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⠹⣿⣿⣿⣿⣷⠆⣼⣿⣿⣿⡇⠘⡿⠁⠀⠘⡄⠀⠘⠉⠏⠉⠿⠁⡇⠀⠩⠂
⠀⢻⣿⣿⡿⠋⣰⣿⣷⣬⡹⡛⢴⠃⠀⠀⠀⣃⡀⠀⣀⠄⠐⠀⠊⠄
⠀⠀⢻⣿⣷⢡⣿⣿⣿⡿⢟⣳⣵⣾⣧⣠⣿⣿⣿⣶⣦⣀⣀⣄⡀
⠀⣦⣬⡷⡭⢾⣛⣉⢷⣾⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣟⣛⠋⢰⣶⣶
⠀⠘⢿⣍⢡⣾⡿⣵⡿⣯⣝⡻⢿⣿⡿⣻⡿⢿⡿⣛⣽⣧⢾⣮⠻⣿
⠀⠀⠈⢿⡸⡏⣾⠃⢄⡁⠙⠹⠋⠻⠛⡟⠛⡟⠻⠁⠃⣸⢤⣾⡇⠘
⠀⠀⠀⠈⢳⣕⡋⣰⣄⡌⢩⠘⡒⠂⠀⠃⠀⡓⢒⠀⡅⢠⡼⢛⣵⡿⠃
⠀⠀⠀⢀⣀⠙⣿⣷⡛⢿⢿⣶⣇⣼⣄⣦⣠⣇⣼⣶⠟⣫⣶⣿⣏⠀⠒⠦⣄⠀
⠀⢠⡾⠙⠤⣮⣝⢿⣿⣷⡑⢭⡻⠿⠿⠿⠟⡿⠟⠅⣾⣿⡿⣫⣿⢟⣶⡀
⠀⠘⠷⢶⣿⣮⡻⣷⡝⢿⡿⠆⠑⣶⣿⣿⣷⣾⣿⠷⣿⠏⠾⡿⣣⡿⣫
⠀⠀⠈⠄⠟⠻⡿⢊⠀⠈⠁⠀⠀⠙⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠑⢄⠑⠀⣡⡸⡗⠀
⡎⢸ ⠉⠐⠢⢌⠑⢄ ⡸ ⡆ ⠣⠱⡀
⡇⢸ ⣀⠗ ⠉⠉⠁ ⠙⠢⠤⡀⢃⢱
⡇⠘⣄⢀⠔⠉ ⠈⠁⠘⡄
⢇ ⠁ ⠘⡄
⢸ ⢀⣀⣀⡀ ⢀⣀⣀⡀ ⢣
⡸ ⢴⣾⡿⠿⠽⠇ ⠘⠛⠛⠛ ⠈⢄
⠰⡁ ⢠⠒⠢⡀⠈⠒⠊ ❤ ⡠⢄ ⡘
⠱⣀ ⢀⠜ ⠇ ⢀⠔⠁ ⡏
⠑⠤⢄⣀⠔⠁ ⡜ ⠊⠁ ⢀⠜
⡎⢸ ⠉⠐⠢⢌⠑⢄ ⡸ ⡆ ⠣⠱⡀
⡇⢸ ⣀⠗ ⠉⠉⠁ ⠙⠢⠤⡀⢃⢱
⡇⠘⣄⢀⠔⠉ ⠈⠁⠘⡄
⢇ ⠁ ⠘⡄
⢸ ⢀⣀⣀⡀ ⢀⣀⣀⡀ ⢣
⡸ ⢴⣾⡿⠿⠽⠇ ⠘⠛⠛⠛ ⠈⢄
⠰⡁ ⢠⠒⠢⡀⠈⠒⠊ ❤ ⡠⢄ ⡘
⠱⣀ ⢀⠜ ⠇ ⢀⠔⠁ ⡏
⠑⠤⢄⣀⠔⠁ ⡜ ⠊⠁ ⢀⠜
⡎⢸ ⠉⠐⠢⢌⠑⢄ ⡸ ⡆ ⠣⠱⡀
⡇⢸ ⣀⠗ ⠉⠉⠁ ⠙⠢⠤⡀⢃⢱
⡇⠘⣄⢀⠔⠉ ⠈⠁⠘⡄
⢇ ⠁ ⠘⡄
⢸ ⢀⣀⣀⡀ ⢀⣀⣀⡀ ⢣
⡸ ⢴⣾⡿⠿⠽⠇ ⠘⠛⠛⠛ ⠈⢄
⠰⡁ ⢠⠒⠢⡀⠈⠒⠊ ❤ ⡠⢄ ⡘
⠱⣀ ⢀⠜ ⠇ ⢀⠔⠁ ⡏
⠑⠤⢄⣀⠔⠁ ⡜ ⠊⠁ ⢀⠜
⡎⢸ ⠉⠐⠢⢌⠑⢄ ⡸ ⡆ ⠣⠱⡀
⡇⢸ ⣀⠗ ⠉⠉⠁ ⠙⠢⠤⡀⢃⢱
⡇⠘⣄⢀⠔⠉ ⠈⠁⠘⡄
⢇ ⠁ ⠘⡄
⢸ ⢀⣀⣀⡀ ⢀⣀⣀⡀ ⢣
⡸ ⢴⣾⡿⠿⠽⠇ ⠘⠛⠛⠛ ⠈⢄
⠰⡁ ⢠⠒⠢⡀⠈⠒⠊ ❤ ⡠⢄ ⡘
⠱⣀ ⢀⠜ ⠇ ⢀⠔⠁ ⡏
⠑⠤⢄⣀⠔⠁ ⡜ ⠊⠁ ⢀⠜
⡎⢸ ⠉⠐⠢⢌⠑⢄ ⡸ ⡆ ⠣⠱⡀
⡇⢸ ⣀⠗ ⠉⠉⠁ ⠙⠢⠤⡀⢃⢱
⡇⠘⣄⢀⠔⠉ ⠈⠁⠘⡄
⢇ ⠁ ⠘⡄
⢸ ⢀⣀⣀⡀ ⢀⣀⣀⡀ ⢣
⡸ ⢴⣾⡿⠿⠽⠇ ⠘⠛⠛⠛ ⠈⢄
⠰⡁ ⢠⠒⠢⡀⠈⠒⠊ ❤ ⡠⢄ ⡘
⠱⣀ ⢀⠜ ⠇ ⢀⠔⠁ ⡏
⠑⠤⢄⣀⠔⠁ ⡜ ⠊⠁ ⢀⠜
┊ ┊ ┊ ┊ ˚★⋆｡˚ ⋆🤍
┊ ┊ ┊ ⋆🤍
┊ ┊ ★⋆🤍
┊ ◦🤍
★⋆ ┊ . ˚🤍
˚★🤍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ╱|、
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ (˚ˎ 。7
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ |、˜〵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀ じしˍ,)ノ
┊ ┊ ┊ ┊ ˚★⋆｡˚ ⋆🤍
┊ ┊ ┊ ⋆🤍
┊ ┊ ★⋆🤍
┊ ◦🤍
★⋆ ┊ . ˚🤍
˚★🤍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ╱|、
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ (˚ˎ 。7
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ |、˜〵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀ じしˍ,)ノ
┊ ┊ ┊ ┊ ˚★⋆｡˚ ⋆🤍
┊ ┊ ┊ ⋆🤍
┊ ┊ ★⋆🤍
┊ ◦🤍
★⋆ ┊ . ˚🤍
˚★🤍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ╱|、
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ (˚ˎ 。7
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ |、˜〵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀ じしˍ,)ノ
┊ ┊ ┊ ┊ ˚★⋆｡˚ ⋆🤍
┊ ┊ ┊ ⋆🤍
┊ ┊ ★⋆🤍
┊ ◦🤍
★⋆ ┊ . ˚🤍
˚★🤍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ╱|、
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ (˚ˎ 。7
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ |、˜〵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀ じしˍ,)ノ
┊ ┊ ┊ ┊ ˚★⋆｡˚ ⋆🤍
┊ ┊ ┊ ⋆🤍
┊ ┊ ★⋆🤍
┊ ◦🤍
★⋆ ┊ . ˚🤍
˚★🤍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ╱|、
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ (˚ˎ 。7
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ |、˜〵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀ じしˍ,)ノ
┊ ┊ ┊ ┊ ˚★⋆｡˚ ⋆🤍
┊ ┊ ┊ ⋆🤍
┊ ┊ ★⋆🤍
┊ ◦🤍
★⋆ ┊ . ˚🤍
˚★🤍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ╱|、
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ (˚ˎ 。7
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ |、˜〵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀ じしˍ,)ノ
┊ ┊ ┊ ┊ ˚★⋆｡˚ ⋆🤍
┊ ┊ ┊ ⋆🤍
┊ ┊ ★⋆🤍
┊ ◦🤍
★⋆ ┊ . ˚🤍
˚★🤍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ╱|、
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ (˚ˎ 。7
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ |、˜〵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀ じしˍ,)ノ
⣿ ⠀⠀⠀ ⠙⢦⡀⠀⠀⣠⠞⠁ ⠀⠀⠀⢸⡇⠀⁺⊹
⢿⡄ ⠀⠀⠀⠀ ⠹⣄⡼⠁ ⠀⠀⠀⠀⠀⣼⠇
⠘⢷⣄⣀⡀⠀⠀⠀⠙⠁⠀⠀⠀⣀⣀⣴⠟
ㅤ⠀⣼⠛⠉⠉ ⠀⠀⠀⠀ ⠈⠉⠙⢻⡄
ㅤ⠘⣷ ⠀⠀⠀⠀ ⡞⣦⠀⠀⠀⠀⣰⡟
⊹⠀⠈⠻⣦⣤⡶⠋⠀⠈⠳⣦⣤⡾⠋ ⠀
⢿⣟⣿⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠉⠉⠀⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡴⠚⡙⢻⠑⢶⣄⠀⣠⠔⠊⠉⠉⠻⣷⣦⡀⢀⣴⣦⠀
⢀⠏⠀⡴⠁⢸⠀⠀⣻⣴⣧⣤⣤⡀⠀⠀⢹⣯⢿⡀⠙⠉⠀
⣾⡀⠀⣿⣄⠸⣆⣰⣿⠻⣽⢯⣟⠇⠀⠀⢸⣯⢿⡇⣠⣤⡀
⠸⣷⡀⠈⠻⠿⡻⠯⠋⠀⠀⠀⠀⠀⠀⠀⣸⣿⣻⠀⠈⠛⠁
⠀⠻⣿⣳⣄⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡳⠁⠀⠀⠀⠀
⠀⠀⠈⠙⠿⣻⣷⣦⡀⠀⠀⠀⠀⠀⣠⡿⠏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⣷⠻⣿⣆⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢹⡀⠈⠻⡶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣟⣿⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠉⠉⠀⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡴⠚⡙⢻⠑⢶⣄⠀⣠⠔⠊⠉⠉⠻⣷⣦⡀⢀⣴⣦⠀
⢀⠏⠀⡴⠁⢸⠀⠀⣻⣴⣧⣤⣤⡀⠀⠀⢹⣯⢿⡀⠙⠉⠀
⣾⡀⠀⣿⣄⠸⣆⣰⣿⠻⣽⢯⣟⠇⠀⠀⢸⣯⢿⡇⣠⣤⡀
⠸⣷⡀⠈⠻⠿⡻⠯⠋⠀⠀⠀⠀⠀⠀⠀⣸⣿⣻⠀⠈⠛⠁
⠀⠻⣿⣳⣄⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡳⠁⠀⠀⠀⠀
⠀⠀⠈⠙⠿⣻⣷⣦⡀⠀⠀⠀⠀⠀⣠⡿⠏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⣷⠻⣿⣆⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢹⡀⠈⠻⡶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣟⣿⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠉⠉⠀⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡴⠚⡙⢻⠑⢶⣄⠀⣠⠔⠊⠉⠉⠻⣷⣦⡀⢀⣴⣦⠀
⢀⠏⠀⡴⠁⢸⠀⠀⣻⣴⣧⣤⣤⡀⠀⠀⢹⣯⢿⡀⠙⠉⠀
⣾⡀⠀⣿⣄⠸⣆⣰⣿⠻⣽⢯⣟⠇⠀⠀⢸⣯⢿⡇⣠⣤⡀
⠸⣷⡀⠈⠻⠿⡻⠯⠋⠀⠀⠀⠀⠀⠀⠀⣸⣿⣻⠀⠈⠛⠁
⠀⠻⣿⣳⣄⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡳⠁⠀⠀⠀⠀
⠀⠀⠈⠙⠿⣻⣷⣦⡀⠀⠀⠀⠀⠀⣠⡿⠏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⣷⠻⣿⣆⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢹⡀⠈⠻⡶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣟⣿⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠉⠉⠀⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡴⠚⡙⢻⠑⢶⣄⠀⣠⠔⠊⠉⠉⠻⣷⣦⡀⢀⣴⣦⠀
⢀⠏⠀⡴⠁⢸⠀⠀⣻⣴⣧⣤⣤⡀⠀⠀⢹⣯⢿⡀⠙⠉⠀
⣾⡀⠀⣿⣄⠸⣆⣰⣿⠻⣽⢯⣟⠇⠀⠀⢸⣯⢿⡇⣠⣤⡀
⠸⣷⡀⠈⠻⠿⡻⠯⠋⠀⠀⠀⠀⠀⠀⠀⣸⣿⣻⠀⠈⠛⠁
⠀⠻⣿⣳⣄⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡳⠁⠀⠀⠀⠀
⠀⠀⠈⠙⠿⣻⣷⣦⡀⠀⠀⠀⠀⠀⣠⡿⠏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⣷⠻⣿⣆⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢹⡀⠈⠻⡶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣟⣿⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠉⠉⠀⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡴⠚⡙⢻⠑⢶⣄⠀⣠⠔⠊⠉⠉⠻⣷⣦⡀⢀⣴⣦⠀
⢀⠏⠀⡴⠁⢸⠀⠀⣻⣴⣧⣤⣤⡀⠀⠀⢹⣯⢿⡀⠙⠉⠀
⣾⡀⠀⣿⣄⠸⣆⣰⣿⠻⣽⢯⣟⠇⠀⠀⢸⣯⢿⡇⣠⣤⡀
⠸⣷⡀⠈⠻⠿⡻⠯⠋⠀⠀⠀⠀⠀⠀⠀⣸⣿⣻⠀⠈⠛⠁
⠀⠻⣿⣳⣄⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡳⠁⠀⠀⠀⠀
⠀⠀⠈⠙⠿⣻⣷⣦⡀⠀⠀⠀⠀⠀⣠⡿⠏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⣷⠻⣿⣆⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢹⡀⠈⠻⡶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣟⣿⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠉⠉⠀⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡴⠚⡙⢻⠑⢶⣄⠀⣠⠔⠊⠉⠉⠻⣷⣦⡀⢀⣴⣦⠀
⢀⠏⠀⡴⠁⢸⠀⠀⣻⣴⣧⣤⣤⡀⠀⠀⢹⣯⢿⡀⠙⠉⠀
⣾⡀⠀⣿⣄⠸⣆⣰⣿⠻⣽⢯⣟⠇⠀⠀⢸⣯⢿⡇⣠⣤⡀
⠸⣷⡀⠈⠻⠿⡻⠯⠋⠀⠀⠀⠀⠀⠀⠀⣸⣿⣻⠀⠈⠛⠁
⠀⠻⣿⣳⣄⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡳⠁⠀⠀⠀⠀
⠀⠀⠈⠙⠿⣻⣷⣦⡀⠀⠀⠀⠀⠀⣠⡿⠏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⣷⠻⣿⣆⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢹⡀⠈⠻⡶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⠋⢬⣔⣆⡉⡭⠀⠀⢰⡄⠀⢠⡄⠀⣄⡚⢻⢋⡵
⠀⠀⠀⠀⠀⣿⠇⠒⢺⢩⣤⣿⣥⣆⡆⢸⣷⠀⢸⣷⠀⣿⣿⣤⠘⢿
⠀⠀⠀⠀⠀⠘⠁⢰⠾⣿⣿⣿⡟⠁⣵⡇⢹⢸⣸⡇⡠⢿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠄⢰⣿⠿⣿⣿⣿⣦⣀⣿⣷⣿⣿⣿⣿⣧⠚⢻⣿⣿⣿
⣀⢠⠀⠀⠌⠀⠢⣹⣾⡿⠋⣛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿
⠈⠛⠀⠀⠀⠐⠓⡛⢃⡎⠀⠀⠶⠀⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠿⣿
⠀⢠⣔⡷⡔⢦⡙⢷⡜⣇⢀⠀⠀⢠⣾⣿⡟⠛⣿⣿⣣⣶⣿⣷⣦⣩
⠀⡽⢭⣎⣟⡡⣿⠐⠪⣾⣴⣭⣴⣿⣝⠛⠋⠘⢛⣫⣿⣿⣿⣯⡭⠭
⠀⢿⣾⣟⣻⣵⣿⣾⣦⡘⢿⣿⣿⣿⣿⣰⣶⡦⣼⣿⣿⣿⣿⣿⣶⢯
⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣆⢿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⠿⠿⠟⠋
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷
⠀⠀⠀⠀⠀⣾⣿⠋⢬⣔⣆⡉⡭⠀⠀⢰⡄⠀⢠⡄⠀⣄⡚⢻⢋⡵
⠀⠀⠀⠀⠀⣿⠇⠒⢺⢩⣤⣿⣥⣆⡆⢸⣷⠀⢸⣷⠀⣿⣿⣤⠘⢿
⠀⠀⠀⠀⠀⠘⠁⢰⠾⣿⣿⣿⡟⠁⣵⡇⢹⢸⣸⡇⡠⢿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠄⢰⣿⠿⣿⣿⣿⣦⣀⣿⣷⣿⣿⣿⣿⣧⠚⢻⣿⣿⣿
⣀⢠⠀⠀⠌⠀⠢⣹⣾⡿⠋⣛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿
⠈⠛⠀⠀⠀⠐⠓⡛⢃⡎⠀⠀⠶⠀⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠿⣿
⠀⢠⣔⡷⡔⢦⡙⢷⡜⣇⢀⠀⠀⢠⣾⣿⡟⠛⣿⣿⣣⣶⣿⣷⣦⣩
⠀⡽⢭⣎⣟⡡⣿⠐⠪⣾⣴⣭⣴⣿⣝⠛⠋⠘⢛⣫⣿⣿⣿⣯⡭⠭
⠀⢿⣾⣟⣻⣵⣿⣾⣦⡘⢿⣿⣿⣿⣿⣰⣶⡦⣼⣿⣿⣿⣿⣿⣶⢯
⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣆⢿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⠿⠿⠟⠋
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷
⠀⠀⠀⠀⠀⣾⣿⠋⢬⣔⣆⡉⡭⠀⠀⢰⡄⠀⢠⡄⠀⣄⡚⢻⢋⡵
⠀⠀⠀⠀⠀⣿⠇⠒⢺⢩⣤⣿⣥⣆⡆⢸⣷⠀⢸⣷⠀⣿⣿⣤⠘⢿
⠀⠀⠀⠀⠀⠘⠁⢰⠾⣿⣿⣿⡟⠁⣵⡇⢹⢸⣸⡇⡠⢿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠄⢰⣿⠿⣿⣿⣿⣦⣀⣿⣷⣿⣿⣿⣿⣧⠚⢻⣿⣿⣿
⣀⢠⠀⠀⠌⠀⠢⣹⣾⡿⠋⣛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿
⠈⠛⠀⠀⠀⠐⠓⡛⢃⡎⠀⠀⠶⠀⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠿⣿
⠀⢠⣔⡷⡔⢦⡙⢷⡜⣇⢀⠀⠀⢠⣾⣿⡟⠛⣿⣿⣣⣶⣿⣷⣦⣩
⠀⡽⢭⣎⣟⡡⣿⠐⠪⣾⣴⣭⣴⣿⣝⠛⠋⠘⢛⣫⣿⣿⣿⣯⡭⠭
⠀⢿⣾⣟⣻⣵⣿⣾⣦⡘⢿⣿⣿⣿⣿⣰⣶⡦⣼⣿⣿⣿⣿⣿⣶⢯
⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣆⢿⣿⣿⣿⣷⣿⣾⣿⣿⣿⣿⠿⠿⠟⠋
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷
⠀⠀
⠀⠀ ⠀⠀
⠀⠀ ⠀⠀ ⠀⠀
⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀
⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀
⠀ ⠀⠀ ⠀⠀ ⠀⠀𝓗𝓪𝓿𝓮 𝓪 𝓷𝓲𝓬𝓮 𝓭𝓪𝔂!
⠀⠀
⠀⠀ ⠀⠀
⠀⠀ ⠀⠀ ⠀⠀
⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀
⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀
⠀ ⠀⠀ ⠀⠀ ⠀⠀𝓗𝓪𝓿𝓮 𝓪 𝓷𝓲𝓬𝓮 𝓭𝓪𝔂!
⠀⠀
⠀⠀ ⠀⠀
⠀⠀ ⠀⠀ ⠀⠀
⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀
⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀
⠀ ⠀⠀ ⠀⠀ ⠀⠀𝓗𝓪𝓿𝓮 𝓪 𝓷𝓲𝓬𝓮 𝓭𝓪𝔂!
⠀⣸⡏⠀⠀⠀⠉⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⡰⠋⢙⣿⣦⡀⠀⠀⠀⠀⠀
⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣦⣮⣤⡀⣸⣿⣿⣿⣆⠀⠀⠀⠀
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⣿⢟⣫⠟⠋⠀⠀⠀⠀
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⣷⣿⡁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⣿⣧⣿⣿⣆⠙⢆⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣤⣿⣿⣿⡟⠹⣿⣿⣿⣿⣷⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⠏⢧⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⢳⡀
⠀⠀
⠀⠀ ⠀⠀
⠀⠀ ⠀⠀ ⠀⠀
⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀
⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀
⠀ ⠀⠀ ⠀⠀ ⠀⠀𝓗𝓪𝓿𝓮 𝓪 𝓷𝓲𝓬𝓮 𝓭𝓪𝔂!
⠀⠀
⠀⠀ ⠀⠀
⠀⠀ ⠀⠀ ⠀⠀
⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀
⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀
⠀ ⠀⠀ ⠀⠀ ⠀⠀𝓗𝓪𝓿𝓮 𝓪 𝓷𝓲𝓬𝓮 𝓭𝓪𝔂!
⠀⠀
⠀⠀ ⠀⠀
⠀⠀ ⠀⠀ ⠀⠀
⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀
⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀ ⠀⠀
⠀ ⠀⠀ ⠀⠀ ⠀⠀𝓗𝓪𝓿𝓮 𝓪 𝓷𝓲𝓬𝓮 𝓭𝓪𝔂!
⣿⢣⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿
⢧⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⡦⣠⡟⢿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⡟⣿⢇⠸⣿⣿⣿
⠃⠀⠀⠀⢀⡄⠀⠀⠀⣄⠀⠀⣰⡄⠀⠀⠑⡹⢦⣄⠀⠀⠉⠛
⠀⠀⠀⠀⢸⣹⡄⣧⡀⢸⠆⠀⠐⢠⠀⠀⠀⠀♡
⠀⠀⠀⠀⢘⣿⣿⣿⣧⣿⣧⣴⣄⣠⣇⡀⣦ 𝒽𝒶𝓋𝑒
⠀⠀⠀⠀⠘⣿⠟⠉⡻⣿⣿⣿⣿⣿⣿⣿⡟ 𝒶
⡄⡀⠀⠀⠀⠉⠀⢤⣄⣹⣿⣿⣿⣿⣿⣿⠃ 𝓁𝑜𝓋𝑒𝓁𝓎
⣧⣷⡠⡀⠀⢀⣄⠀⠙⢿⣿⣿⣿⣿⡿⠃⠀ 𝒹𝒶𝓎
⣿⣿⣷⣿⣦⣾⣿⡀⠀⠀⠀⠀⠀⢉⣴⣶⣤⣀♡
⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⠀⠀⣴⣿⣿⣿⣿⣿⣿⣶⡄
⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃
⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡇⠘⣿⣿⣿⣿⣿⣿⣿⡙
⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡇⠀⢹⣿⣿⣿⣿⣿⡏
⣿⢣⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿
⢧⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⡦⣠⡟⢿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⡟⣿⢇⠸⣿⣿⣿
⠃⠀⠀⠀⢀⡄⠀⠀⠀⣄⠀⠀⣰⡄⠀⠀⠑⡹⢦⣄⠀⠀⠉⠛
⠀⠀⠀⠀⢸⣹⡄⣧⡀⢸⠆⠀⠐⢠⠀⠀⠀⠀♡
⠀⠀⠀⠀⢘⣿⣿⣿⣧⣿⣧⣴⣄⣠⣇⡀⣦ 𝒽𝒶𝓋𝑒
⠀⠀⠀⠀⠘⣿⠟⠉⡻⣿⣿⣿⣿⣿⣿⣿⡟ 𝒶
⡄⡀⠀⠀⠀⠉⠀⢤⣄⣹⣿⣿⣿⣿⣿⣿⠃ 𝓁𝑜𝓋𝑒𝓁𝓎
⣧⣷⡠⡀⠀⢀⣄⠀⠙⢿⣿⣿⣿⣿⡿⠃⠀ 𝒹𝒶𝓎
⣿⣿⣷⣿⣦⣾⣿⡀⠀⠀⠀⠀⠀⢉⣴⣶⣤⣀♡
⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⠀⠀⣴⣿⣿⣿⣿⣿⣿⣶⡄
⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃
⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡇⠘⣿⣿⣿⣿⣿⣿⣿⡙
⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡇⠀⢹⣿⣿⣿⣿⣿⡏
⣿⢣⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿
⢧⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⡦⣠⡟⢿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⡟⣿⢇⠸⣿⣿⣿
⠃⠀⠀⠀⢀⡄⠀⠀⠀⣄⠀⠀⣰⡄⠀⠀⠑⡹⢦⣄⠀⠀⠉⠛
⠀⠀⠀⠀⢸⣹⡄⣧⡀⢸⠆⠀⠐⢠⠀⠀⠀⠀♡
⠀⠀⠀⠀⢘⣿⣿⣿⣧⣿⣧⣴⣄⣠⣇⡀⣦ 𝒽𝒶𝓋𝑒
⠀⠀⠀⠀⠘⣿⠟⠉⡻⣿⣿⣿⣿⣿⣿⣿⡟ 𝒶
⡄⡀⠀⠀⠀⠉⠀⢤⣄⣹⣿⣿⣿⣿⣿⣿⠃ 𝓁𝑜𝓋𝑒𝓁𝓎
⣧⣷⡠⡀⠀⢀⣄⠀⠙⢿⣿⣿⣿⣿⡿⠃⠀ 𝒹𝒶𝓎
⣿⣿⣷⣿⣦⣾⣿⡀⠀⠀⠀⠀⠀⢉⣴⣶⣤⣀♡
⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⠀⠀⣴⣿⣿⣿⣿⣿⣿⣶⡄
⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃
⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡇⠘⣿⣿⣿⣿⣿⣿⣿⡙
⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡇⠀⢹⣿⣿⣿⣿⣿⡏
⣇⠈⠙⠿⣦⣀⣀⣀⣤⡴⠶⠛⢓⡄
⠈⠛⠛⠛⢋⡿⠋⠻⣯⡑⠒⠛⠋
⠀ ⁺⠀⢠⡟⠀⠀⠀⠘⣿⣆⠀ ⁺
⠀⠀⠀⣾⡇⠀⠀⠀⠀⢸⡿ ⟡
⠀⠀⠀⣿⣷⠀⠀⠀⠀⡼⠁
⠀⠀⠀⢸⣿⡄⠀⠀⠀⢷⣄
⟡⠀⠀⢸⣿⠃⠀⠀⠀⠀⠉⠀⠀⁺
⠀⠀⠠⠞⠁
⠀⠀⠀⠀⣴⠒⠒⠮⢿⡏⠀⢀⡿⠀
⠀⠀⠀⠀⠘⢦⣀⣀⣠⢷⡒⠋⢹⡄
⠀⠀⣀⡀⠀⠀⢸⡁⣀⠖⠉⠛⠋⠀
⠀⢸⠁⠘⢦⣄⡀⠉⠁⠀⠀⠀⠀⠀
⠀⣸⣄⡀⢘⡿⠛⠋⠉⣷⠀⠀⠀⠀
⠰⣇⣀⣩⡟⠠⢤⣤⠴⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠹⣄⣠⠃⠀
⠀⠀⠀⠀⣴⠒⠒⠮⢿⡏⠀⢀⡿⠀
⠀⠀⠀⠀⠘⢦⣀⣀⣠⢷⡒⠋⢹⡄
⠀⠀⣀⡀⠀⠀⢸⡁⣀⠖⠉⠛⠋⠀
⠀⢸⠁⠘⢦⣄⡀⠉⠁⠀⠀⠀⠀⠀
⠀⣸⣄⡀⢘⡿⠛⠋⠉⣷⠀⠀⠀⠀
⠰⣇⣀⣩⡟⠠⢤⣤⠴⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠹⣄⣠⠃⠀
⠀⠀⠀⠀⣴⠒⠒⠮⢿⡏⠀⢀⡿⠀
⠀⠀⠀⠀⠘⢦⣀⣀⣠⢷⡒⠋⢹⡄
⠀⠀⣀⡀⠀⠀⢸⡁⣀⠖⠉⠛⠋⠀
⠀⢸⠁⠘⢦⣄⡀⠉⠁⠀⠀⠀⠀⠀
⠀⣸⣄⡀⢘⡿⠛⠋⠉⣷⠀⠀⠀⠀
⠰⣇⣀⣩⡟⠠⢤⣤⠴⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠹⣄⣠⠃⠀
⠀⠀⠈⠀⠀⠁⠒⠠⢀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠈⠀⠀⢰⠀⠀
⠀⠀⠀⠇⠀⠀⠀⠀⠀⣈⣲⣤⣦⣧⣦⣴⠁⠀⠀⠀⠀⠀⠈⠀⠀
⠀⠀⠀⢀⠀⠀⠀⢠⣴⣿⡿⠏⠿⠿⠿⢿⢻⣧⣄⠀⠀⠀⡆⠀⠀
⠀⠀⠀⠘⠀⡀⠀⠰⠟⠁⠀⡴⢿⣿⢷⠀⠀⠙⠷⠀⢠⠐⠀⠀⠀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⣀⡑⠺⠿⢊⣀⣀⠀⠀⠀⠀⡄⠀
⠀⠀⠀⠀⠀⡀⠀⢀⣮⠙⢻⣿⣿⣾⣿⡟⠋⢷⡄⠀⠀⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠑⢀⣸⣿⣤⣾⣿⣏⣽⣿⣷⣤⣾⣇⣀⠈
⠀⠀⠈⠀⠀⠁⠒⠠⢀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠈⠀⠀⢰⠀⠀
⠀⠀⠀⠇⠀⠀⠀⠀⠀⣈⣲⣤⣦⣧⣦⣴⠁⠀⠀⠀⠀⠀⠈⠀⠀
⠀⠀⠀⢀⠀⠀⠀⢠⣴⣿⡿⠏⠿⠿⠿⢿⢻⣧⣄⠀⠀⠀⡆⠀⠀
⠀⠀⠀⠘⠀⡀⠀⠰⠟⠁⠀⡴⢿⣿⢷⠀⠀⠙⠷⠀⢠⠐⠀⠀⠀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⣀⡑⠺⠿⢊⣀⣀⠀⠀⠀⠀⡄⠀
⠀⠀⠀⠀⠀⡀⠀⢀⣮⠙⢻⣿⣿⣾⣿⡟⠋⢷⡄⠀⠀⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠑⢀⣸⣿⣤⣾⣿⣏⣽⣿⣷⣤⣾⣇⣀⠈
⠀⠀⠈⠀⠀⠁⠒⠠⢀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠈⠀⠀⢰⠀⠀
⠀⠀⠀⠇⠀⠀⠀⠀⠀⣈⣲⣤⣦⣧⣦⣴⠁⠀⠀⠀⠀⠀⠈⠀⠀
⠀⠀⠀⢀⠀⠀⠀⢠⣴⣿⡿⠏⠿⠿⠿⢿⢻⣧⣄⠀⠀⠀⡆⠀⠀
⠀⠀⠀⠘⠀⡀⠀⠰⠟⠁⠀⡴⢿⣿⢷⠀⠀⠙⠷⠀⢠⠐⠀⠀⠀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⣀⡑⠺⠿⢊⣀⣀⠀⠀⠀⠀⡄⠀
⠀⠀⠀⠀⠀⡀⠀⢀⣮⠙⢻⣿⣿⣾⣿⡟⠋⢷⡄⠀⠀⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠑⢀⣸⣿⣤⣾⣿⣏⣽⣿⣷⣤⣾⣇⣀⠈
⣿ ⠀⠀⠀ ⠙⢦⡀⠀⠀⣠⠞⠁ ⠀⠀⠀⢸⡇⠀⁺⊹
⢿⡄ ⠀⠀⠀⠀ ⠹⣄⡼⠁ ⠀⠀⠀⠀⠀⣼⠇
⠘⢷⣄⣀⡀⠀⠀⠀⠙⠁⠀⠀⠀⣀⣀⣴⠟
ㅤ⠀⣼⠛⠉⠉ ⠀⠀⠀⠀ ⠈⠉⠙⢻⡄
ㅤ⠘⣷ ⠀⠀⠀⠀ ⡞⣦⠀⠀⠀⠀⣰⡟
⊹⠀⠈⠻⣦⣤⡶⠋⠀⠈⠳⣦⣤⡾⠋ ⠀
⢿⣿⣿⣷⣿⣿⣿⡆
⠈⠻⣿⣿⣿⠿⠛⠁
⠀⠀ ⠙⠟⠁
⢿⣿⣿⣷⣿⣿⣿⡆
⠈⠻⣿⣿⣿⠿⠛⠁
⠀⠀ ⠙⠟⠁