⠀⠀⠀私⠀の⠀⠀⠀⠀⠀⠀死⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀な⠀⠀⠀⠀⠀⠀そ⠀⠀⠀⠀⠀ど⠀⠀⠀
⠀⠀⠀た⠀一⠀⠀⠀⠀⠀⠀と⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀た⠀⠀⠀⠀⠀⠀の⠀⠀⠀⠀⠀こ
⠀⠀⠀ち⠀変⠀⠀⠀⠀⠀⠀隣⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠄⢰⡆⠄⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀は⠀⠀⠀⠀⠀⠀価⠀⠀⠀⠀⠀に
⠀⠀⠀は⠀し⠀⠀⠀⠀⠀⠀り⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀私⠀⠀⠀⠀⠀⠀値⠀⠀⠀⠀⠀も
⠀⠀⠀ま⠀か⠀⠀⠀⠀⠀⠀合⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡇⢸⡇⢸⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⠀⠀⠀⠀の⠀⠀⠀⠀⠀⠀は⠀⠀⠀⠀⠀行
⠀⠀⠀だ⠀見⠀⠀⠀⠀⠀⠀わ⠀⠀⠀⠀⠀⠀⣿⣿⡿⠃⠄⠉⠛⠛⠛⠛⠃⠸⠇⠘⠛⠛⠛⠛⠉⠄⠘⢿⣿⣿⠀⠀⠀⠀猛⠀⠀⠀⠀⠀⠀な⠀⠀⠀⠀⠀け
⠀⠀⠀天⠀て⠀⠀⠀⠀⠀⠀せ⠀⠀⠀⠀⠀⠀⣿⣦⣄⠄⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠄⣠⣴⣿⠀⠀⠀⠀毒⠀⠀⠀⠀⠀⠀い⠀⠀⠀⠀⠀な
⠀⠀⠀国⠀い⠀⠀⠀⠀⠀⠀。⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⣠⣶⣿⣿⣿⣿⡇⢸⡇⢸⣿⣿⣿⣿⣶⣄⣰⣿⣿⣿⠀⠀⠀⠀だ⠀⠀⠀⠀⠀⠀。⠀⠀⠀⠀⠀い
⠀⠀⠀⠀⠀ な⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⭒⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀。⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀。
⠀⠀⠀⠀⠀ い⠀⠀⠀⠀⭑⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⊹
⠀⠀⠀⠀⠀ 。⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⭑⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⭑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀☾⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀✧⠀
⭒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⭑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⭑⠀⠀⠀⠀⠀⊹⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⊹⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⭑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠄⠘⠃⠄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀𖦹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⭒⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⭒⠀
⠀⠀⠀⠀⠀⠀⭑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⭒⠀⠀⠀⠀⠀⠀⠀⭑⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

ᅟᅟᅟ⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣿⣿⣿⣾⣿⣷⣾⣾⣿⣿⣿⣿⣿⣿⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⣤⣤⣤⣤⣼⣿⣧⣤⣤⣤⣤⣤⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠀⠀⠀⠀⠉⠛⠙⠋⢻⣿⡟⠋⠛⠙⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠀⠀⠀⠀⠀⣿⣦⣴⣼⣦⣼⣿⣷⣦⣶⣤⣤⣶⡄⠀
⠀⠀⠀⠀⠀⠀⣴⣤⣀⣀⣀⣀⣀⣀⣸⣿⣧⣀⣀⣄⣀⣀⣀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⣿⡿⠀⠀⠀⠀⠀⣿⣯⠉⠉⠉⢹⣿⡏⠉⠉⠉⢹⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠿⠿⠛⠛⠻⠛⠟⠛⣿⣿⣿⡟⠛⠛⠛⠛⠛⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿⡀⣀⣀⣸⣿⣇⣀⡀⣀⣸⣿⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⡿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⠀⠀⠀⠀⠀⠿⠿⠟⢿⣿⠿⠻⠟⠟⠻⠿⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠃⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⠟⠁⠀⠀⠈⢻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣾⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣄⣠⣶⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣦⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣀⣀⣤⣶⣿⠟⠻⢿⣷⣶⣤⣄⣀⣀⣀⠀
⠀⠀⠀⠀⠀⠀⠙⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⢻⠟⠛⠉⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠟⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢰⣠⢀⠀⠀⣰⣇⣀⣀⣀⣀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣄⣀⣤⡄⠀⠞⢿⣿⣷⢿⠋⠉⠉⢉⡍⠉⣩⢋⣴⡖⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣠⡿⣿⣿⠉⠁⠙⣶⣤⣾⣿⣿⣿⣦⣭⣭⣿⣤⣾⣵⣿⡟⠀⠀⠈⠻⣶⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⣠⡶⠛⣏⠀⠸⡿⣷⣤⣤⣾⣿⣿⣿⣿⣭⣭⣭⣭⣭⣽⣿⣿⣿⣷⣴⣧⣀⠀⠈⠻⣦⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⢹⣾⡻⣦⣀⣘⣷⣤⣿⣿⣿⢿⣿⣿⠟⢋⣽⣿⡿⠟⠛⠛⠿⢿⣿⣿⣿⣿⣯⣶⣾⣤⡤⠛⠻⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⠹⣿⣛⠿⣿⣿⣿⣿⢿⡿⠋⠀⢸⣟⡵⢊⣽⣿⠋⠀⠀⣀⣀⣀⠀⠙⣿⣿⣿⠉⢻⣿⣿⣷⠖⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⣤⣈⣙⣿⢿⣿⣿⣿⣿⠖⠋⠀⠀⠀⢸⣧⡎⢁⠼⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⠀⠀⠻⢾⣿⣧⡤⠂⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣶⠿⠋⢹⣼⠀⠀⠀⠀⠀⠸⣯⣞⠵⢚⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠀⠀⠀⠀⣼⣿⣶⣤⣀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠾⢻⣿⣄⠀⠀⠻⣆⠀⠀⠀⠀⠀⢻⣧⠔⠁⣠⠞⢻⡿⣿⣿⣿⣿⠁⢙⣿⠏⠀⠀⠀⠀⠈⢻⡿⠉⠙⣧⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢟⣩⣿⣤⣀⡀⠈⠳⣄⠀⠀⠀⠀⠻⣷⣾⣡⡾⢋⡴⣫⣾⣿⣿⣿⠿⠋⠀⠀⠀⠀⣠⠴⣠⣧⣠⡼⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⣰⡿⠛⠻⢶⣤⠈⠓⠦⣀⠀⠀⠈⠙⠻⠿⠿⠾⠿⠿⠟⠋⠁⠀⠀⠀⣀⣤⢄⡽⠚⠉⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠼⠋⠀⣠⠶⠛⢻⣷⣄⡀⠀⠈⠑⠒⠲⠤⣄⣀⣀⣤⣤⠤⢤⣄⡀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠃⠀⠀⠉⠀⠉⢹⠶⠟⣷⣶⣦⣶⢶⡆⣡⡄⢰⣤⡀⠉⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠏⠀⠀⡟⠉⡏⡇⠈⢿⠏⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁⠀⠀⡇⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀