖⠛⠉⠁⠀⠀⠀⠀⠀⡔⠀⠀⣠⠞⠁⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠃⠈⢀⡤⠞⠁⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠈⠙⠲⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠚⠉⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠈⠉⠓⠒⠲⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠖⠒⠚⠋⠉⠁⠀⠀⢀⡠⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠤⠴⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁




⣿⣿⡿⠻⠟⠻⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠄
⠀⠀⠀⡀⠀⡀⢠⠖⠁⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣵⡤⢤⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣢⡀
⠀⠀⠘⠉⣸⠓⡟⣧⠀⠀⣱⣥⡶⠆⠀⠀⠀⢠⡄⢇⣀⣀⡈⣿⠏⢀⡾⣧⢀⠀⠀⢀⠤⠴⠂⢸⠡⠾⠏⣹⢆⠐
⠀⠀⠘⠀⠉⠀⠧⡿⠂⠈⡝⢙⡀⠀⠀⠀⠀⠙⠛⠛⡛⠛⠘⠛⢓⣾⡽⠃⡁⠀⠀⠀⠲⠅⣆⢸⣧⠀⣶⢧⡼⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠙⢲⣂⣁⣀⣀⣴⢫⡿⡅⠀⠀⠀⠀⠀⠀⠀⠟⠚⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⢀⣤⣦⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠁⠈⠉⣫⢾⢣⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⢀⡔⠉⠀⠈⢣⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢤⢀⣀⡄
⠀⠀⣠⠾⢋⠢⣴⠾⢛⣾⠃⠀⠀⠀⠤⠄⢠⡶⠂⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⣠⠀⠀⠀⠀⠀⠀⠀⣀⣤⢽⢏⡰⠄
⠀⢰⣧⠀⠀⣰⣥⣾⣛⠟⠁⠀⠘⠀⠀⠀⠸⡦⣦⡀⠀⠀⠀⣤⠸⢠⣆⢐⢸⣥⡀⠀⠀⠀⠱⣄⠻⠋⠀⢸⠯
⠀⠀⠹⣦⡐⠟⣫⡼⠋⠀⠀⠀⠂⣜⠃⠒⠐⢸⣧⡄⠀⠀⡐⠂⢀⢸⢈⡿⠿⠋⠳⠂⠀⠀⠀⠘⠷⡶⠞
⠀⠀⠉⠉⠈⠙⠋⠀⠀⠀⠀⠀⠀⠉⠀⠀⠤⠼⠉⠀⠀⠀⠀⠰⠬⠽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣴⣶
⠀⠀⠀⣔⣀⣉⣀⣀⣠⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣴⡾⠀⠉⠁⠤⣄⠀⠀⠀⠀⠁⠀⠀⠘⠛⠃⠖⢀⡀
⠀⠀⣤⠋⠻⠙⢿⣿⠛⠀⣧⡄⡀⠀⣀⠀⠀⢠⡖⠩⠉⠉⠉⡇⠀⠀⠀⢰⠉⠀⠀⠀⠀⠀⠁⣤⣤⣜⣱⡾⢹⣷⢀
⠀⠀⠀⠁⠀⠄⠨⠷⢴⠚⠁⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠔⣿⣶⣂⡴⠛⠐⠀⠀⠀⠀⠀⠇⠈⠁⠈⢿⣦⠞⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠄⠶⣯⠙⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⠒⢠⠠⡄⠨⠖⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢂⠐⠠⠀⡇⠠⠔⠲⠤⣀
⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠁⠐⠀⠂⠀⠀⡀⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠐
⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠒⠀⠂⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠀⠂⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠠⠄⡄⠨⠤⠠⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡀⠀⢠⠄⡇⠰⠄⠠⢤⡀
⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⡈⠁⢀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠶⠇⠀⠀⠀⠀⠀⠠⠀⠃⠀⠀⠈⠁⡀
⠀⠀⠀⠀⠐⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠃⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠂⢠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠄
⠀⠀⠀⠀⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁
⠀⠀⠀⠀⠀⠀⠈⠐⡀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢆⠀⠀⡀⠀⠀⠀⡀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠐⠂⠀⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠂⠀⠒⠊

⣶⠶⢶⢷⣷⠾⣶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⠶⡶⢶⣶⡶⢶⡶

⠀⠀⠀⠀⠀⠀⢠⡄⢠⠀⢠⠀⣤⠀⣤⠀⣤⠀⣄⠀⡀⠀⡀⠀⡀⠀⡀⠀⡀⠀⡀⠀⡀⢠⡀⢠⡀⣀
⠀⠀⠀⠀⠀⠀⠸⠂⠺⠀⠻⠀⠿⠀⠿⠀⠿⠀⠿⠀⠟⠀⠗⠀⠗⠐⠗⠘⠇⠐⠇⠐⠇⠘⠃⠘⠃⠘⠃




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀⢦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⢀⣀⣀⠀⠀⠀⢀⣠⣴⡶⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠚⠭⠍⠹⠿⣷⠀⠚⠛⠥⠉⠀⠀⠀⠩⢅⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣉⠀⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⡄⡀⠀⠀⠀⢠⡞⠀⠀⠲⠄⠀⠀⠀⠀⢸⣧⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⡁⠠⠀⣴⢟⠻⣷⡾⢃⣀⠙⠀⠀⠀⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣷⡀⢀⡀⠈⠩⣥⣬⠥⠀⠀⡀⢀⣼⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣦⡀⠀⠀⠀⣠⣴⣴⣿⡿⠛⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⢠⣠⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⣿⡿⠛⣿⣿⣿⣿⣿⣿⣻⣿⣿⣞⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠟⠛⢿⣿⠛⣿⠜⣿⣷⣿⠋⣀⣿⡿⣿⣿⣿⠏⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠛⣻⠟⠑⣛⣿⣿⢥⣿⡿⣇⣤⡿⢓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠐⠛⠙⠋⠛⣹⢿⡿⢋⡾⠋



⠀⠀⠀⠀⠀⠀⠄⢀⣀⣀⣙⣛⣛⣻⣿⣿⣿⣿⣍⠉⢀⡀⠀⣉⣉⣉⣿⣿⣛⣿⣿⣀⣀⣀⣀⣤⣤⣤⣴⠆
⠀⠀⠀⠀⠀⠀⠠⢤⣄⣤⣤⣬⣽⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠂⠀⢄⣂⣠⣼⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⢤⠄⢠⣀⠀⠴⠦⠀⠀⣷⠠⣠⠶⠟⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⢀⣴⡆⠀⣠⡶⠂⠉⠂⢀⣀⣀⣀⣺⡞⠋
⠀⠀⠀⠀⠀⠀⠀⠰⣦⠠⢛⠟⠉⠈⠉⠛⠂⠀⠀⠴⣿⣿⣟⣻⣤⠁⠐⢄
⠀⠀⠀⠀⠀⠀⢠⠎⠀⢀⣼⣄⢀⣤⠗⠀⠀⠛⣻⠿⣏⠉⢹⡆⢛⣶⡿⡏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢰⢃⣄⣰⣿⠃⠀⠀⣴⡆⣀⣐⠛⠁⠂⣼⡷⠜⣿⠆⣿⣟⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡄⣴⣾⢿⡆
⠀⠀⠀⠀⠀⠘⢼⠟⠁⣹⣄⣰⡞⢀⣤⣼⡃⣰⡗⣐⣿⣧⡴⣷⣾⡿⠿⠿⠷⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣸⣿⣿⣿⠃⣿⠅
⠀⠀⠀⠀⠀⠀⠈⡄⠀⢺⣿⠏⢐⣲⣾⠿⣽⢿⣶⣿⣮⣿⡿⠟⠛⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢿⣿⣏⠋⢴⡗
⠀⠀⠀⠀⠀⢸⠀⣷⣎⠻⠿⣴⡽⠟⢽⣿⣯⣼⣿⣿⡿⠉⠀⠀⠀⢀⡎⠀⠀⣀⣤⣶⠿⠖⠀⠠⡈⠃⠀⢠⣸⣿⡟⣠⡢⠁
⠀⠀⠀⠀⠀⠘⣄⡻⠟⢵⣿⢿⠃⣤⣽⣿⣱⣿⣿⡟⠃⢠⡎⠀⠀⠀⠀⣳⡟⠉⠉⠉⠀⠀⠀⠀⠀⢂⠀⢸⡿⠁⣌⠔⠁
⠀⠀⠀⠀⠀⠀⠈⢻⠀⣾⠃⢶⠠⣿⣿⣿⣼⣿⠋⠀⠐⣏⠀⠀⢀⣀⣼⣿⣦⣀⡀⠀⠀⢀⣀⣳⣄⣤⣶⣿⣷⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢦⣙⡀⢸⣄⣸⣿⣿⣿⣧⠀⢀⣿⡿⠒⠀⢈⣉⡛⠉⠀⣀⣄⡤⠖⠂⢀⣭⣛⣻⣿⡋⢠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣶⣧⣻⣿⣷⣿⡿⠃⣠⠀⠀⢀⣠⡿⠿⢇⠀⠺⠿⠋⠀⠀⠰⣿⣿⡿⣿⢿⣇⠈⢻⣿⣵
⠀⠀⠀⠀⠀⠀⠰⠾⣿⣶⣾⣿⣛⡛⠻⠋⡉⠀⣴⠿⢤⡀⠉⠀⠀⢀⠃⢠⣾⠀⠀⠀⠀⠰⠛⠛⣷⣿⠈⢀⣿⣷⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⢨⠻⠀⠈⢧⠀⠐⢂⣾⡄⢠⣿⣿⣶⡆⠀⠀⠀⠠⣽⣏⣼⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⣠⡄⠀⠀⢠⣿⣿⡿⠁⢀⣿⣇⠀⠀⡀⣼⠛⠋⣡⡿⢻⡿⢹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣸⣷⣀⣈⣿⡿⣿⣷⡀⠀⢹⠿⢋⣼⣿⡿⢿⣿⠛⣳⣾⣥⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠸⢿⡟⠉⠉⠀⢘⣿⣿⡿⠛⠀⠰⢻⣿⣿⣿⣾⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢤⣥⣀⠀⠀⢩⣿⢿⣶⡞⣂⣴⠿⣿⣽⣿⣿⣿⣟⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣈⣧⣜⣿⣿⡿⢿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢬⣛⠿⣿⣷⣿⣛⣋⣺⣿⣿⣿⣿⣿⣿⣟⣠⣾⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣿⢿⡿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣉⣙⣛⣿⣿⡿⣿⠿⠯⠟⠛⠒


⣿⣿⡿⠻⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠒⠚⠚⠛⠓⠶⠤⣍⡓⢾⡁⠀⠀⢈⡷⠚⠉⣀⡤⠽⠷⠶⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠁⠀⢀⡤⠖⠚⠛⠛⣓⣶⡦⢭⣦⣳⣀⡤⠾⣄⣠⣾⠥⠶⠶⣖⡒⠒⠲⠤⣌⡙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⣠⠞⠉⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⡽⠁⠀⠀⠀⠉⢧⡀⠀⠀⠀⠙⠲⣄⠀⠀⠙⠲⡌⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢀⡞⠁⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠘⢦⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣰⠏⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠈⢳⡀⠻⡄
⠀⠀⠀⠀⠀⠀⣰⠃⠀⡴⠃⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠳⡄⠙⣆
⠀⠀⠀⠀⠀⢰⠇⠀⡼⠁⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠹⡄⠘⣆
⠀⠀⠀⠀⢠⡏⠀⡼⠁⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠹⡄⠘⣆
⠀⠀⠀⢀⡞⠀⡼⠁⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠹⡄⠘⣆
⠀⠀⠀⡼⠀⣼⠁⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠹⡄⠸⡆
⠀⠀⠀⢳⣴⠃⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⢻⣴⠃
⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢳
⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠸⡅⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠙⠓⠲⠶⠶⠶⠶⠒⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠒⠲⠖⠒⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⢀⣀⣠⡼⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠧⣄⣀⡀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠋⠉⠉⠀⠀⠀⠙⠲⠦⣤⣄⣀⣠⣤⠤⠶⠛⠁⠀⠀⠈⠉⠙⠛⠛⠛⠋⠉





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠄⡘⠁⣰⡄⠀⠀⠀⠸⡀⠀⠀⠀⢀⣢⣤⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠀⠄⢀⡶⠈⡠⡄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠤⢤⠶⠀⠀⠀⠀⠀⠀⠀⢠⡨⣅⠀⠀⠁⠃⠀⠀⠀⠁⠉⠁⠀⠁
⠀⠀⠀⠀⠒⠒⣒⠶⠀⠀⠉⠒⠒⠛⠷⠀⠀⢀⠐⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠘⢀
⠀⠀⠀⠞⢺⠃⠈⢈⣦⠀⠀⠀⠀⠀⡀⠀⠀⣰⣆⣈⡤⠀⠀⠀⡆⠀⠀⠀⠀⣾⠞⠃⠀⠀⠀⢀
⠀⠀⠀⠆⠄⠀⢀⠀⣿⠀⠀⠀⠀⢤⠚⢠⠀⠀⠀⠀⠀⠀⡬⣤⠙⣀⢀⠀⠀⠎⠀⠀⠀⠀⠀⠘⣀
⠀⠀⠀⠀⠀⠀⠀⢠⡋⠀⠀⠐⠆⠉⡶⠉⠐⠀⠀⠀⠀⢠⢃⡭⠁⢘⡯⣱⠂⠀⠀⠀⠀⠠⡵⠎⣥
⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⡶⠿⠿⠿⠿⠿⠿⠿⠿⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠈⠛⠿⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⡾⠟⠋⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠟⠛⠛⠋⠉⠁⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⣦⣄⡀
⠀⠀⠀⣠⣶⠿⠛⠉⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠙⠻⢷⣦⡀
⠀⣰⡿⠛⠁⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠙⠻⣷⡀
⣼⡟⠁⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠙⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⡶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿
⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠿⠿⠷⠶⠶⠶⠶⠿⠿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠉⠻⢷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⢷⣶⣦⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣶⣶⢿⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣤⣉⣉⡙⠛⠛⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠟⠛⠛⣋⣉⣡⣴⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠾⠿⠿⠟⠛⠛⠉⠁
⣿⣿⠛⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿