Fish Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠈⡉⠉⠉⠉⠉⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠐⠂⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣀⣀⣀⣀⡀⣀⣀⣀⣀⣈⣁⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⡂⠉⠀⠀⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠢⠤⣄⣀⣈⣠⣤⠤⠀⠌⠥⠴⣺⠁⠀⠀⠀⠀⢀⠀⠔⠁⠀⠀⠀⢀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠀⠀⠀⠀⠐⠂⠀⠣⠁⠎⠀⠀⠀⡸⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠁⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠰⠤⣀⠀⠀⢀⡴⠁⠀⠀⠀⣀⠤⠊⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢀⡠⠖⠉⣀⡤⠒⠈⢁⡠⢀⠔⠀⠀⠉⠉⡁⠀⠀⠁⢉⠁⠀⠀⠀⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⡴⠃⠀⡠⠊⠁⠀⢀⠔⠉⣠⠃⠀⠀⠀⠄⢠⠀⠸⠀⠀⠸⡆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢀⠞⡑⠀⣠⠊⢀⠂⠀⡰⠃⠀⡴⠁⠀⡜⠀⠀⠀⡎⢠⠃⡇⠀⢠⡙⡄⠈⣆
⠀⠀⠀⠀⠀⠀⠀⢸⠰⠀⡔⠁⠀⠀⢀⠜⠁⡠⠊⠀⢰⢰⠁⠀⠀⡜⠀⡜⠀⣻⠀⢸⢡⠸⡄⠘⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠎⠀⢀⡠⠚⠁⠀⠀⡠⠨⠀⠸⢸⠀⠀⡜⠀⡜⠀⢈⠉⡆⢸⢸⠀⢣⠀⠸⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠐⠁⡰⠁⢀⡰⠋⡰⠁⠀⡇⡆⠀⢈⠀⡜⠀⠀⢸⠀⡇⠸⢸⠀⠸⡀⢠⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠜⣁⠔⠉⢀⠜⠁⢀⠜⢰⠁⠄⣡⠞⠀⡀⢀⣾⠀⡇⡇⢸⠀⠀⡇⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⢀⠔⢃⠠⠔⠁⣠⠃⡠⠊⠁⠀⡜⠀⡜⢸⢠⢡⠁⡌⠀⠀⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠋⡇⢰⠁⠀⠀⠌⠀⡼⠀⢸⠀⠆⢠⠃⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠃⠀⠐⠀⠘⠀⠀⡆⠈⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⡀⠀⠀⠀⠀⠰⠁⢀⠊



⣿⣿⠛⢿⠛⠿⣿⢿⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢌⣆⠤⢆⡄⣠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠰⠀⠀⠀⠌⠢⠈⠢⡈⠂⠂⠚⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡵⡇⠀⠄⣀⠂⢄⠢⠀⢈⠀⣀⠠⠄⠤⢱⣄⣣⡀
⠚⠁⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠚⠓⠀⠀⠀⠀⣠⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠑⠳⢄⡀
⠀⠀⠀⠀⠓⠤⢄⡀⠈⠙⠢⢤⣀⠀⠀⠀⠀⠘⣠⠴⠊⠁⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠸⢄⠀⠀⠀⠀⠀⠁⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠐⢤⣀⣁⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠀⠀⠀⠀⠀⠿⠘⡆⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡜⠃⠀⡠⠖⠀⡠⠒⠀⠀⣏⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡠⢹⠀⠀⠀⠀⠀⠨⠭⠄⡠⠾⢑⠟
⠀⠀⠀⠀⠀⠀⢸⠤⠒⡉⡀⢀⠌⠀⠀⠀⠀⢣⠄⠀⡀⠀⠄⠈⠙⢁⡘⠤⠐⠈⠁⠀⠀⠑⢌⠠⠀⠐⠄⡴⠊⣠⠔⠁
⠀⠀⠀⠀⠀⠀⣁⡠⢊⠊⢠⠊⠀⠀⠀⠀⠀⢹⡒⠁⢀⣀⣀⠴⠈⣡⢀⠄⠠⠠⠴⠄⢀⣀⢀⡉⠀⡄⠐⠒⠉
⠀⠀⠀⠀⠀⠀⡝⡰⢁⡴⠁⠀⠀⠀⠀⠀⠐⠓⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⡀⠀⠂
⠀⠀⠀⠀⠀⣠⣟⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠹⡈⠀⢀⡀
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢀⡴⠂⠀⠀⠀⡀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠊⠀⠀⠀⠀⡠⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣶⣄⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠎
⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣻⠋
⣀⣤⢤⣶⣾⡿⠿⢻⡿⢋⣭⠉⠁⣀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⠛⠛⠻⠿⣶⣦⣤⣤⣤⣴⣿⣿⡽⠃
⠻⣿⠀⠫⢥⣀⠒⠛⠳⣿⣿⡀⠀⠀⠀⠌⠉⠁⠃⠀⠁⠀⠁⠁⠉⠉⠁⠀⠄⠀⠠⠀⠤⠰⠨⠭⠭⠭⣼⣿⣏
⠀⠈⠓⠦⣠⠒⠒⠾⡶⠠⠒⠂⠀⠠⡄⠀⡀⠀⢂⠉⢀⣀⣀⡄⠀⣀⣀⠀⠀⠈⠀⢀⣀⡤⣶⠟⠛⠓⢾⣿⣿⣦
⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣴⣶⣶⣤⣤⣤⣤⣤⣄⣤⣤⣤⠤⠤⠤⠤⠤⠤⣶⣖⣚⣩⣵⠞⠁⠀⠀⠀⠀⠙⢮⣋⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡏⠀⠀⠀⠀⠀⠈⠻⢿⠀⠀⠀⠀⠀⠀⠀⠙⠾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠑⠾⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣦
⠀⠀⢻⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣬⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣤⣄⣀⣀
⠀⠀⠘⣿⣿⣿⣿⣆⣀⣀⣀⣰⣶⣶⣶⣶⣾⡿⠿⢿⡟⠛⣿⠛⢛⠉⠻⠏⠁⠉⠙⠟⠛⠛⠿⠻⢿⢿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⣿⣿⣿⣿⠿⠿⠿⠿⠿⠭⠿⠀⠠⠾⠀⠀⠒⠒⠒⠂⠀⠙⠀⠀⠀⠉⠀⠀⠴⠀⠐⠇⠚⠛⠛⠿⠻⠿⠿⠩⣿⣿⣿⣶⣤⡀
⠀⠀⠀⣿⣿⣿⣷⡤⠄⠀⠀⠀⢀⣀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣦⠠⠄⠀⠤⣤⠀⣈⠉⠹⠯⠄
⠀⠀⣸⣿⡿⠟⠋⠀⠀⠀⠀⠀⠈⠿⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠛⠋⠉
⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠁

⠀⠀⠀⠀⠀⠀⠐⠒⢶⣦⣤⣀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢰⣤⣤⣽⣿⣿⣿⢖⣦⣾⣿⡿⣿⣿⡟⢸⢞⢲⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠠⣤⣭⣽⣿⡿⢋⣵⣾⣿⣿⣿⢳⣿⡿⡇⠹⣙⡢⠋⠁⡬⠛⠁
⠀⠀⠀⠀⠀⠤⠶⣾⡿⢋⣴⣿⣿⣿⣿⣿⠃⠙⡛⠀⠀⠠⡀⠀⠀⠈⠉⢙⠇
⠀⠀⠀⠀⠄⠲⣿⠏⢠⣿⣿⣿⣿⣿⣿⣿⣿⡄⠁⡀⠀⠀⠨⡀⠀⢁⠤⠃
⠀⠀⠀⠠⠶⢾⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⢡⡀⠀⠂⠈⠳⠤⠝⠁
⠀⠀⠀⢀⣴⡟⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠋
⠀⠀⠀⢠⣼⠣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢀⢀⡠⠄
⠀⠀⠀⢀⣼⢸⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠀⣴⣤⣶⡿⠋
⠀⠀⠀⠁⣽⠨⣿⣿⣿⣿⣿⣿⣝⡛⣿⢕⣣⢴⠟⠛⠉
⠀⠀⠀⠀⢰⡆⣿⣿⣿⣿⣿⣿⡀⠅⠈⠉⠉⠁⠀⠀⠀⢀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠐⠀⠱⠹⣿⣿⣿⣿⣯⢢⠀⠀⠀⠀⠀⢀⡴⠞⠛⠛⠻⠿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠘⡃
⠀⠀⠀⠀⠸⣄⢣⢽⣿⣿⣿⣿⣫⡆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⢯⠙⢿⣧⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠹⡆⣬⡻⣿⣿⣿⣷⣷⣄⢀⣠⠾⠟⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠉⣿⠑⣮⠿⣿⣿⣿⣿⣀⠉⠋⠉⠙⠶⠆⠀⠀⠀⠀⠀⠀⠐⣘⣧⣤⣶⣾⠟
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠜⡓⢮⡛⢿⣿⣿⣧⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠙⠀⢤⣄⣉⡛⠿⠿⣿⣶⣶⣶⣶⣾⣷⡶⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢏⠟⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⣾⠿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣀⡄⣻⣶⣤⣀⣀⡀⠀⠀⠀⣀⣤⠞⢉⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣦⣤⡎⢀⣀⣤⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢡⠇
⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣻⣿⣿⣟⣻⣯⣿⣿⣟⣾⣻⡿⣻⡟⣻⡿⣻⡿⣿⡿⣿⢿⣿⣿⣿⣿⣷⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⡴⠋⢠⠏
⢀⣠⡴⠾⠟⠛⣿⣶⡛⠀⠙⠻⣮⣉⣠⣤⣤⣥⣿⡬⢥⣬⣧⣭⣠⣟⣘⠛⠁⠋⠘⠋⠾⠇⠸⠟⠹⡿⢻⣿⣿⣿⡿⣶⣦⣤⣤⣾⣷⣶⡟
⠀⠙⢣⡀⣀⠻⠿⠟⠀⠀⢀⠀⣻⡟⡟⠓⠉⠉⠈⠉⠉⣁⣀⣨⠭⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⠾⠿⢿⣿⣿⣻⡅
⠙⠻⢦⣥⣞⡃⠀⠀⠀⠀⣴⡀⣿⣓⣳⣤⣤⠖⠈⠉⠉⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡿⠿⠉⠁⠉⠀⠀⠀⠀⠻⣝⠛⢻⡀
⠀⠀⠀⠀⠉⠛⠻⠶⣶⣮⣿⣿⡟⣛⣛⣿⣿⣿⣭⣭⣭⣵⣶⣶⠶⠶⢷⣴⣤⣶⣴⣶⣶⣾⠿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⣿⣿⣯⣭⣭⣭⡭⠽⠿⠿⠿⠟⠛⠛⠛⠻⣿⡻⠏⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢾⣷⣦⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢋⠟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠠⡀⢷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⢉⡵⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣼⣿⣿⣾⣷⣿⣿⣿⣿⣿⣷⣦⣄⣠⣴⣛⣉⢀⡴⠋⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⡴
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣶⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⡼⠃
⠀⠀⠀⣀⣤⣶⣿⣟⣛⡟⠙⢻⣾⡿⠽⠟⠒⠛⠺⠿⣿⠹⠟⠹⡟⢰⡟⢠⡟⢣⣾⠋⡾⢋⡿⢻⣿⠛⣿⡿⢿⣿⣾⣿⣶⣶⣠⣄⣀⠀⠀⠀⣰⣏⣀⣰⠇
⠠⢶⡿⠋⠉⢰⣴⣿⡧⠇⠀⠀⠈⣻⣶⣶⣶⣞⣿⣿⢻⠿⢿⡟⠛⠳⢶⡾⣶⣦⠀⠀⠀⠈⠀⠚⠃⠀⠉⠁⠘⠋⠘⠛⠟⠛⠛⠻⠟⢿⣿⣾⣿⣿⣻⡏
⣤⣠⠹⢦⠠⣌⠛⠛⠁⠁⠀⠰⠀⣸⡗⢹⠉⠀⠀⠀⣀⣀⣠⡤⠤⠴⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⡶⢾⠟⠛⠛⠛⢿⣿⣿⣼⣧
⠈⠙⠻⠶⣾⣭⣀⣀⠀⠀⠀⣾⣆⣾⣧⠭⣷⣶⣞⣁⣀⣀⣒⣀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⠿⠛⠀⠁⠀⠀⠀⠀⠀⠀⠹⣮⠉⠹⡆
⠀⠀⠀⠀⠀⠉⠙⠛⠾⢯⣭⣿⣿⣟⣛⣛⣭⡽⠿⢿⣷⣶⣶⣶⣶⣶⣶⣿⡿⣯⣭⣭⣵⣶⣿⣿⣿⡿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⢳⣾⣿⣯⣭⡭⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⠙⠻⣿⡛⠛⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢶⣽⣦⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣠⣤⣤⠤⠤⠤⣤⠤⣤⣀⡀⣀⣤⣰⣦⣴⠆
⠀⠀⠀⠀⠀⠀⠀⣰⠿⡿⣍⠻⣗⡒⠰⣟⡳⢉⣽⣟⢿⣿⡿⣶⣭⣟⠯⣫⡿⢿⣶⣆
⠀⠀⠀⠀⠀⠀⠀⢿⢸⠐⣽⡧⠹⡿⠑⠺⡻⡿⠻⠍⡣⢛⢿⣿⡿⣿⣿⣮⣔⢩⠿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢘⣏⣶⣘⣿⡀⠇⢠⢀⡇⠀⠀⠐⠀⢸⣆⡠⢃⣿⣿⣿⣿⣷⣻⣽⣿⡀
⠀⠀⠀⠀⠀⠀⣴⢛⣭⣍⣉⡉⠘⠒⠋⢙⣷⠦⠤⠤⢔⣘⣠⠔⣨⠀⢛⣹⣿⣿⣿⣞⣿⡇
⠀⠀⠀⠀⠀⠀⠙⠦⣦⡐⠀⠀⠉⠉⣛⣯⣤⣤⣄⣤⣾⣉⣁⠚⣠⣿⣿⣾⣽⣿⡿⣿⡾⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⣴⡖⠮⢿⣿⡿⢿⡛⠷⠊⠁⠀⠙⢿⣿⣿⡿⢛⣭⣬⣿⢻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⣴⣤⣄⣀⡀⠀⠈⠁⠀⠙⢛⣫⣿⡿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣤⡀⠀⠙⣿⣯⡹⣿⠀⠀⠀⠀⠐⣿⢿⢿⡇⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⡿⠓⠦⢼⣾⣿⣿⠀⠀⠀⠀⠀⣴⣿⣿⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠋⠀⠀⠀⠀⠘⢿⣿⡄⣤⣄⡀⢰⣾⢷⡏⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⢀⣀⣀⣀⣀⣀⡼⠃⣽⡿⣷⣝⣯⣿⡾⠻⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⠿⣿⣿⠀⠀⢹⣤⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡯⢿⣿⣤⡐⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣟⣽⢿⣿⡿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⣡⢿⡿⠁⠻⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣵⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠐⢂⡄⠉⠉⠉⠁⠐⠒⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣊⣥⣄⣀⠀⠀⠺⣿⢶⣿⣿⠄⣠⣶⣶⠀⠀⠉⠑⠢⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⣼⣿⣿⣿⣿⣧⠀⢀⣠⣀⡠⢋⣾⣿⣿⡿⣣⣼⣿⠟⢠⣄⣤⣬⡉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⡴⠀⣼⠟⡿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠙⠉⠉⠋⣾⣿⣿⣿⠙⠿⠿⠜⠛⠛⢂⠤⣜⡂⠤
⠀⠀⠀⠀⠀⠀⠀⣰⣫⣾⣿⢃⣼⡟⡌⠁⠋⢻⣿⣿⣿⠏⢰⠰⣴⡀⠀⠰⠀⠁⢀⠴⠒⠒⠒⠒⠀⠀⠀⢴⣿⣿⣶⡶⠖⠒⢷
⠀⠀⠀⠀⠀⠀⡼⣱⣿⣿⣷⣾⠛⢡⠀⠀⠀⠸⣻⣿⠃⢀⡟⣧⣿⣧⡀⠀⠀⠠⠃⠀⠀⡀⠊⠐⠀⣠⣶⣿⣿⣿⣿⠿⣆
⠀⠀⠀⠀⣠⣴⣷⣿⣿⣿⣿⡏⠀⢠⠀⠀⡀⡀⠈⠃⢰⣼⡇⠸⣿⣿⣷⢀⠀⠀⠀⡠⠊⠉⠀⢢⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⢰
⠀⢀⡴⢋⠝⣫⣿⣿⣿⣿⣿⠇⠀⢸⡀⠀⠱⡐⣄⠀⢸⣿⣿⣄⠈⠛⠿⣿⣦⠀⢸⠁⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢠⡏
⣰⠋⠀⠀⠊⣡⣿⣿⣿⣿⡵⠂⢀⣾⡇⠐⢄⠘⠮⡳⢎⢿⣿⣿⣷⣦⣄⣀⠈⠀⠀⠀⠀⠀⠀⠨⢿⣿⣿⣿⣿⣿⡃⡜⠀⡞
⢻⣀⠀⠀⠀⠺⣛⣭⠞⢁⣠⣶⡿⠃⠘⡄⠈⠓⢤⣘⣆⠳⢍⡻⠿⠿⠿⢿⣿⡦⠀⠀⠀⡈⠉⠒⠄⡈⠙⠻⠿⣿⠞⠀⡸
⠀⠈⠙⣶⡾⠟⠋⠀⠀⣿⡟⠉⠀⠀⠀⠈⠦⡐⢤⣈⠉⢅⣀⠈⠉⠉⠉⠐⠢⣄⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠤⣉⡒⠇
⠀⠀⢸⡇⠀⢀⣴⣾⣷⠋⣽⣗⡀⡀⢀⣠⣤⣌⡒⠤⣉⠉⠩⠕⠲⣄⡀⠀⠀⠀⠉⠒⠦⠤⠤⣤⣀⣀⣀⣀⠀⠀⠀⠉⣢⠁
⠀⠀⠘⣇⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣷⣤⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠭⠀⠀⠐⠊⠁
⠀⡴⠋⠁⠩⠾⠟⣻⣿⣎⣝⣛⣷⣆⣀⣈⣉⠉⠛⣿⣿⣿⣿⣿⠀⣶⣤⣄⣀⣤⡤⠤⠄⠒⠈⠁
⠾⠒⠒⢶⡠⡄⣍⠹⣿⠟⢿⣿⣿⣿⣫⡞⠁⠀⢸⣿⣿⣿⣿⡏⢸⣿⡟⢿⡿⠙⠀⢀⠁
⠀⠀⠀⠀⠳⡱⣌⢷⡅⠀⠸⢟⢭⣻⡿⣷⣄⠀⠀⠈⠙⠿⠟⢀⣿⣿⣿⢸⣷⡦⢔⡀⢀⣠⣤⣤⣤⣤⣤⣤⣀⣀⣀⡀⣠⣤⠄
⠀⠀⠀⠀⠀⠙⢾⡶⠇⡠⠶⣶⣦⣬⣉⡛⠻⢷⡀⣤⣀⠀⠠⣿⣿⣿⡟⣼⣿⣷⢰⣍⣾⣿⣿⣿⣿⣿⣿⠧⣀⡴⣨⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠂⢬⣛⣶⣮⠉⠛⠛⠛⠚⢻⣦⣝⢷⣤⡀⠈⠉⠰⣿⣿⠏⣰⣿⣿⣿⣿⣿⣿⣿⡇⢰⢋⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣶⣦⣽⣿⣿⣿⣿⣶⣄⣀⠈⠁⠀⠹⠟⠙⠿⢿⣿⣿⣿⢧⣓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠁⠙⠋⠁⣠⠞⠉⠻⢿⣿⣿⣿⣷⣦⣄⡀⠀⣠⣴⣿⣿⣿⠛⡗⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⡼⠁⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠹⡙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣯⣻⣿⣷⣿⡏⠒⠄⢹⡈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣝⢷⡝⢟⢮⡋⠓⠤⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠠⣀⠙⠦⡀⢨⠃⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢔⡀⠑⢄⣸⠿⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⠅⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠐⠲⠶⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠻⢿⣿⣿⣶⣤⣀⠀⣠⣴⣲⣶⣶⣦⣤⢠⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⣷⣾⣿⣿⡿⢛⣠⣿⣿⣿⣷⢹⣿⣿⡇⢰⣟⣭⢹⣿⠿⠻⣷⣶
⠀⠀⠀⠀⠀⠀⠐⠲⣶⣶⣾⣿⠟⢫⣴⣿⣿⣿⣿⣿⣏⢻⣿⠟⡇⠈⠧⣭⠕⠁⠀⣤⡊⠁
⠀⠀⠀⠀⠀⢀⠶⠶⣛⣿⡟⢁⣴⣿⣿⣿⣿⣿⣿⡋⠂⢛⠁⠀⠀⠐⢄⡀⠀⠀⠀⠉⠉⠹⠃
⠀⠀⠀⠀⠀⠤⢖⣾⣿⠋⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⢁⠀⠀⠀⠀⣇⠀⠀⠅⣀⠔⠁
⠀⠀⠀⠀⢀⣠⣴⣾⢃⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡀⠀⠁⠤⠄⠲⣌⣑⡲⠞⠁
⠀⠀⠀⠀⠁⢀⣽⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠛⠑⡤⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠔⢿⡏⢼⣿⣿⣿⣿⣿⣿⣿⣿⣟⣵⣿⣿⣤⡄
⠀⠀⠀⢀⠴⣾⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣀⣀⡠⠖⠢
⠀⠀⠀⠀⣠⣾⠰⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⠇⢀⡖⣶⣶⣿⠟⠁
⠀⠀⠀⠈⠁⣹⠀⣿⣿⣿⣿⣿⣿⣿⣏⠿⢳⡿⡋⠶⣤⣾⡿⠛⠛⠁
⠀⠀⠀⠀⠘⢉⡄⣿⣿⣿⣿⣿⣿⣿⡇⡙⠃⠙⠊⠿⠖⠉
⠀⠀⠀⠀⢁⠘⢇⠸⣿⣿⣿⣿⣿⣿⢇⠈⠁⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣷⡶⣶⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠈⣀⠜⡀⢿⣿⣿⣿⣿⣿⡮⡖⠀⠀⠀⠀⠀⠀⡼⠋⠉⠀⠀⠈⠉⠙⢻⡻⣿⣿⡦⡀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠸⣦⢉⡖⣿⣿⣿⣿⣿⣯⣚⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡌⠈⢿⣗⡄⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠹⣷⢰⣾⢻⣿⣿⣿⣿⣾⡼⣀⠀⣀⣴⠿⠟⠒⠒⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣿⣷⠀⠀⠀⠀⣠⢿⠟
⠀⠀⠀⠀⠀⠀⠀⠘⢸⣿⢰⣜⢿⣿⣿⣿⣿⣳⠄⠙⠛⠛⠈⠷⢦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠔⡹⣟⣤⣤⣶⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠄⣿⢦⣝⢻⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡸⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠁⠢⢼⡗⠀⠙⠛⢿⣿⣿⣿⣶⣤⣀⣀⣀⣀⣀⣠⣔⣁⢀⣤⣾⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠳⠶⢦⣤⣹⣻⣝⣿⣛⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣽⠏
⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⠿⡿⠟⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠛⠛⠛⠻⠛⠿⠿⠿⠿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⢀⣤⣞⡿⣶⠋
⣴⣺⡛⢿⣿⠟⠛⠉⣨⡟⣡⣼⣇⠀⠀⠂⠀⠠⢄⣀⠀⠀⠀⠤⠀⠠⠤⠄⡤⠤⠄⠀⡀⠀⢀⣈⡉⡉⡛⠿⠿⠿⠿⠿⢿⣿⣿⠟⠁
⠈⠺⣇⠈⠑⠶⠲⠉⢀⠈⠿⠟⠷⠉⠉⠉⠉⠀⠀⠀⢀⠑⣀⢀⠈⠈⠁⠀⠈⠀⠀⠀⠀⠀⣒⠒⠐⡒⠈⠐⢒⣒⣚⡒⢿⣿⣿⡀
⠀⠀⠈⠓⠦⣔⣊⠁⠻⣿⣂⠎⠁⠂⠐⠀⠤⠀⠀⠈⢈⣁⢀⣀⡀⠡⠤⠄⠤⠄⣀⠉⠉⠀⠀⠀⢀⣠⠴⣺⠟⠉⠉⠙⢿⣻⣿⡿⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢧⣶⣾⣷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⡦⠤⠤⠤⠴⠦⠶⢶⣖⣚⣋⣡⣴⠟⠁⠀⠀⠀⠀⠀⠙⢢⣉⡹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠳⢿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣻⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡟⠻⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠈⠛⢿⣶⣶⣤⣤⣤⣄⣀⡀
⠀⠀⠀⢸⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡾⠿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⠟⠻⢷⣦⣄⡀
⠀⠀⠀⠀⢻⣧⠈⠉⠻⢷⣦⡀⢀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠈⠻⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⢀⣴⣦⠀⠀⠈⢻⣦
⠀⠀⠀⠀⠀⠀⢈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠛⠛⠀⠀⠀⠀⣹⡇
⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⢀⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⣴⡟⠁⣀⣤⣾⠟⠋⠈⠛⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⢸⣿⡶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⣦⣴⡾⠟⠋
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⢀⣠⣴⡿⠻⠿⠿⠿⠿⠟⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠊⠈⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠐⡋⠐⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢪⠖⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣁⣈⣀⡰⢁⡎⠀⣀⠀⠀⠀⠘⠂⣀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⡞⠛⠙⠽⡯⠙⠙⣿⣿⠿⢷⣤⣀⡠⠀⠀⠀⠠⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠙⣙⣾⢄⠀⠀⠠⠁⠚⡉⠨⢢⡙⣐⠒⢹⠕⠶⣤⠴⠀⠀⠀⣠⢏⡔⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠐⠒⠀⢀⣴⡿⣙⣍⣵⠋⢠⡔⠄⢢⠀⠀⠀⠀⠝⠀⠀⠀⠱⠌⠊⠀⢤⣀⣴⣷⡿⢀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⣤⡤⠀⢀⣴⣯⣿⣟⠛⠿⠷⠤⠟⠛⠦⠀⠀⣄⢀⠤⠀⢧⢪⠔⠁⠀⠀⠀⠸⢏⢻⣿⣿⡀⠀⠀⠀⠀⡠⠖
⢀⠏⠀⢔⡕⣊⠒⣍⠿⠀⢀⡶⠀⠀⠈⠀⠠⠄⠋⠅⠰⠈⠊⠼⠇⡠⠀⠀⠠⠠⣀⣾⣿⡋⠁⠀⠀⠀⢸
⡋⢣⠀⠸⡘⠿⢀⡾⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠨⠡⠁⠡⢠⢁⣠⣀⡶⠖⠒⣶⣾⣿⣯⡁⠀⠀⠀⠀⠈⢣
⠑⠈⠓⠀⢈⢙⡉⠄⠀⠀⠀⠀⢀⠘⡠⡀⠂⢀⡤⠰⣢⣌⣋⣰⣽⠏⠱⠈⠀⠸⣿⣿⠎⠓⠄⠀⠀⠀⠀⠐⢆
⠀⠀⠲⢄⠀⢠⠀⡀⠀⠠⠠⠐⢁⣼⡇⡀⠠⠀⡰⠀⣶⣿⣿⣿⡟⠀⠀⠀⠒⠒⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠉⠒⠄⣀⣀⣤⣖⣄⢺⣿⣧⣈⢀⣀⣠⡾⣿⣿⣿⠏⠀⠀⠀⠀⠀⣸⡟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⠳⡿⣿⣿⣿⣷⣻⣿⣿⡿⠟⠀⠀⠀⡐⠀⢠⠇⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠙⢿⣛⠛⠛⠛⠿⠛⠦⡀⠠⠀⠈⠀⠀⢸⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠡⠀⠀⠀⠁⠙⠲⠤⡀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠡⡀⠀⠀⠀⠁⠀⠀⠀⠰⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀⢆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣧⣄⣀⣀
⠀⠀⢿⣿⣷⣤⠀⠀⠀⢀⣄⣀⣠⣤⣴⣶⣶⣾⣿⠿⠿⢿⡿⠛⠿⣿⠿⢿⣿⣿⣷⣶⣶⣤⣄⡀
⠀⠀⢸⣿⣿⣿⠿⠿⡿⢿⣿⠏⠉⠽⠁⠠⠧⠤⠁⠐⠃⠀⠀⠒⠀⢠⠀⠰⠀⠒⠾⡿⣿⢿⠟⣿⣷⣦⣄
⠀⠀⣸⣿⣿⣶⠄⠀⠀⠀⢀⡀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠤⠀⠀⢤⡀⣌⣉⠻⠁
⠀⢠⡿⠟⠋⠁⠀⠀⠀⠀⠘⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⢋⠝⢋⡹⠿⣦⡀⠀⠀⠀⠀⠀⣠⡶⡿⢛⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⡁⡰⢁⠔⣁⠔⢊⡭⠟⢶⣦⠀⢠⡾⢫⠊⢀⠼⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠾⠿⠿⠷⠷⢧⣾⣡⣞⡡⠖⣻⡟⠁⢠⡟⣰⠃⢠⠏⢈⠝⣻⣷⠆
⠀⠀⠀⠀⠀⢀⣴⠾⠛⠉⠀⠐⠲⢤⡀⠀⠉⠙⠒⠭⣛⢷⣯⣽⠃⢀⡿⣰⠇⣠⠏⢠⠏⢈⡾⠃
⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠈⠑⢌⠳⣄⣸⡷⢋⡴⢋⣴⠏⢠⡟⠁
⠀⠀⢀⣴⡏⠀⠀⠀⢰⣿⣳⠀⢠⠀⠀⢹⡆⠀⠀⠀⠀⠀⠈⠀⠈⠻⠿⠿⢞⣋⠵⢢⡟
⠀⠀⠸⣏⠳⠆⠀⠀⠈⠛⠋⠀⢸⠇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⣒⠂⢸⠃
⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⡼⠀⠀⣸⣧⣀⠀⠀⠀⠀⠀⣠⠶⢶⣦⣍⠲⢤⡀⠸⣇
⠀⠀⠀⠀⠀⠈⠛⢶⣤⣤⠄⠈⠀⣀⡼⢿⣗⢭⡳⣆⢀⣠⡾⣟⢦⣄⠹⣿⣝⢦⣍⠢⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠳⠿⢯⣤⣤⣽⣿⠾⣿⣿⡧⡙⢮⣱⣿⠇⠹⣟⢧⡈⢷⡀⠈⡻⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣾⣟⢦⡑⢌⠪⣳⡾⠋⠉⠀⠀⠀⢻⡆⠻⡄⠹⣄⠪⣑⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡜⣝⣧⡙⢦⡑⢽⣧⠀⠀⠀⠀⠀⠀⢻⣄⠹⡄⠘⢦⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣮⣺⣿⣦⣝⢎⣿⠀⠀⠀⠀⠀⠀⠀⠙⢦⣘⢦⡸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠙⢯⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠛⣻⠿⠛⢛⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⢿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⢀⡞⠁⣠⠞⢉⣠⠤⠿⣷⣤⣀⠀⠀⠀⠀⣠⡾⢋⡵⠋⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⣰⢢⠏⣠⠞⢁⡴⠋⣠⠴⠚⢉⣉⣿⡷⠀⢀⣾⠏⣠⠏⠀⣠⠎⣹⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⠶⠿⠿⠿⠿⠿⠿⢷⣶⣯⣤⠞⣁⡴⠚⢉⣿⠋⠀⢀⣾⠃⣰⠏⠀⣰⠏⠀⣠⠞⣹⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠛⠉⠁⠠⢤⣄⡀⠀⠉⠉⠙⠒⠦⢭⣙⠻⣷⣴⣚⣹⡿⠀⠀⣼⡏⣰⠏⠀⣰⠏⢀⡼⠁⠜⣵⡟⠁
⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠈⠓⢦⡙⢿⣿⡁⠀⢰⡿⣰⠏⢀⣼⠏⢀⡾⠃⢀⣾⠏
⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠙⢦⠙⢿⣦⣿⡿⣋⣴⠟⣁⣴⠟⢁⢀⣾⠃
⠀⠀⠀⢀⣠⣿⠁⠀⠀⠀⠀⢰⣿⠛⣷⠀⠘⡆⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠻⠿⠿⠷⠟⣋⡡⠖⢁⣾⠃
⠀⠀⠀⢸⡟⢿⣦⣄⠀⠀⠀⠘⠿⠿⠛⠀⠀⣿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⣭⣥⠤⠄⢸⡏
⠀⠀⠀⠈⢿⣦⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠠⣍⡓⠒⠒⠀⢸⡇
⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⣰⣿⢷⣄⡀⠀⠀⠀⠀⠀⢀⣴⠟⠛⠻⣿⣶⣤⡉⠳⢦⡀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣶⡤⠤⠀⠈⠀⠀⢀⣴⠿⣯⡳⢬⡛⢷⣄⠀⢀⣴⣿⣛⢷⣤⡀⠘⣿⣯⡙⢷⣤⡉⠳⣜⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣶⣤⣶⣾⣛⣁⣀⣈⣻⣶⣭⣾⣿⣾⣟⡙⠲⣌⠓⢬⣻⣧⠘⣿⡻⣦⡈⠻⣦⡀⠀⠙⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣿⢟⣿⣿⠛⢯⡙⢯⡙⣯⡙⢦⣬⡿⠿⠛⠁⠀⠘⣷⡈⢷⣄⠘⢷⡄⠀⠲⢍⡻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢸⣿⣯⠳⣄⠙⢦⡙⢮⣿⡟⠉⠀⠀⠀⠀⠀⠀⠹⣷⡀⢻⣆⠀⢻⡄⠑⢤⣹⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⢳⡹⣧⡈⠳⣄⠙⢮⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠹⣆⠀⠙⣦⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡳⣝⣿⣶⣌⠳⣄⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠙⢦⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣾⣿⠿⣮⡳⣌⢦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣬⣳⣤⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢄⣘⣂⣄⡤⢀⣀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢈⣄⠀⠉⠀⡀⠫⡀⠙⢜⠐⠣⠠⠄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡲⢄⠀⠀⠀⢀⠑⠄⠑⠀⠑⠄⠀⠀⠀⠂⠉⠻⣀⠀⡄
⢀⡀⠤⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣙⠂⠈⠑⠢⠄⡉⠢⡈⢀⣠⡤⠄⠖⠚⡛⠘⠓⠚⠒⠲⠦⣀⠠⡀
⠉⠑⠀⠀⢀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠉⠉⠁⢀⠐⠀⠀⢀⡰⠖⠋⠁⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢄
⠀⠀⠀⠀⠈⠓⢤⢤⣀⠀⠀⢉⠳⢤⣄⡀⠀⠀⠀⠀⠈⠐⣀⡬⠖⠉⠀⠁⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣀
⠀⠀⠀⠀⠀⠀⠸⣄⠀⠈⠀⠀⠈⠀⠈⠉⠹⠓⢀⠀⠠⠉⠀⠀⢀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠈⠫⣀⠀⠐⠒⠄⠀⠀⠀⠀⠀⠄⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠓⠒⠂⠀⠀⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢘⠀⠀⢀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠁⢠⡤⢣⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠁⢀⠠⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣬⠀⠀⠀⠀⠀⠀⢈⣋⣸⠂⠀⠀⣀⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠉⠀⣠⠔⠁⠀⡠⠊⠁⠀⠰⣉⠉⠉⠐⠀⠀⠀⠀⠀⠀⡀⣀⡀⠀⡠⠤⣂⠥⠘⡆⠀⠀⠀⠀⠀⠐⠠⠴⢂⡴⠞⠃⡪⠓
⠀⠀⠀⠀⠀⠀⠀⠀⣇⡤⠖⣉⠀⠀⢠⠎⠀⠀⠀⠀⠀⢧⡄⠀⠀⡀⠀⠄⠀⠙⠋⠀⣛⠤⠤⠒⠉⠀⠀⠀⠘⢄⠑⢄⠀⠈⢆⡀⢔⠋⢀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⡜⠁⣢⢞⡕⠋⡰⠃⠀⠀⠀⠀⠀⠀⢣⠤⠒⠉⠐⡀⠀⣀⠔⠂⢉⠄⡠⢀⡀⢀⣤⡀⠀⠀⠀⠙⠒⠤⢀⡀⠬⠵⠚⠉
⠀⠀⠀⠀⠀⠀⠀⢱⠞⢡⠞⢀⡴⠁⠀⠀⠀⠀⠀⠀⣠⣜⡂⠠⠖⠚⠓⠒⠁⠀⠀⠁⠊⠁⠁⠈⠁⢀⡉⠁⠒⠃⠘⢀⠌⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡠⠃⡠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⠄⠀⠄⡴⡀⠰⠀⠂⢀
⠀⠀⠀⠀⠀⢀⣴⣯⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠈⠌⠀⠳⡄⠀⠀⡬
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢠⡷⠋⠀⠀⠀⢀⡄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠋⠀⠀⠀⠀⠀⣸⠵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡚
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠈⠉⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⢀⡰⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⣢⠄⢀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠈⡠⠊⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⡠⠀⠀⠀⠀⢀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⡔⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣣⣀⢁⡀⡰⢀⣮⠀⢀⣈⠀⠀⠀⠀⠙⢂⣀⠀⠀⠀⠀⠀⠀⢀⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠾⠛⠻⢿⣿⠟⠛⡳⣿⣿⣶⣾⣅⣀⠄⢂⡀⠀⠀⠀⠁⠄⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢺⡻⣥⣎⠀⠀⠈⠠⠘⣀⠴⠚⠞⢝⠱⠄⡩⠍⠻⡟⣀⣀⣀⣠⠄⠀⠀⠀⢀⡾⢁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⢀⣀⡀⠀⠀⢰⣿⣅⠾⠿⣫⡖⠀⢀⠄⢉⠀⠐⠂⠈⠒⠱⣔⠒⠀⢈⢋⠈⢝⡯⠉⠀⠀⠀⣠⣟⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖
⠀⠀⠀⠀⠩⠁⠀⣠⣴⣿⣟⣮⣧⡼⠃⠀⣾⣾⡢⠀⠳⠁⠁⠀⠀⠘⢈⡀⢀⠀⢠⠑⢀⠄⠀⠙⣶⣾⣿⣾⣟⡡⠂⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⢰⣶⠆⠀⣠⠾⠿⣾⠿⣍⠉⠛⠻⠗⠶⠋⠍⡓⠀⠀⢀⡦⡀⡱⠄⡈⢖⠡⡾⡁⠀⠄⠀⠀⠘⠛⡀⢿⣿⣿⣁⠀⠀⠀⠀⠀⡤⠚⠁
⢀⡜⠁⠠⢊⡔⢊⠛⢢⡙⡗⠀⠁⣳⠆⠀⢘⠈⠈⠀⢤⠜⠉⠼⠈⡇⢑⢪⠽⠇⣀⠀⠠⠀⠰⠀⢆⢢⣿⣿⣋⠁⠀⠀⠀⠀⢸⡁
⡞⢶⡀⠀⢸⠰⣿⡅⢀⡇⠀⠂⠉⠁⠀⠀⢀⡠⠀⠀⠀⠀⢘⢣⠃⡐⡂⢠⠃⠀⡀⢠⣥⠶⠴⣤⣤⣿⣿⣛⠁⠀⠀⠀⠀⠀⠈⢣⡀
⢣⠈⢷⡁⠈⠳⠦⠴⠛⠀⠀⠀⠀⠀⠀⠀⠸⠁⡄⢠⠀⠐⠈⢱⡄⠪⢶⡗⠨⢛⣼⠻⡄⠂⢀⠙⣿⣿⣿⠹⢧⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠑⢀⡀⠀⠑⠒⠒⠉⠀⠀⠀⠀⠀⣠⠆⣠⡦⠇⠀⠀⡖⠋⢘⠰⣻⣷⣾⣾⣿⠇⠀⠑⢀⠀⠀⣿⣿⡏⠑⠀⠁⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠙⠤⣠⠰⠂⠠⠀⠀⠒⠐⠁⠀⢰⣿⡇⠧⡀⠒⠢⠙⠀⣼⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⠁⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠈⠙⠣⢀⣀⣠⣴⣬⣥⣐⢿⣿⣷⣀⣁⣀⣀⣰⡟⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⣰⢿⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⡟⢷⢿⣿⣿⣿⣿⣗⢿⣿⣿⣿⡿⠗⠀⠀⠀⠀⠒⠀⢀⡟⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⠈⢲⣿⠿⠿⠿⠿⠿⣿⠻⢧⣀⠀⠀⠀⠀⠊⠀⠀⢸⠁⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠉⠛⢶⣄⡀⠀⠀⠈⠁⠈⠀⠉⠁⠀⠀⠀⠀⢸⠀⠀⡀⠀⠀⠹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠌⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠡⠀⠀⠀⡀⢽⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⡐⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠣⡀⠀⠀⢐⠀⠈⠙⠒⠤⠀⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⠀⠀⠀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣟⠓⠉⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠿⠿⠌⠁⠀⠀⣠⣤⣶⣽⣿⠷⣆⣀⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⡿⠛⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡻⠇⣀⣀⣤⣼⣿⣟⣯⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⡿⢻⠋⣠⣾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠭⣠⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣵⣿⣿⣿⡿⠛⠻⡿⣇⠛⠸⣽⢿⡟⢁⣡⣾⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡼⠛⠉⠹⠁⠀⠀⠀⠈⠓⠓⠛⢉⠞⢠⣿⣿⣿⣿⣿⣇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢟⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠴⢟⣋⣉⠉⠉⠉⠉⠁⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡠⢃⡴⠊⢉⣤⠄⠉⣰⣶⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠘⡟⢧⠀⠀⠀⢀⡀⠈⠒⠀⠀⠀⠐⠈⠀⠀⠉⣀⣤⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣿⣎⠓⢦⣰⣆⡙⠳⠦⠔⠀⠀⠀⢀⡤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣾⣿⣿⣿⣿⣿⠋⠀⠀⠀⣤⣶⣿⠿⣛⠓⠂⢉⣿⣿⠟⠛⠶⢦⣭⣉⣉⣀⣠⣤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⠿⣾⣿⣿⣮⣶⣭⣾⠏⠀⠀⠀⢀⣠⣴⣿⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠋⢀⣠⣤⠶⢾⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠁⠀⠀⠀⢿⣽⠀⠀⢉⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⣀⡀⠙⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⣀⣀⣊⢻⣧⣦⣸⣾⡇
⠀⠀⠀⡠⠂⠀⠀⢰⣿⠏⠉⡉⠑⠒⣨⣿⣿⣷⣄⠀⠀⠀⠀⠀⡿⠁⢐⣢⣾⣿⣿⣿⣿⣿⣿⠃⠈⠻⣿⡿⠏⠙⣛⡡⡄⠁⢄⠀⠀⡀
⠀⠀⢸⡇⠀⡆⢧⣷⡉⠻⣟⣀⠀⠠⢄⣄⡈⠻⣿⣷⣄⡀⠀⠀⠛⣿⣿⣿⣿⡯⠥⢴⣶⣿⣧⣤⡤⠾⢷⠿⠛⠉⠀⣠⢡⠆⡜⣀⡼⠛
⠀⠀⠀⠻⡠⣟⠿⣿⡻⢷⣾⣿⣟⠲⡶⢭⣉⣉⠉⣙⣿⣿⣿⣦⣾⣿⣿⣿⣿⢷⣿⣿⡟⢛⣿⣶⡶⠿⠛⠭⡠⠴⢚⣥⢟⡼⠣⠋
⠀⠀⠀⠀⠘⠪⢻⣾⣿⣿⣿⣿⣿⣷⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⡭⢛⣫⡥⣶⣦⣤⣤⣶⣾⡻⣵⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠀⠹⠿⣿⣿⠿⢿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⢿⣿⡿⠟⢯⠵⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⠛⠿⠿⣶⣾⣿⣿⣷⡶⠟⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⡿⠏⠙⠿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⢯⡙⠃⠁⠀⢀⣀⣬⣻⣿⣦⡄⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣾⡿⠟⠓⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢿⡀⠀⠀⣀⣴⣶⡿⣟⣻⣭⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠏⣠⣴⡆⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣟⡛⢐⣨⣽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⠿⡿⣿⠱⡆⡟⣿⣿⡟⠁⢡⣾⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⡿⠟⠻⡏⠉⠀⠀⠘⠮⣵⡼⠾⢣⠟⢠⣾⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⣠⡿⠟⠛⠛⠿⠿⠗⠒⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠁⢐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⣨⠴⠒⣒⡒⠂⢠⣀⣤⡴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠿⠉⠀⠀⠀⠀⠀⠀⢸⡿⣇⠀⠀⠀⢠⠀⠑⢄⡀⠀⠀⠸⡥⠚⠁⠀⠞⠉⠀⣰⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡙⢦⡀⠀⡀⠷⣄⡀⢀⡀⠀⠀⠀⠀⢀⣤⡴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣿⣿⣿⣿⠟⠀⠀⠀⠀⣀⣤⣤⣤⣐⡒⠶⣶⣿⣿⣦⣉⡓⠿⠦⠬⠍⠉⠀⢀⣀⡤⠞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠰⣿⣿⣯⣭⣦⡠⣀⡴⢿⡿⠁⠀⠉⠉⠛⢒⣶⣶⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⣻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⡿⠟⠁⠀⢀⣀⣤⣶⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠛⠋⠙⣿⠿⠟⠛⠻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⡘⣿⡆⠀⠀⢺⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣮⣤⣤⣴⣀⡉⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣼⠏⠁⠀⢀⣀⣀⣠⣤⣤⣤⡜⠿⣿⣶⣿⣿⢀⣠⣄⠀⠀⡀
⠀⠀⢀⡔⠁⠀⢀⣀⢿⣏⣀⠀⠀⠉⠑⠒⠻⣿⣿⣄⠀⠀⠀⠀⠸⣏⣀⣠⣽⣿⣿⠿⠟⠻⣿⡿⠁⠀⢈⣻⣟⣋⣤⠭⠴⠺⠁⠀⡆⠀⢢⡄
⠀⠀⠘⣧⠀⣆⢺⣾⣦⣉⠻⣤⣄⡀⠒⠴⣦⣈⣻⣿⣷⣤⣀⣀⠀⢩⣿⣿⣿⣿⣟⣒⣻⣿⣿⣷⠶⠖⣚⣛⣟⠉⠀⠀⣠⢆⡾⣰⢁⡦⠛⠁
⠀⠀⠀⠘⢆⢻⣝⠷⣭⣻⣿⣿⣿⣉⠫⠓⠦⣤⣄⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣩⣿⣿⠿⠛⠋⠑⠦⠒⣋⣵⢞⣱⠋⠊
⠀⠀⠀⠀⠀⠑⠫⣿⣻⣿⡿⢿⣿⣿⣷⣶⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣶⣪⣥⣴⣢⣷⣶⣶⣾⣿⠯⢷⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠃⠀⠛⠻⢿⠟⠛⠿⠷⢶⣿⣿⣟⣛⣛⠛⠿⢿⣿⣿⣿⠿⣿⣿⣟⣿⣿⠿⠿⠿⠛⠻⠖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠈⠉⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒⠒⠒⠒⠤⢄⣀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠤⠤⠤⠤⠤⠄⠀⢀⣀⣤⡄⠀⠁⠀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠐⠈⠄⣀⣀⠐⠐⠂⠤⢀⠀⠀⠀⠀⢀⡀⠀⢀⠴⠊⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⢤⠔⠒⠒⠂⠒⡒⠚⡽⡀⣀⠀⠀⠀⡀⠐⠁⠀⠀⠀⠀⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠉⠀⠀⠀⠀⠀⠈⠁⠀⠑⠒⠁⠀⠀⢀⠏⠀⠀⠀⠀⢀⡜⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⣀⠤⠐⠀⣀⡀⠄⠀⠈⠑⠢⠤⠤⠴⢋⢀⢀⡀⠤⠐⠉⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⣠⠔⠋⢀⡤⠚⠁⠀⡠⠂⡠⠀⠀⠀⠀⠀⠀⠰⠀⠀⢄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡠⡚⠁⢀⠔⠁⠀⠀⡠⠊⢀⡜⠀⢠⠀⠀⠁⡜⠀⢀⡀⠀⠸⡄⠀⡆⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⡜⠰⠀⡰⠋⠀⠂⢀⡜⠀⣠⠊⢰⠀⠇⠀⠀⢰⠁⡜⠘⡇⠀⡴⡚⡄⠘⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠁⠜⠀⠀⢀⡤⠊⠀⠊⡁⠂⢸⢸⠀⠀⠠⠃⡰⠁⢸⢱⠀⡇⡇⢹⠀⠸⡀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠊⡱⠀⠀⡠⠊⡔⠀⡈⡘⠀⠰⠁⣠⠃⠀⠸⢸⠀⡇⡇⠀⡇⠀⡃⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡜⢁⠠⠊⢠⠎⠀⢠⠃⡇⠀⠈⡰⠁⠀⠀⡇⢸⠀⡇⡇⠀⢱⠀⢃⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠒⠁⢀⠴⠁⣀⠔⢁⡜⠐⡥⠊⠀⡠⠀⡜⡇⠸⠸⠀⡃⠀⠸⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⡀⠔⠛⢠⠎⠀⠀⡐⠀⡰⠁⡇⢀⠃⡰⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢆⠀⠠⠀⡐⠁⠀⡇⠊⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⢰⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁


⣿⣿⠿⢿⢻⠿⡿⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣄⣠⠤⠤⠤⠤⠤⢤⣄⣀⡀⠀⣀⣠⣠⣾⣦⣴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣯⣛⠻⣿⡤⠮⢍⣴⡞⡏⠒⣛⡿⠿⣿⣿⣶⣮⣭⣛⠯⣟⡟⣺⣿⣿⣦⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⠁⢻⣧⡘⢿⢷⠦⣝⣿⣵⣾⣿⡟⢷⡜⡿⣷⣮⣿⣿⣿⣮⣝⠋⡡⠾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣼⡆⠸⣿⣣⠈⣎⠡⠀⠹⡌⠋⠈⠁⡰⠁⢰⠘⠛⠻⢨⣿⣿⣿⣷⣮⡺⣹⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣧⣿⣇⣽⣷⢄⠃⢀⣇⣼⠀⠀⠀⠀⠈⠀⢸⠧⡤⠊⣰⢿⣿⣽⣿⣿⣷⣝⢾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢰⡟⢉⣤⣄⣀⢈⡉⠙⠛⠋⠀⣹⣻⠷⠶⠤⠤⣐⣙⢠⡴⢋⣜⠀⠛⣩⣿⣿⣿⣿⣯⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠈⢷⣌⣄⠰⠄⠬⠬⠭⠝⠳⢾⣭⣄⣀⣀⣀⣴⣛⠉⠥⢰⠋⢸⣿⣷⣭⣟⣟⡿⣿⣿⣧⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣤⡄⢠⣤⣌⣻⣿⣿⢿⣿⡿⣷⣭⡽⠋⠁⠚⢿⣿⣾⣿⣿⣿⡿⠗⣉⣿⡞⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡈⠉⠛⠛⠓⠙⠒⠈⠁⠀⠀⠀⠀⠀⠙⠻⠿⠛⠁⣾⣿⣿⢯⣷⢻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⢼⣿⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠈⣩⣴⣿⣿⢸⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣦⣄⠀⠀⠹⣿⣿⣜⢫⡇⠀⠀⠀⠀⠀⠘⣿⢿⡛⣿⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢹⣿⣿⣿⠟⠳⢦⣜⣞⢿⣿⣇⠀⠀⠀⠀⠀⢀⣴⣿⣿⡟⣸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣿⠟⠁⠀⠀⠀⠈⠙⢿⣿⣿⠀⢀⡀⠀⠀⣬⣙⣩⣿⢣⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⠇⢻⣿⣷⣄⢿⡿⣿⢛⣼⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⡶⠋⠀⣿⡏⣹⣿⣶⣶⣿⡟⠁⠉⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⢿⣿⣿⡁⠀⠀⢸⣧⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣟⣯⡭⢾⣿⣷⣄⠰⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣷⣾⡿⣻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠟⢫⣾⣿⠃⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣕⡴⣫⣾⠃⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⢀⣤⠉⡁⠁⠀⠐⠀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⣩⣶⣦⣤⠀⠘⠛⠻⢿⢗⣴⣿⣷⠀⣠⣬⠑⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⡋⠀⣼⣿⣿⣿⣿⣧⣴⣶⠖⠡⠾⠿⠿⣿⣾⣿⢧⣼⣆⣿⣦⠈⠑⣄⡀
⠀⠀⠀⠀⠀⠀⡰⣫⣾⠇⣼⢇⠚⠻⣿⣿⣿⡿⢋⠐⣤⠀⠠⠀⠋⣉⠭⠥⠬⠄⠀⠀⣠⣾⣷⣤⡤⠤⣤
⠀⠀⠀⠀⠀⡜⣽⣿⣿⣾⠛⠀⠀⠀⠸⣿⡟⠀⡜⣶⣿⣄⠀⠀⠰⠁⠀⡀⠂⠀⢀⣴⣿⣿⣿⡿⢦⠀⢸
⠀⠀⢀⣠⣾⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠘⠀⣾⣇⠹⣿⣿⣀⠀⠀⢠⠊⠉⠀⣴⣿⣿⣿⣿⣿⡇⠀⠀⡜
⢀⡴⠋⢈⠵⣿⣿⣿⡿⡃⠀⣦⠀⠈⢎⢦⡘⣿⣿⣦⡀⠙⠛⠷⠀⠇⠀⠀⠘⢿⣿⣿⣿⣿⣿⠃⠀⣰⠁
⣎⠀⠀⠀⢺⠿⣿⠿⠋⣠⣾⠛⡄⠑⢄⠙⠍⢌⡻⣿⣿⣿⣶⣤⡀⠀⠀⠐⠠⢈⠛⠿⣿⣿⣷⠎⢠⠃
⠈⠓⢦⣴⡶⠛⠁⢰⡿⠋⠁⠀⠘⢄⠀⣉⠚⢂⠉⠑⠒⠒⠨⢍⡁⠀⠀⠀⠀⠀⠀⠂⠠⠈⣑⠢⠎
⠀⠀⣿⠁⣀⣴⣶⡞⣱⣇⣀⣀⣀⣤⣕⠢⠍⡉⠉⠒⢢⡄⠀⠀⠈⠑⠢⠤⠤⠤⣄⣀⣀⠀⠀⠉⡢
⠀⢀⣹⢾⢿⣿⣿⡟⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣆⠀⠊⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠀⠀⠀⠈
⣠⣋⣀⠐⠉⠽⣿⣿⣶⣿⣿⣥⢄⠆⠀⣹⣿⣿⣿⡟⣸⣷⣶⣶⠾⠂⠂⠁
⠀⠀⠈⢣⢣⠳⣝⠁⢸⡿⡻⣿⣿⡀⠀⠙⠻⣿⡿⢁⣿⣿⣹⣧⣀⡀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠱⣷⣽⠀⢤⣤⣍⣛⡛⠿⣦⢠⣀⠀⢠⣾⣿⣿⢹⣿⡇⢝⢲⣿⣿⣿⣿⣿⡏⢉⣍⡷⠚⠉
⠀⠀⠀⠀⠀⠀⠁⠨⢟⣶⣎⣙⡛⠛⠚⢷⣭⣳⣤⡀⠉⠁⣿⡿⠃⣾⣿⣿⣿⣿⣿⣯⡰⣣⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⢿⢿⣿⠶⢿⣿⣿⣿⣷⣤⣀⠀⠀⠛⠉⠛⣻⣿⣿⣳⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⡰⠋⠀⠉⠛⠿⣿⣿⣷⣦⣤⣴⣿⣿⣿⡏⢷⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⢰⠁⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣻⣿⣿⣿⠧⠀⢣⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⢿⡽⠿⣝⠓⠤⣈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢅⡀⠀⠈⠓⢄⣸⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⣱⠴⠃⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠉⠻⢿⣦⣄⣀⣀⣀⡀
⠀⠀⠀⢠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣼⣿⠄⠀⠀⠀⠉⠛⠛⠛⠛⠻⠿⣿⣶⣦⣤⣀
⠀⠀⠀⠀⢻⣿⠛⠿⣷⣦⣄⡀⠀⠀⠀⠀⢀⣠⣴⡾⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠈⠙⠻⢿⣦⣄
⠀⠀⠀⠀⠈⢿⣧⠀⠀⠉⠛⢿⣦⣄⣴⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣾⣿⡆⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣨⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⣽⡷
⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⣠⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⢀⣾⡟⠀⢀⣠⣴⡿⠛⠉⠛⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⢀⣤⣾⠟⠁
⠀⠀⠀⢀⣾⣿⣴⡾⠿⠛⠁⠀⠀⠀⠀⠀⠈⠙⠻⠿⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⣠⣴⣾⠿⠋⠁
⠀⠀⠀⠈⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡿⠁⠀⢀⣠⣶⣶⣶⣶⣶⣶⣶⣶⡾⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣃⣤⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠛⠉

⠀⠀⢀⡠⠐⠟⠠⣀⠀⠀⠀⠀⠀⢠⣶⠒⢲⣶⠒⢲⣆⠀⠀⠀⠀⠀⠰⠀⣀⡀⠰⠀⠀⠀⠀⠀⢀⡤⠖⠚⠒⢦⡀
⠀⣴⣾⣶⣶⣶⣶⣾⣶⡄⠀⠀⠀⢿⣏⣀⣸⣿⣀⣈⡿⠇⠀⠀⠀⠀⣶⢲⣾⣷⣶⡆⠀⠀⠀⠀⡞⢠⢠⣄⡄⣤⢹
⠀⣿⡏⠍⢉⡉⠍⡙⣿⡇⠀⠀⠀⢸⡏⢹⡏⠉⣿⠉⣿⠀⠀⠀⠀⣠⣿⣴⣿⣿⣿⣧⡀⠀⠀⠀⢷⡈⠉⠉⠉⠉⡸
⠀⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⣼⣿⣿⠇⠀⢿⣿⣿⡄⠀⠀⠀⢧⣶⣶⣶⣶⣶⣦⠇⠀⠀⠀⠀⠙⠶⠤⠶⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀
⠛⠻⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠉⢦⡀⠀⠀⠀⠀⠀⠀⢀⣎⡏⣻⣳⠀⠀⠀⠀⠀⢠⣸⣭⠆⣯⢿⣠
⠀⠀⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢤⣼⣥⣤⣤⣤⣝⣤⠄⠀⠀⠀⠀⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠶⠶⠆⣶⠰⠶⠶
⠀⠀⠘⢛⡛⠛⣛⠋⠀⠀⠀⠀⠀⠈⣷⣺⣒⣗⣺⣲⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⠀⠀⠀⠀⢸⣿⡇⣿⢰⣿⣷
⠀⠀⠀⠻⠟⠘⠿⠃⠀⠀⠀⠀⠀⠀⠸⠾⠧⠧⠿⠞⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠼⠀⠀⠀⠀⠘⠿⠇⠿⠘⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⣉⠀⠁⠈⠀⠉⠈⡁⠀⠀⠀⠀⢸⠀⣿⢸⢸⡆⣿⢸⠀⠀⠀⠀⠀⡿⣶⣶⣤⣭⣭⡷⠀⠀⠀⠀⠀⡠⢪⢭⡙⣦
⠀⠤⠰⣒⠄⢀⣠⠄⠄⠀⠀⠀⠀⢸⠀⣿⢸⢸⡇⣿⢸⠀⠀⠀⢀⣶⣶⣶⣶⣶⢾⡍⡇⠀⠀⠀⣿⣾⣶⣾⣶⣷⣾
⠀⠒⠀⣊⠖⣯⡒⠐⠂⠀⠀⠀⠀⢸⠀⣿⢸⢸⡇⣿⢸⠀⠀⠀⢠⣿⠿⠿⠿⢿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⠽⠀⠀⠉⠁⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠈⠿⠒⠒⠲⠞⠛⠃⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣀⡀⢀⡀⢀⣤⣤
⠀⣴⡶⣶⣶⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠘⡇⣤⣤⣤⠀⠀⠀⠀⢠⣮⣤⣤⣿⣧⣤⣬⣧⠀⠀⠀⢹⠁⢹⡏⠈⠻⠟
⠀⢸⣧⣇⣆⣇⣸⣿⣶⣐⣆⠀⠀⠀⠀⠀⠷⢿⣿⣿⡇⠀⠀⠀⢸⡇⡀⠀⡉⢁⠀⠀⢸⠀⠀⠀⠈⠀⢈⡁⠀⣈⣁
⠀⠿⣿⣿⠿⠿⠿⠿⠿⣿⣿⠧⠀⠀⠀⠀⣞⣻⠜⠒⠀⠀⠀⠀⢸⡃⠏⠘⠞⠚⠃⠃⢸⠀⠀⠀⠰⣤⡞⠁⠈⠙⠋
⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⡿⠟⢛⣉⡩⠤⠤⠤⠤⠤⠤⢍⣉⡛⠻⢿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠋⣡⡴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢦⣌⠙⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⢁⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣦⡈⠻⣿⣿⣦
⠀⠀⠀⠀⢀⡾⣿⡿⠁⡰⠛⡽⠁⠀⢀⣀⣀⣀⣀⣀⣀⡀⢀⣀⣀⣀⣀⣀⣸⡟⠀⠈⢿⠻⢦⠈⢿⣟⢷⡀
⠀⠀⠀⠀⡼⠱⢹⣀⠜⠀⠀⠀⠀⠀⢻⣿⠛⠛⣿⠛⠛⣿⡟⠛⢻⡟⠛⢻⣿⠃⠀⠀⠀⠀⠀⠱⣀⡏⠂⠁
⠀⠀⠀⠈⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠘⣿⡶⣶⣿⣷⡶⣿⣷⣶⣿⣷⡶⣾⡏⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠁
⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣀⣽⣇⣀⣿⣇⣀⣿⣁⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢹⣟⣉⣿⣏⣹⣿⠉⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⢸⣇⣠⣴⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⠉⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣦⣄⣸⡇
⠀⠀⠀⢀⣤⣾⢿⡿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⡿⣷⣾⣶⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⡟⣶⣤⡀
⠀⠀⠀⢿⣿⣿⡎⢧⠀⠃⢉⣊⠣⠉⢈⣁⢃⡘⠐⣈⠙⣉⢊⠁⣂⢂⣘⢓⣀⠋⢉⡋⣉⢡⠀⠀⡾⢱⣿⣿⡿
⠀⠀⠀⠈⢿⣿⣿⡌⢣⠀⣿⡿⣥⣼⡟⢉⣟⢹⣿⣿⣾⣷⣿⣿⣿⣿⡯⢿⣽⣿⡟⠉⣿⠿⠀⡼⢡⣿⣿⣿⠁
⠀⠀⠀⠀⠈⢿⣿⣿⣄⠡⡙⠛⠀⠀⠙⠋⠙⠋⠉⠉⠁⠉⠋⠉⠙⠙⠛⠉⠈⠁⠙⠋⠙⢛⠊⣠⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣦⡀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠼⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⠿⢿⣿⣶⣶⣤⣤⣤⣤⣤⣤⣶⣶⣿⣿⡿⠿⠛⠛⠁




⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣋⣉⣉⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢦⡀⣠⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⡀
⠀⠀⢸⠉⠩⡍⢉⢉⠉⠉⢻⠀⠀⠀⠀⠀⠀⠀⠹⢤⡀⣣⡇⣠⠼⠃⠀⠀⠀⠲⠲⡄⠀⠀⠀⠾⠗⠀⠀⠀⠀⠀⠀⠀⢠⡼⣛⣭⣷⣮⣍⡻⣤
⠀⠀⢸⠀⠀⠹⡿⡿⠀⠀⢼⠀⠀⠀⠀⠀⠀⢰⠒⠒⠒⣶⡶⠒⠒⢲⠀⠀⠀⠀⠀⢻⣶⢶⡶⢶⡶⣶⡶⣶⡆⠀⠀⠀⣾⠁⣿⠛⡟⡛⢻⡟⢸⡆
⠀⠀⠸⣤⣤⣤⣤⣤⣤⣤⡾⠀⠀⠀⠀⠀⠀⠘⡿⠿⠿⣿⡿⠻⠿⡟⠀⠀⠀⠀⠀⠀⢿⡾⢳⡞⢳⡞⢶⡿⠀⠀⠀⠈⣿⠀⣿⣚⣛⣷⣸⣇⢸⡏
⠀⢀⣾⣿⣿⣿⠛⢻⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⠻⡛⠿⠿⢻⠟⠁⠀⠀⠀⠀⠘⢧⣝⠿⢿⠿⢟⣩⠿
⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠳⠶⠶⠿⠷⠶⠶⠃⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠛⠋⠉

⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⢠⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤
⠀⠀⡏⢰⣶⣶⡆⡶⢦⡖⠘⡇⠀⠀⠀⠀⠈⢷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠖⠶⠶⠤⣤⣤⣤⣤⠀⠀⠀⠀⣾⣿⣿⣿⣿⣋⢀⣈⣿⡆
⠀⠀⢧⡘⠷⠛⠳⠃⠘⢀⣰⠇⠀⠀⣠⠤⣤⠤⣿⣶⠶⠦⠤⠄⠀⠀⠀⠀⠀⣿⠁⣴⡶⠶⠶⢤⣤⣝⣛⣀⣤⠀⠀⢸⣿⢫⠶⠶⠶⠶⠶⠶⠶⠶⡄
⠀⠀⠀⠉⠉⠁⢻⣶⣭⡍⠁⠀⠀⠀⠓⠶⠋⠐⠊⠻⣆⠒⠀⠒⠐⠂⠀⠀⠀⣿⠇⡟⠁⠀⣴⡋⢿⡄⠈⠻⣿⠀⠀⠈⣿⢸⣷⣶⣶⣶⣶⣶⣶⣾⡇
⠀⠀⠀⠀⠀⠀⠈⠿⢻⣦⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠓⠀⠀⠀⠃⠀⠀⠀⠀⠀⣿⣧⣄⣘⣯⡞⠁⢀⣴⣿⠀⠀⠀⠀⢸⠀⠶⠶⠶⠆⠠⠶⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠁⠘⠀⠉⠀⠉⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠉⠉⠀⠀⠀⠀⠈⠙⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⣿⠀⠀⠉⢓⣆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠈⠳⢤⣘⣉⣉⣭⢹⡇⠀⠀⠀⠀⠀⠸⢋⣴⠏⠛⢿⡿⠋⢸⡇⠀⠀⠀⣠⣤⣤⣀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⢀⡟
⠀⠀⠀⣠⠞⣡⠀⠉⠉⠉⢸⡇⠀⠀⠀⠀⢀⡴⡏⠚⢷⡾⠋⠀⠀⢸⡇⠀⠀⣾⢣⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣤⣤⢀⡾⠋⠀⠸⣧⠤⢤⡀
⠀⠀⢾⡁⠞⢿⣷⣤⢀⡴⠋⠀⠀⠀⠀⠀⢸⣷⣖⡾⠋⠀⠀⠀⠀⢸⡇⠀⠀⠹⣧⣻⣿⣿⣿⣟⡽⢒⠶⣄⠀⠀⠀⢸⣿⣿⢸⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠙⢦⡀⢟⡵⠋⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠻⣿⣿⣿⢸⡑⢾⠗⣸⠀⠀⠀⢸⣿⣿⢸⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⠒⠒⠚⠃⠀⠀⠀⠀⠀⠈⠙⠋⠀⠙⠒⠚⠁⠀⠀⠀⠘⠛⠛⠘⠓⠒⠒⠒⠒⠒⠛
⠀⠀⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢠⡞⠛⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⠀⢀⠴⠛⠛
⠀⠀⠀⡾⢻⡟⠿⠟⣿⢻⡆⠀⠀⠀⠀⠲⢠⡶⠶⠶⠶⠶⠶⠶⡆⠀⠀⠀⠀⠀⠀⠘⣇⠀⣀⣠⣴⣦⠀⠀⠀⠀⠀⠀⢀⣶⣶⣶⣶⣶⣶⣶⣦
⠀⠀⠀⡇⠈⢁⠀⠀⠉⢸⡇⠀⠀⠀⠀⠠⢸⡇⠀⠀⠀⠀⠀⠀⣷⡤⠤⡄⠀⠀⠀⢠⡿⡜⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⡟⣛⣛⡛⠛⠛⠛⠛⠛⡇
⠀⠀⠀⡇⠐⣿⣿⣿⡇⢸⡇⠀⠀⠀⠀⠈⢸⡇⠀⠀⠀⠀⠀⠀⣿⣶⣶⣿⠀⠀⠀⠈⢧⢛⣽⣛⠿⢟⣻⡄⠀⠀⠀⠀⡇⠉⠉⠁⢠⣦⠀⣶⠀⡇
⠀⠀⠀⡇⠀⠈⠛⠋⠀⢸⡇⠀⠀⠀⠀⠀⠸⢿⠫⢻⠶⠶⠶⠶⢿⡟⢝⡿⠇⠀⠀⠀⠀⣏⠶⣸⡇⠉⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸⠇⠀⠿⠀⡇
⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡍⠛⠿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠙⠻⣷⣶⣶⣶⣦⣤⣤⣀⣀
⠀⠐⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢉⣿⡿⠿⣷⣦⣄
⠀⠀⠹⣿⡌⠙⠻⢿⣶⣤⡀⠀⠀⠀⣀⣤⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠉⠛⢿⣦⣄
⠀⠀⠀⠹⣿⣄⠀⠀⠈⠙⢿⣷⣴⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⢀⣀⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠘⢿⣧⡀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣿⣿⡷⠀⠀⠀⠘⢿⣦
⠀⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣸⣿⠁
⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⣠⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁
⠀⠀⢀⣾⡟⠁⢀⣠⣴⣾⠟⠉⠈⠛⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠀⠀⢀⣤⣾⠟⠋
⠀⠀⣾⣿⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⣠⣴⣾⠿⠋⠁
⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⠁⠀⠀⣀⣴⣶⣶⣶⣶⣶⣶⣶⣶⡿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣃⣠⣴⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠶⠶⠶⠦⠄⠉⢙⣳⣤⣀⣀⣤⣤⣤⣄⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡛⢛⣣⡤⠶⣚⡛⠉⢩⡄⠀⣀⠀⠶⠀⠀⠀⠀⠈⠉⠉⠙⠓⠲⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡧⠞⠋⠁⠤⢀⣈⠀⠠⠄⠀⠀⠉⠀⠀⠈⠀⡴⠁⠀⡴⣢⡒⡄⠀⠀⠀⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢫⠀⠘⠃⠴⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠙⠾⠚⢁⣠⡴⠖⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⡀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠾⣿⣿⠤⠄⣲
⠀⠀⠀⠀⠀⠀⢀⣤⣾⢃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⣛⣋⠙⠓⠒⠄⠀⠀⠙⠄⠀⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⢰⢏⢠⡇⠈⢀⣀⡤⠀⠀⠀⠀⢀⣀⣀⣼⣯⡡⠄⠀⠀⢀⣄⣀⣀⣀⣀⣤⣤⠴⠖⠛⠉
⠀⠀⠀⠀⠀⢸⣧⢸⠇⢠⡯⢒⠀⠀⣠⠴⠚⠉⠁⠀⠀⠀⠙⠺⠶⠚⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠙⢻⡄⠀⠛⠗⠋⣰⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠇⢸⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⣠⠏⠀⠐⣄⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡶⠖⠊⠁⢀⠈⣦⠞⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠐⡄⠘⣶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⢸⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⡼⠋



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

⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠈⢉⣉⡉⠁⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⣰⢠⡆⣰⠀⣆⢰⡄⣆⠀⠀⠀⠀⠀⢰⣦⣤⣤⣶⣴⠂
⠀⠀⠀⠀⠀⠸⠻⠀⣾⣷⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⠃⡘⠁⢹⣄⠛⠈⢣⠘⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠰⠔⠂⠈⠁⠀⠀⠀⠀⠀⣯⣭⣽⣯⣭⣭⣿⣿⡇⠀⠀⠀⠀⠀⣇⣀⣀⣁⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠸⠿⠭⠿⠇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿


⠀⠀⠀⠐⠒⠒⠒⠒⢲⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⣶⣖⣶⣶⣶⢰⠋⠉
⠀⠀⠀⠀⠀⠻⠟⠀⣴⢲⣦⠀⠀⠀⠀⣭⣤⣼⡟⢻⣷⣤⣬⡅⠀⠀⠀⠀⠀⠹⠿⠿⠿⠇⡟⠀⠀⠀⠀⠀⠀⠀⠘⠙⠈⠉⠸⣶
⠀⠀⠀⠀⠀⣤⢠⠀⢿⣠⡿⠁⠀⠀⠀⣟⠛⠻⢯⡽⠟⠛⢻⡁⠀⠀⠀⠀⠀⠀⣛⡛⢛⣏⠁⠀⠀⠀⠀⠀⠀⢠⣠⣀⣀⣀⣀⣀⣠
⠀⠀⠀⢠⣤⣤⢠⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠓⠉⠙⠞⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠿⠿⠏⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⣃⣈⣇⣀⣀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡾⣵⡋⣝⣷⣹⡀⠀⠀⠀⠀⣀⡔⣀⣾⠉⣩⠉⠉⢹⡆⠀⠀⠀⠀⢩⢯⣯⣭⣿⣽⣽⡍
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣶⠁⠀⠀⠀⠀⠀⢷⡻⣝⣢⡿⣸⠁⠀⠀⠀⠀⢿⣿⡿⠿⠷⠷⢶⣥⡾⠀⠀⠀⠀⠀⠘⡟⡅⣧⡟⣓⣹⠁
⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠙⠒⠖⠋⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉

⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠠⡀⡠⠤⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣠⣄
⠀⠀⠀⣉⣉⣉⣉⣉⣉⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠿⢻⡆⠀⠀⠀⠀⠀⠀⢠⣤⣤⣼⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄
⠀⠀⠀⡟⠛⢛⠛⡟⠛⠀⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⣄⠀⡀
⠀⠀⠀⡇⠤⠨⠠⡇⢽⠀⠀⠀⠀⠀⠀⠀⢈⣿⡷⢶⣟⣏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⣀⣛⡃⣸⣷⣿⡄
⠀⠀⠀⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠘⠿⠟⠿⠛⠿⠿⣿⠆


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⣀⡀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠈⠄⠀⠀⠀⠉⠡⡷⠽⠀⡌⠤⣄⢤⣤⣤⢤⢤⣼⣼⢢⡀⠀⠁⢶⣶⣶⣶⣶⣶⡆⢀⣚⡠⡄⣌⡂
⠀⠀⠀⠀⣀⠀⠀⠀⠤⠘⠀⡄⠾⠟⠳⠆⠀⠀⠀⡏⢁⠢⠁⠀⠀⠈⠿⠛⠛⠛⠛⠀⠀⡜⠁⠽⠏⡀
⠀⠀⠈⠉⠀⠁⠀⠀⠀⠀⠀⡇⠘⡃⠛⠘⠛⠃⠻⠈⢹⠀⠀⠀⠀⠀⢸⡿⠉⢽⡇⠀⠀⢢⣄⡀⣴⠃
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⣸⡟⠛⠛⠒⠚⠀⡄⠤⠀⢀⠀⠀⠀⠀⠀⠀⣀⡈⢀⡀⠈
⠀⠀⣡⠤⠤⠤⢬⡀⠀⡀⠀⠀⠀⠀⠦⠥⠈⠄⠀⠀⠀⠀⠑⠚⠘⠐⠲⠃⠀⠀⢀⠀⠫⠠⡀⠀⢃⣨⠇
⠀⠀⡇⣀⣝⣉⠘⠐⢣⡁⠀⢀⣥⢧⠀⡄⠀⣠⡀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠐⠉⢀⣄⠑⡮⢷⠻
⠀⠀⡇⣻⣏⣿⢰⠀⠀⠀⠈⡂⠉⠈⠀⠴⠾⠓⣷⠤⠀⠀⠀⢀⣰⡈⠁⣦⣀⠀⠐⠛⠛⠀⠇⠟⠁
⠀⠀⠃⠛⠛⠛⠐⠀⠀⠀⠀⠳⠄⠐⠈⠃⠀⠀⠈⠀⡆⠀⠀⠀⣂⣒⣴⣀⠃⠀⠀⠀⢀⡀⠀⠠⣄
⠀⠀⠃⠀⠐⠁⠀⠀⠀⠀⣀⡀⠀⠀⣀⠀⢐⠢⠀⠀⡀⠒⠒⠂⠒⡒⣒⠒⠀⠐⠂⢀⡈⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠤⠀⢈⡔⠆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⡏⠃⠀⣀⠀⠀⠀⠳
⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠎⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣰⣀⣦⠀⡤⠀⠈⠈⠈⠉⠈⠉⠀⠀⠀⠀⠀⠀⡀⠀⡤⡀⡄⠐⠆
⠀⠀⠀⠀⣀⢀⠀⠀⢸⡁⠀⠀⠀⣀⠟⣠⠚⠆⠀⠀⠀⠀⠈⠀⠀⠀⢤⣄⠲⡢⢀⣰⣦
⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇⠀⢀⣀⣉⣉⡝⠀⠃⠀⠀⠀⠃⠐⠀⢰⠀⠆⠍⡍⠲⡇⣟⠋
⠀⠀⣀⣀⠀⠀⢀⣀⣀⡄⠀⠀⠀⠀⠈⠑⠒⠃⢀⡀⠀⢀⡀⠀⠀⠤⠤⣄⣣⠠⠛⢀⣀⣄⣀
⠀⠀⠀⠀⢠⡆⢠⠀⢸⠖⠶⠦⡀⠀⠀⣠⡔⣪⠥⣦⢤⡐⢈⢢⠀⠀⠀⠀⠀⠦⠖⠇⡁⡀⠄⠘⠦⠤⠂
⠀⠀⢀⣀⣘⠀⠙⠀⢸⡇⣀⢀⠙⡄⠈⠻⢽⡃⠈⠙⠀⢹⠉⡢⠄⡀⡂⠀⠉⡖⠂⠀⠴⢻⠃⠀⠀⠐
⠀⠀⠹⣅⡽⠁⠀⠀⠈⠉⣏⢹⠟⠁⠀⠀⠈⠓⠤⣀⣀⢈⡠⠁⠈⠀⠀⠀⠀⠁⠀⠉⠐⠈⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⣿⣟⣛⣟⣛⣻⣛⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠒⢶⠶⠒⠢⠤⣄⡀⠀⣀⡤⠤⠒⠒⠛⠉⠉⠉⠉⠉⣩⠗⠒⠢⠤⣄⡀
⠀⠀⠀⠀⠲⣶⡒⠋⠀⠀⠀⣀⠴⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢠⣤⣤⡀⠉⠓⠲⠤⠤⠤⣤⣄
⠀⠀⠠⣤⡔⠃⠀⠀⢀⡴⠊⠁⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠘⠀⠀⠀⠀⣿⢸⣿⣷⠀⠀⠀⠀⣠⠖⠉⡟
⠀⠀⠀⠈⡇⠀⢀⡴⠋⠀⠀⠀⠈⢀⡢⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠁⠀⠀⢠⠞⠁⠀⡜
⠀⠀⢰⡛⠀⣠⠎⠀⠀⠀⠀⠀⠁⠀⠁⠘⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣞⠀⠀⠀⠃
⠀⠀⠀⡇⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣀⣸⣀⠀⠀⠳⢦⣀
⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⡀⠀⠤⠭⢽⣛⣒⣛
⠀⠀⢠⡇⠀⠀⠀⠀⣤⠞⠉⠉⠀⠀⠀⠀⠀⠀⠑⢄⡈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⡤⠔⠊⠁
⠀⠀⣸⠀⠀⠀⠀⢸⡗⠂⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁
⠀⠀⣿⠀⠀⠀⠀⠀⠻⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣲⠶⠒⠚⠉⠁
⠀⠀⣯⠀⠀⠠⠈⡄⢄⠀⠉⠛⠒⠒⠒⠊⠁⠀⠀⠀⠀⢀⣤⢾⢫⠃
⠀⢰⢿⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠘⠀⠘⡆
⠀⡼⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠸⡄⠀⠀⠀⢳
⢀⡇⠀⢳⠀⠀⠀⠀⠀⠀⠠⠡⠐⠀⠀⢀⡴⠋⠀⠀⠀⠙⠦⣀⡀⠈⣇
⣸⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠁⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⡏⠀⠀⠀⠸⣆⠀⠀⠀⠀⡀⠀⢠⠞
⠻⣄⠀⠀⠀⠸⣆⠀⠀⢰⠁⠀⣿⠀⠀⠀⢶⠤⢤⣀
⠀⠈⠙⠒⠶⠴⠋⢧⡀⣾⠀⠀⢹⠀⠀⠀⢸⡄⠀⠈⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣧⡀⠀⠣⣀⣀⣸⢃⠀⡀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⠀⠈⠉⠙⢮⢖⡡⢠⣼⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⢸⣿⠦⠤⠀⠀⠀⠉⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠪⢍⣑⠒⠀⠀⠀⠀⠀⠀⠈⢣⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠿⠿⠿⠿⠿⠿⠿⠖⠾⠶⠿⠿⠿⠿⠿⠿⠗⠒⠒⠒⠲⠷⠿⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⡄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠛⠛⠛⠛⠛⠛⠛⠛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢠⡾⠛⠻⣦⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣼⣷⡶⣶⣶⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣇⣀⣠⡿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠋⣵⠟⠁⠀⣿⠀⠈⠻⣮⡉⠛⠷⣤⡀⠀⠀⠀⠻⣦⣈⣉⣉⣀⣀⣀⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⣼⠏⠀⠀⠀⣿⠀⠀⠀⠘⣷⡀⠀⠈⠻⣦⡀⠀⠀⠀⠉⠉⠉⠉⢹⡏⠉⣿⠉⠁
⠀⠀⠀⠀⠀⠀⣠⡿⠻⠶⣤⣄⣼⣏⠀⠀⠀⠀⣿⠀⠀⠀⠀⢘⣧⣠⣤⡶⠞⠻⣦⣤⣤⣤⣤⣤⣤⣼⠇⠀⣿
⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⢩⡿⠙⠛⠛⠛⠛⣿⠛⠛⠛⠛⠋⢻⡏⠀⠀⠀⠀⠹⣧⣀⣀⣀⣀⣀⣀⣀⣠⡿
⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⢻⡏⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⢾⡷⠶⠶⠶⠶⠶⣿⠶⠶⠶⠶⠶⠶⣿⠶⠶⠶⠶⠶⠶⣿⠶⠶⠶⠶⠶⠶⣿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⢈⣷⣀⣤⣤⣤⣤⣿⣤⣤⣤⣤⣄⣼⡇⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠙⣧⣴⠶⠛⠋⢻⣏⠀⠀⠀⠀⣿⠀⠀⠀⠀⢩⡟⠙⠛⠷⢦⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⢻⣄⠀⠀⠀⣿⠀⠀⠀⢠⡿⠁⠀⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⣀⡻⣦⡀⠀⣿⠀⢀⣴⠟⣁⣤⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠷⠿⠿⠿⠛⠛⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⡿⠿⠿⠿⠿⠿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⢛⣉⣥⣤⣤⠶⠶⠦⠤⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣾⣟⣥⡶⢚⣋⣩⣥⣴⠶⠶⠦⠤⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠛⠉⠁⣸⡿
⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠿⠛⠋⠉⠉⠉⠁⠀⠉⠉⠉⠉⠛⠛⠻⠿⣶⣶⣶⡒⠒⢒⣠⣾⠏⠀⠀⠀⠀⠀⠀⣠⡾⠛⣡⡴⠚⠁⣰⡿⠁
⠀⠀⠀⠀⢀⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣭⡀⠀⠀⠀⠀⠀⣠⡾⢋⡴⠟⣁⣤⠀⣼⡟⠁
⠀⠀⠀⣠⡿⠋⣠⠤⠤⣄⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣤⣤⠾⠋⠀⣩⠶⠛⣉⣀⣼⡟
⠀⠀⣼⠟⠀⣼⣥⣈⣷⡌⡆⠀⠀⠘⣆⠀⠀⠀⣀⣴⣶⣶⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠉⠁⣿⡇
⣠⣾⠏⠀⠀⠹⣌⣛⣛⡴⠃⠀⠀⠀⣿⠀⣠⠾⡋⠁⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⠛⠛⠓⠻⣿⡄
⢻⣷⣤⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢠⣿⠘⢑⣪⠀⣾⠏⠀⠀⠀⠀⠀⠀⠐⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣍⡛⠶⢤⣰⡿⠃
⠹⢷⣬⡛⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠰⠶⠶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣤⡶⠶⢶⣄⠀⠀⢮⣙⠦⣄⣿⡇
⠀⠀⠈⠙⠷⣦⣀⡀⠀⠀⢀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⣤⡾⠋⠁⠀⠀⠀⠙⢷⣌⠢⣍⠳⣄⠻⣧
⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣟⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣶⣾⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡈⠳⣌⡙⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⢿⣿⠿⣿⠷⠶⠶⠶⠿⠿⣿⡻⢟⡻⢟⡦⠭⠙⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣌⡙⠢⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⡻⣕⡘⣷⠀⠀⠀⠀⠀⠘⢿⣦⣙⠲⢭⣙⡒⠂⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⣶⣾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣭⣸⡧⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⣬⣉⣛⣓⣨⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣶⣶⣶⣶⣦⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⣉⣉⣹⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣀⣀⡀⠀⣀⣀⡀⠀⣀⣀⣀⠀⣀⣀⣀⡀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠘⠿⠿⠇⠀⠿⠿⠇⠀⠿⠿⠟⠀⠿⠿⠿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣤⣤⠀⣤⣤⡄⠀⣤⣤⡄⢠⣤⣤⡄⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⠿⠿⠀⠸⠿⠇⠀⠿⠿⠃⠸⠿⠿⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢰⣶⡄⢠⣶⡆⠀⣴⣶⠀⣰⣶⠄⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠈⠉⠁⠀⠉⠁⠀⠉⠉⠀⠉⠉⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣀⣈⠙⣿⣿⣿⣿⡟⢉⣀⡈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠇⢸⣿⣿⣿⠀⢾⣿⣿⠆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣉⣁⣤⣿⣿⣿⣿⣷⣄⣉⣁⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇⠤⢾⣿⣿⢩⣤⣾⢡⣦⡙⣿⠀⢿⠁⢹⠇⠸⡏⠈⡏⠠⢼⡇⠴⠌⡟⢡⣦⡿⠠⠴⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣇⣛⣻⣶⣷⣌⣛⣻⣌⣛⣡⣇⣰⣀⣇⣸⣀⣇⣰⣄⣇⣘⣛⣇⣰⣄⣧⣈⣛⣧⣘⣛⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⠿⠿⠛⠛⠉⠉


⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠿⠟⠻⣿⣷⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⠉⠀⠀⣀⠀⠘⠋⡽⠛⠛⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⣤⡄⠘⠋⠀⠀⠄⣴⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢯⣧⡁⢸⡀⠀⠠⠸⣄⡟⡇⠀⢠⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠈⠻⣌⠀⢰⠂⠀⣼⢃⡷⠀⠸⣇⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠶⠛⠛⠛⠛⠛⠿⠶⣤⣄⠀⢀⡾⠁⠀⠀⠀⠀⠀⠈⠢⣤⣤⣶⣿⠿⠁⠀⠀⣿⠀⠀⣠⣿⣦
⣠⡤⠤⠤⠶⠶⠶⠶⠾⠛⠋⠉⠀⠀⠰⠶⢦⣿⡷⢰⡄⠀⠙⢿⣾⠁⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠁⠀⠀⠀⠀⢰⣿⡦⠞⠉⠹⡝⣧⡀
⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠄⠀⢿⡄⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⢀⡼⠀⠀⢀⡾⠙⠳⢦⣀⡀⠙⠙⠙⢢⡀
⠀⠹⣦⠀⣀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣼⢷⡀⠀⠀⠀⠀⠀⠛⠻⣦⣴⢎⡴⢃⡤⠊⠀⠀⠀⠀⠹⣟⠂⠀⠀⢳⡙⣆
⠀⠀⠈⠻⣦⣀⠀⠀⢀⣤⣶⠻⢛⡯⢹⣽⣇⣶⣄⠀⢀⣄⡀⢀⣿⡄⠻⣦⡄⢀⡤⠞⠛⠻⢿⣷⣫⢄⣿⠁⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠑⠘⡆
⠀⠀⠀⠀⠈⠙⠳⣾⣯⣳⣞⢛⣁⡴⠼⠒⠛⠛⠻⠷⢈⠓⣌⠛⢧⡻⠦⠹⣤⡿⢤⡀⠀⠀⠈⠻⣿⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣏⣉⣀⣀⣀⣉⣉⠀⢠⡏⠤⠀⠀⠀⠀⠈⠓⠒⠻⢻⣆⠙⠂⠀⠀⠀⠛⠾⠶⢤⣀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣈⣳⣄⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠛⠛⠉⠉⠉⠉⠉⠛⠶⣭⠥⠀⠀⢀⣀⡀⠀⠀⣈⣉⣛⣦⣜⠦⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⣰⠋⠀⠀⠀⠉⠙⢷⡀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⣠⠞⠓⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠙⠛⠻⢯⣭⣭⣶⠶⠛⠉⠉⢙⡷⣍⣲⠤⣤⠀⠀⠀⠤⢀⡈⠙⠛⠓⠚⠉⢀⡒⠢⣄⠳⣄⢠⠹⣄
⠀⠀⠀⠀⠀⣼⠃⢀⡴⠺⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠤⠖⠋⢠⢿⠉⠙⠛⠛⠛⠒⠒⠶⠦⣤⡀⠀⠀⠀⡏⠉⠉⠁⠀⠈⢢⣼⠃
⠀⠀⠀⣠⡾⠃⣀⢿⡀⠀⠈⠳⢤⣘⠳⠦⣤⣤⡤⠖⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠖⠁⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠠⠐⠀⠀⠀⠀⠀⠀⡷
⠀⠀⣾⠁⠀⢠⣴⠞⠛⢦⡀⠀⢀⣹⣿⣦⡼⠟⠛⢒⡶⠮⠭⣭⡤⠤⣤⣶⣿⣛⣋⠉⠰⣄⢀⡿⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠦⣴⣦⣤⣤⠾⠃
⠀⠀⢿⣄⢀⡞⠁⠀⠀⠈⢷⣴⠏⠀⠀⡿⠁⠀⠀⠋⠀⣀⡴⠋⢀⡼⠛⠉⢁⠟⠉⠙⣦⡘⣿⢁⣤⠶⠛⠿⢦⡀
⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⣠⡟⠁⠀⢀⠎⠀⠀⢰⢿⣿⣳⡿⣡⣾⣟⡛⠋⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⡄⠀⠀⠀⠀⣀⣠⠴⢾⡟⠀⠀⠀⠈⠀⠀⣠⢣⠟⠀⠛⣼⠃⠀⠀⠉⠢⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⣴⠟⢉⣁⣤⣴⡟⠀⠀⠀⠀⠀⢠⠞⡱⠋⣤⡀⢰⣿⣀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣠⠞⠋⡍⠀⠉⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢸⣿⣿⣇⡉⠓⠦⠀⠀⡀⠀⠐⠂⠉⠀⠀⠈⠙⡷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠁⠀⠰⡇⠀⠀⠴⠋⠀⣀⣠⠞⠁⠀⠀⡀⠘⢹⠏⢻⡝⠳⠒⠒⠤⠼⣶⣶⠾⣇⠀⠀⠀⢠⡇⠈⠻⣆
⠀⠀⠀⠀⠀⢠⡾⠋⢙⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⢱⣀⣰⣦⣤⠾⢿⣄⣀⡀⣀⠴⠁⣠⠟⢦⡀⠙⠀⠀⠀⣠⡾⠋⠈⢻⡦⢄⣠⣴⠏⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⢸⡇⠀⢺⡀⠀⣀⣤⡤⠶⠶⠖⠚⠛⠛⠉⠉⠁⠀⠀⠀⠙⢿⣤⣴⡶⠛⠣⣄⠀⠀⠀⠈⢀⣴⠏⠀⠀⠀⠈⢷⣄⡿⠉⠛⠳⢦⣄⠀⠀⠹⣆
⠀⠀⠀⠀⠀⢰⠅⢀⠎⢙⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠶⢤⣤⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠳⣄⠀⢘⣦
⠀⠀⠀⠀⠀⣿⠀⠸⢧⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⠉⠛⢧
⠀⠀⠀⠀⠀⠹⣆⡀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠛⠻
⠀⠀⠀⠀⠀⠀⣈⣛⣶⣾⣏⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣿⣤⣀⣀⣀
⣀⣀⣀⣀⣀⣉⣛⣛⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣛⣛⣛⣉⣉⣉⣉
⣿⣿⡿⠛⠟⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣠⣶⣿⢶⡦⣄⠀⠀⠀⠀⠀⠴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠷⠾⠁
⠀⣀⠀⡀⢻⠸⣿⢸⠃⠘⠓⠒⠄⢀⠀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠉⠀⠈⠁⢸⠀⡇⠘⢸⡇⠀⠀⠀⠘⠉⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣈⠙⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠂
⠀⠀⠀⠀⠀⣶⠀⣆⢸⡧⠀⠊⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⣠⡄⠰⠘⣿⣁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠙⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⢩⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣉⣀⡤
⠀⠀⠀⠀⠀⠀⢠⣶⠤⠶⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⣠⣤⠴⠶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⢀⠂⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠾⠿⠛⠻⠿⢶⡆⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢤⠄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡱⠆⠀⠀⠠⣶⣛⠉⠠⠄⠐⠒⠒⠛⢛⣫⣇⠘⠀⠀⠀⠀⠀⢰⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣛⡛⠿⠿⠿⢛⡛⠉⠁⠀⠀⠀⠀⣠⣦⠈⠻⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⢠⠘⣿⡷⠂⢤⡆⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠄⠁⠀⢹⣇
⠀⡤⠤⢤⡀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢰⠀⠞⠆⢰⠀⡆⢸⠋⢠⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢃⢴⣿⣶⠀⠹
⠸⠁⢠⣶⣿⣯⠈⠉⠀⠀⡀⠈⠁⠀⠀⠀⠒⠤⢄⡀⠀⠀⢸⡀⢸⠀⢆⠀⢸⠀⡇⢸⠄⠘⣄⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⣾⣿⠑⣠⣦⡀
⠈⠰⣿⣷⣿⣿⠀⠀⠀⠀⠡⠈⠀⠀⠀⠀⢀⣠⠤⠄⠀⠀⢸⠀⢸⠀⠀⢣⢸⡤⡇⢸⠀⠀⠈⠆⠀⠀⠈⠁⣀⠄⠀⠀⠀⠀⠀⢀⣉⣼⣿⣿⠏
⠀⠀⠈⠛⠿⠃⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⢸⠀⢸⠀⠀⠈⢸⠀⡇⢸⠀⠀⠀⢸⠀⠀⠀⠢⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠸⠀⠸⠀⠦⠜⠸⠀⠇⠸⠄⠘⠤⠎
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣦⣠⣄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣤⣤⣄
⠀⠀⠀⠀⠀⡀⠘⢿⣿⡌⠙⢿⣿⡄⠐⣦⣤⡀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⣤⠀⠀⣠⠄⢸⡿⠁⣼⠋⢈⡷⠂
⠀⠀⠀⠀⠈⠋⠀⢸⣿⡿⠀⢸⣿⡇⠀⣼⣿⡧⠙⠿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⡷⠀⣿⠀⢸⡇⠀⣿⠀⢸⡇⠐
⠀⠀⠀⠀⠀⠀⠰⠿⣿⣁⣴⣿⡟⠁⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⢠⡾⠟⠀⠀⠻⠀⢸⣧⠀⢿⡄⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠛⠛⠁⠀⠀⠀⠀⠀⢀⡀⠆⠠⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⢀⣴⣇⠀⠀⢻⡇⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢿⠀⠀⠸⡟⢂⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠈⠻⢉⣾⡿⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡆⠀⠰⣷⢼⣷⡀
⠀⠀⠀⠀⠚⢿⣷⡄⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠉⢿⡶⠖⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢰⣧⢼⡿⠁
⠀⠀⠀⠀⢤⠄⢹⡇⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢁⣴⣦⠉⠝⠃⣄⡀⠀⣠⣶⠇⠀⠀⠀⠀⠛⠃⠤⠐⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡇⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠙⢁⠆⠿⢟⣻⠡⣾⣿⣯⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢻⡿⠶⡗⠘⣿⠇⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣠⣤⣬⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣿⣿⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠲⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⠢⢁⠂⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠻⣄⠢⡀⠠⡁⠢⡁⠐⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡁⠀⠀⠘⢷⣀⠀⡈⠂⠐⡈⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠙⢦⡀⢀⣐⣽⣷⣤⣤⣦⣤⣤⣀⣹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣀⣠⠴⠛⠋⠩⠋⠈⢁⢀⣷⠰⣄⣸⠋⢙⡶⢤⡀
⠀⠀⠀⠀⠀⠀⢀⡶⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠟⢻⡁⠀⢀⠠⢀⠰⣄⠀⣼⣏⣐⣅⣨⡵⠛⢧⠀⠈⠳⣄
⠀⠀⠀⠀⠀⣰⠏⠰⣌⣳⡀⠀⠀⠀⠀⠀⠀⢀⣴⠗⢋⣽⢷⡀⠀⠀⠁⠀⣼⣶⡋⢀⣿⠈⣽⠀⠦⣼⠇⣀⣀⡈⢳
⠀⠀⠀⠀⢰⠏⠀⠀⠌⠛⢷⣄⠀⠀⠀⢀⣴⡻⣥⠞⣋⡴⠞⢳⠀⢀⣠⣬⡏⠨⡙⢦⢀⣷⠷⣄⣠⠟⠸⣩⠤⠤⣌⢧⡀
⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠈⣹⠋⡶⢻⠉⢣⠹⡜⣏⡥⠶⠚⢛⡇⣿⢀⢄⠱⣄⠑⣘⣟⡙⣆⠌⢻⡀⠀⣧⣤⠀⠘⡆⠙⠲⢄
⠀⠀⠀⠀⡏⠄⠀⠄⠀⠀⠀⢹⡄⡇⢸⡀⠀⣇⢳⠸⡶⠖⠚⠛⣿⢘⣦⣄⣳⣬⣷⣾⣿⡷⠾⣤⣽⠁⠀⣿⡿⢀⡴⠃⠀⠀⠈⡇
⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠈⢧⠹⡀⢧⠀⡼⣸⠀⡗⠒⠒⠛⣿⡏⠀⠀⠠⠤⠽⠟⣿⣒⠃⢠⢿⣄⡀⠈⠙⠋⠠⣄⡀⠀⣠⠇
⠀⠀⠀⠀⢧⠀⠀⠀⠁⠀⠀⠀⡸⠷⢵⣼⣰⣣⠇⢰⡋⠑⠒⢾⡟⢻⡄⠀⠀⡈⠊⣠⣏⠘⣿⣧⣸⡟⢹⢦⡀⠀⠀⠘⣏⠉⠁
⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢀⡞⠁⠀⠀⠈⠛⢧⣰⢯⡉⠙⠲⣾⠃⡄⠟⣶⠬⠴⠞⣿⡈⢋⠈⣷⠍⡻⣧⡈⣹⡄⣀⡤⠞⠂
⠀⠀⠀⠀⠀⠘⢧⡀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠉⠳⢬⣷⣶⠏⠀⠀⠤⢿⡇⣃⡼⠏⠛⠲⣄⣟⠸⠇⣻⣦⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠚⢶⠶⣴⣞⡛⣋⣱⣈⣱⣄⣽⠤⠚⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠈⠉⠉⠉⠉⠁⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣤⣠⣄⣀⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⣀⣀⣀
⠀⠀⢠⠾⠻⢭⡉⠛⠷⣦⣀
⠀⢀⡟⠀⠀⠀⠙⣆⠀⠀⠙⢷⣄⡀
⠀⢸⠃⠀⠀⠀⠀⡈⢧⠀⠀⠀⠘⢿⣆
⠀⣼⢿⠃⠀⠀⠀⢿⠎⠳⡀⠀⠀⠘⠛⠛⠛⠛⠳⢶⣄
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⡘⠲⣶⠒⣲⠆⢹⣦⣄
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢯⡁⠀⠈⠁⠙⢧⣀⣀⣀⡀
⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠈⢿⣍⣍⣉⣙⣛⡲⠦⢤⣀⡀
⠀⠀⠈⢷⣤⣀⣀⣀⣠⣤⢴⠖⢺⠛⣶⣦⣄⠀⠀⠀⣷⠀⠀⠀⠈⣷⠀⠀⠀⠀⠈⠉⠐⠚⠙⠳⢦⣀
⠀⠀⠀⠀⢹⡈⣯⢉⣿⣀⣾⣠⣾⣰⣇⡼⢻⣷⡀⠀⢸⡆⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⢀⣤⠶⠖⠛⠛⠁⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠙⠋⠟⠈⠋⢸⣫⣿⣿⣿⣿⣿⣾⡗⠀⠘⡇⠀⠀⠀⠀⢻⡄⠀⠀⢀⡼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡇
⠀⠀⠀⠀⠀⢠⢻⣴⢻⣤⣾⣽⣿⠿⠿⣿⣿⣿⣷⠀⠀⣇⠀⠀⠀⠀⠀⢻⣆⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢷
⠀⠀⠀⢠⡶⠛⠚⠳⠾⣥⡋⣹⠎⣷⣠⠉⠉⠉⢻⡆⠀⣿⠀⠀⠀⣦⠀⠀⠻⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⣇
⠀⠀⠀⠘⣧⣀⠀⠠⢄⡀⠉⠓⢤⣏⣸⢛⡷⣦⣸⡇⠀⣿⠀⠀⠀⡿⢠⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠘⣦
⠀⠀⠀⠀⠈⠙⣧⡀⠀⠉⠓⢦⣀⠉⠻⣿⠴⣽⣹⡇⠀⣿⠀⠀⣼⢇⡞⣠⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠘⣧
⠀⠀⠀⠀⠀⢀⣼⢷⡄⠀⠀⠀⠀⠀⠀⠈⠙⠚⠋⠀⣰⡇⢠⡾⢣⡾⣱⠏⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⢸⡇
⠀⠀⠀⠀⣠⠟⠁⠈⠻⣦⡀⠀⠀⠀⠀⠀⠒⠲⠖⠚⠉⣷⠀⠀⣉⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣄⣀⣀⣀⣠⡼⠗⢀⡀⢿⡄
⠀⠀⢀⣼⠋⠀⠀⢀⣀⣨⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⣠⡴⢿⡀⠀⠻⣄
⠀⠀⣼⠃⣀⣴⠾⠛⠋⠉⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣁⣀⠈⠻⢦⣀⠈⠳⣄
⠀⠐⣧⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⣀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⢀⣀⡠⢤⣶⡿⠿⠯⠤⠶⠛⠁⠀⠀⠀⠉⠓⠶⠼⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣿⠀⠀⠀⠀⠀⠀⢸⡏⠉⣉⣉⣭⠴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣼⠏⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⢀⣴⣶⣖⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣤⣄⣀⣤⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠔⠈⠀⠀⠀⠉⠘⠹⢿⠆⢀⣴⡟⠀⠀⠀⠀⠀⠀⠀⣸⣭⣷⣿⣾⣯⣧⣽⡷⢆⢻⠅⠀⠀⠀⠀⠀⠀⠀⡀⠶⠶⠶⠿⠾⠦⠥⣦⢠⡾⡇
⠀⠀⠀⢀⠊⠐⠀⠀⠀⠀⣀⡀⠶⠂⡀⢀⣿⡇⠀⠀⠀⠀⠀⢴⣿⣿⣿⡿⢿⣛⣫⡷⠚⠀⠘⠿⠀⠀⠀⠀⠀⢀⡔⣨⠀⠂⣠⣴⡰⠖⠛⣒⡢⠉⢽⡇
⠀⠀⠀⠘⠇⠀⠀⠀⠌⠛⠋⠠⠶⠟⠃⠀⠙⠻⠀⠀⠀⠀⠦⠀⠉⠛⢁⡒⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠈⠀⢈⡉⠀⠐⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠘⠿⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇

⠀⠀⠀⠀⠀⠀⠀⣄⠀⣀⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣳⣦⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀
⠀⠀⠀⠀⠀⠠⠒⠌⣉⠈⠙⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⣿⣾⣿⣿⣿⢿⣿⣿⡠⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣶⣶⣦⡀
⠀⠀⠀⠐⠀⠀⠁⠂⣀⣀⠍⠄⡏⠠⣾⡇⠀⠀⠀⠀⠀⠀⠠⣊⠈⢁⡸⢿⣟⣿⡿⣻⢯⠈⠐⠻⠏⠀⠀⠀⠀⠀⠀⠐⠡⠄⠀⠀⠿⣿⣿⣿⣿⣤⣲⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠚⠀⣠⠆⠰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠠⣺⡏⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢀⠀⠸⢿⣼⣿⡏⠉⠚⠛
⠀⠀⠀⠀⠀⠀⠑⠤⠄⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣦⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢠⣴⣤⣄⣀⢠⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣶⣤⣾⠁⠀⢀
⠀⠀⠀⠀⠀⠀⢿⡏⢻⡝⣏⢠⡇⠀⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣴⡯⢉⣭⡍⢹⡿⢅⣠⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⠀⠶⢤⣀
⠀⠀⠀⠀⢺⡆⢸⣇⡸⡇⣿⢸⣗⣒⠱⡟⠀⠀⠀⠀⠀⠀⠀⣘⣻⣇⢸⡟⣻⣼⣇⡞⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠒⠾⠠⣨⢿⡟⠙⣿⠿⠿⠧⢴⣶⡆
⠀⠀⠀⢤⢐⡇⠘⣷⣾⠟⢻⣼⡏⠀⠑⠿⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⠿⠛⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⢠⣼⠁⠐⠶⠷⠒⠀⠈⠛⠁
⠀⠀⠀⠀⠉⠉⠱⣿⣧⠀⠉⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡠⢤⠤⣄⣀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣦⣄⣠⣤⡀
⠀⠀⠀⠀⠀⡀⢈⣿⣿⣿⣿⣿⣿⣦⡤⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⠆⠐⠒⠚⡻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢿⡿⣿⣿⣿⣿⣿⣀⣴⣶
⠀⠀⠀⠠⢀⡄⠴⠿⣟⣿⣍⣙⡄⠀⠀⠛⠇⠀⠀⠀⠀⠀⠀⠠⠊⠈⢁⣠⠒⠄⠉⠀⡈⠀⢰⣅⠄⠀⠀⠀⠀⠀⢠⡞⠻⠃⠈⠓⣹⣾⡽⣼⡏⠿⢿⣿
⠀⠀⠀⠦⠀⠀⠀⣨⣍⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⢶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠃⠀⣤⢀⣻⠗⠚⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣃⠱⢤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠠⠈⠃⠀⠀⢀⣻⡄⡡⣽⠫⡤⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⢩⣯⠽⡽⣿⡷⠆⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠿⣤⣴⡆⠀⠘⠻⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⡞⠀⠐⠻⠛⠋⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⡆⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⣾⣷⡄⠀⠀⠀⠀⠀⠀⡠⠂⢦⡀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣤⡀⠀⠀⠀⠀⢀⡴⠲⣄
⠀⠀⣼⣧⡀⠀⠀⠀⠀⠀⢸⣻⡟⡟⣿⠀⠀⠀⠀⠀⠛⣿⣿⡿⠃⠀⠀⠀⠀⠘⢇⠙⠟⠛⠁⠀⠀⠀⠀⠈⠧⣤⣞
⠀⠰⢿⣿⠗⠀⠀⠀⠀⠀⠘⠷⠧⠧⠏⠀⠀⠀⠀⠀⠀⠛⠉⠓⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘


⢀⣰⣶⣶⣶⠖⠀⠀⠀⠀⠀⠰⠩⠡⠂⠀⠀⠀⠀⠀⣶⣶⣶⣶⡆⠀⠀⠀⠀⢠⣤⡤⢤⣤⡀⠀⠀⠀⠀⠀⠁⠀⠈
⢸⣿⣿⣿⣿⠿⠀⠀⠀⠀⠃⢃⢘⣘⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠿⣿⣌⣸⣿⠟⠀⠀⠀⠀⠀⠀⠛⠁
⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠑⠒⠂⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⢀⣄⣤⣤⡄⠀⠀⠀⠀⠀⢰⠛⠛⢿⡆⠀⠀⠀⠀⠀⢳⡰⣶⣿⡀⠀⠀⠀⠀⢰⣯⣴⣿
⠀⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸⣯⣭⣯⡇⠀⠀⠀⠀⠀⠘⢿⣶⡾⠃⠀⠀⠀⠀⠀⠀⣷⡭⠒⠃⠀⠀⠀⠀⠸⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⣀⢀⣀⣀⡀⠀⠀⠀⠀⠀⢠⡀⣠⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡄⠀⠀⠀⠀⠀⣀⣤⣀
⠀⣤⣤⣸⣿⡇⠀⠀⠀⠀⢸⣿⡄⣿⡏⠀⠀⠀⠀⢿⣿⣿⣿⣇⣈⡆⠀⠀⠀⠠⠀⠀⠀⠸⠃⠀⠀⠀⠀⢸⣻⡛⣟
⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠨⣿⠇⣿⡇⠀⠀⠀⠀⠙⠞⠛⠛⠛⠟⠃⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠈⠻⠿⠟


⠠⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⡤⠤⠀⠤⣄⠀⠀⠀⠀⠀⣠⠤⢤⣄⠀⠀⠀⠀⠀⢰⠒⠒⠐
⠀⠘⣿⣿⣿⡏⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⢹⣶⣴⣾⡏⠀⠀⠀⠀⠀⠿⣧⣼⠟⠀⠀⠀⠀⠀⢸⣿⣿⣿
⣀⣀⣈⣁⣉⣀⣀⣀⣀⣀⣸⣿⣿⣿⣧⣀⣀⣀⣀⣀⣀⣙⣛⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣛⣛⣛
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣽⣿⡎⢿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡌⣷⡀⢀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡧⠸⣇⣼⣿⡓⢮⡝⢿⣯⣿⣷⣒⣦⣤⣤⣤⣤⣤⣤⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⣭⠶⠛⣿⣿⢲⣇⠂⠙⠶⠥⢏⣿⣿⢿⣿⡿⣿⢿⣿⣿⣿⣶⣼⣵⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡜⢧⡀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠉⠀⣀⣤⣿⣿⣿⣿⣟⣥⣪⣿⣿⣿⣥⡿⠋⠀⠀⠀⠈⠙⠛⠿⠋⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡌⢷⡀⠀⢠⣀⣠⣾⠟⠁⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠁⠀⠐⠀⢀⡤⠬⢅⡀⠀⠀⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠈⢷⣀⣼⡿⠋⢀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠛⣛⠭⠍⢉⠀⢀⡀⠀⣉⠉⢉⠉⠁⠛⠭⣅⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⡰⣻⠏⢀⣴⣿⣿⣿⡿⣿⣿⣿⠟⠁⠀⢈⠁⡤⢄⣠⠬⣥⠌⢡⡤⢍⣀⣒⡩⠤⣓⡀⠦⡀⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣴⠃⣰⣿⣿⣿⣿⢿⠁⣿⡿⠁⠀⢊⢴⣿⣴⣧⣼⣧⣾⣿⣴⣿⣆⣼⡇⣰⣯⢀⣶⠀⠒⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣼⢃⣾⣿⣿⣿⡟⡇⣿⠀⡿⢁⢀⣴⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⢚⡱⠣⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣾⣿⣿⣿⡏⢠⠧⠹⡄⡇⢇⢺⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡁⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠃⠀⢑⡙⠨⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠊⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⢿⣛⡿⠋⠀⠀⠀⠀⠀⠀⢻⡆⡱⣆⣿⠛⡿⢿⣿⢿⣿⡿⣞⣶⡋
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⣋⣉⣩⣷⣦⣵⡶⠶⠛⠡⠀⠀⠀⠀⠀⠀⠀⠀⠹⣜⢌⠫⡐⡛⠜⢻⡼⢎⠰⣃⡿⢭⣳⢦⣄⡀
⠀⠀⠀⢀⣀⣴⣾⣯⣶⣾⠿⠿⠛⠛⣉⣁⣤⣤⡖⢋⡟⠉⠑⠲⠦⠤⠤⠤⠤⠤⣌⠪⣷⡤⢤⡈⠙⠀⠚⠉⣉⠷⢤⣈⠉⠛⠿⠿⢶⣤⣄⣀
⠚⠿⠿⢿⣿⣿⣯⠭⠤⠶⠒⠒⠋⠉⠁⠀⣹⣿⢃⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠭⣭⣭⣭⡤⠿⠛⠁⠀⠀⠈⠉⠉⠛⠛⠓⠚⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣣⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁

⠀⠀⠀⠀⠀⠀⠪⠼⡀⠀⠀⠀⠀⣴⣶⣄⠀⠀⡃⠀⠉⠀⠀⠀⠘⣌⠁⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠅⠀⠀⢀⣿⠀⠙⣧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⢠⠀⠀⠀⠀⠀⠣⠀⠀⠀⡼⠼⣷⡄⠈⡷⢦⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈
⣠⣤⣼⡀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠈⠻⡄⣧⠀⠰⠤⢘⣿⠿⣅⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⣠⣤⡀
⡟⠉⠈⢻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⢸⣷⠶⢿
⠁⠀⠀⡾⡁⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣸⣄⣠⣤⠀⠀⠐⠿⠷⠺⢆⠀⠀⠀⠀⠈⢳⠀⠈⠻⡄⠈
⠀⠀⠀⠔⠛⠀⡿⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠉⢷⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠈⢆⡀⠀⠀⢤
⠀⠒⠀⠀⠀⠀⠀⠀⣤⣴⠿⠏⠈⠡⠁⠀⠀⠐⠦⣴⢶⣦⢤⣤⣀⣀⣠⡤⠤⠀⠀⠀⠹⠿⠛⠛⠇
⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⣠⠄⠐⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢜⢭⡻⢯⣤⣀⡀
⠀⠀⢱⣆⠐⠊⢁⡀⠀⠔⠀⠀⠀⡠⠀⠉⠢⠀⠀⠀⠀⠀⢀⡌⣇⠈⠛⠛⠿⠿⣿⣦⣄⢀⣠⠀⠀⠀⠐
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠊⠻⡎⠀⠀⠀⠀⠀⠀⠈⢹⠋⠀⠀⠀⠀⠇
⢦⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⠉⠀⠀⠀⠀⢆⠀⠀⠈⠀⣀⡤⠰⠶⣄
⡴⡞⢰⡀⢀⡠⠞⠁⣠⣤⣴⠒⠒⠞⠀⠀⠀⡁⠀⠀⠀⣴⣧⠈⠓⢆⡀⠀⠀⠈⣇⠀⡠⣄⠘⠉⠤⢤⡤
⠀⠇⠉⠉⠁⠀⠀⢸⡏⣵⠬⠉⣚⠋⠀⠀⠈⢰⡀⠀⠐⣓⡹⠄⠀⠀⠀⠀⠀⠀⠋⡴⣡⠈⠐⣇⡀⡰⠄
⠸⠁⠀⠀⠀⠀⠀⣸⣷⢿⣿⣿⣥⡰⡀⡀⠀⡄⢱⠀⠀⢱⠖⢛⡀⠀⠀⠀⠀⠀⢸⡛⠛⢶⡞⠀⢈⡧⢰
⠀⠀⠀⠀⠀⠀⠠⠏⢡⡎⢾⠈⢳⣭⣙⣋⣼⠁⠃⠀⠀⢸⡅⡄⠶⠀⠀⠀⠀⡴⠈⢉⣦⣰⣟⣀⠞⠉⠉
⢤⡀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⢸⣏⡟⢿⡏⣴⠀⠀⠀⠘⢧⣔⠞⠁⠀⠀⠘⠀⠥⠈⠈⠉⠉⠋⠙⠛⠛
⠉⠁⢀⣤⡶⡟⠓⢦⠀⠃⠀⠀⣸⣿⠀⠀⢿⠁⠀⠀⠀⠀⢸⠅⡠⢄
⠀⠀⢸⠁⠁⠀⣠⣐⠆⠀⠀⢠⢿⡟⠠⣄⡾⠀⠀⠀⠀⠀⠀⠣⠿⠗⠀⠀⠀⠀⠀⢀⠴⠒⠒⠠⠄⣀
⣀⣀⣨⣪⣄⣀⣀⣈⣀⣀⣀⣀⣚⣀⣀⣀⣀⣀⣀⣀⣒⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣍⣀⣲⣂⣀⣀⣀⣷
⣿⣟⣙⣙⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠉⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣲⣤⣤⣠⣀⣀⠀⢣⠀⠀⣀⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⢿⠿⡿⠳⡿⣿⠛⠛⣿⣿⡳⣾⣷⣶⣶⣿⣿⠂⠀⠀⠀⢀⡠⠔⣲⡇
⠀⠀⠀⠰⢾⠟⠿⠛⠟⣽⡿⣆⣻⣤⣴⠿⣿⠀⢩⢿⡏⠀⢻⣿⡿⣿⡿⠝⢿⠟⠿⣿⣶⣦⡋
⠀⠀⠀⠙⠪⢍⠐⠚⢥⡍⠞⠠⠬⠛⠿⠒⠛⠀⠈⠿⠄⠀⠑⠋⠀⣈⡀⠀⠀⠀⠀⠛⢺⣄⣐⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠄⢀⣀⣄⠀⠀⠀⠀⠀⠀⡀⠄⠀⠂⠨⠄⠈⠄⠀⠀⠀⠀⠀⠈⠙⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡉⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠴⠖⠒⠒⢛⠉⠉⠉⠉⠉⠉⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠚⢉⡩⠄⠀⠀⢪⣗⢂⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⢁⣠⠤⠀⠀⠀⠀⠀⠀⠀⠑⠃⠀⠀⠀⠀⠙⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⡤⠔⢃⣀⣀⣠⣤⣤⣤⣤⣤⣤⣀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⡆⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⡀⠊⣠⠿⠛⠛⠁⠃⠘⠃⠓⠚⠳⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠑⢤⡀⠀⠀⠀⢀⡴⠋⠁⡀⢸⠀⡇⠀⠀⠀⠀⠀⠘⡃⠀⠀⢀⣠⠞⠁⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠓⠒⡶⠋⡀⢰⠘⡇⠸⠀⠃⠀⠀⠀⠀⠀⢀⠉⡩⠔⠺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⣠⠞⠀⠀⢹⡈⢇⢹⠀⠆⠈⠀⠀⢀⡠⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡴⠃⠀⠀⠀⠀⢇⠈⠀⠆⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡞⠁⠀⠀⠀⠀⠀⠈⡄⠀⠈⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⡤⠈⡄⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⡆⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠂⠀⠹⣘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢀⡰⠃⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠣⠑⢄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠔⣫⠟⡀⠔⢈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠠⣁⠞⡡⠊⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⡞⠀⠀⢐⣃⠔⡡⢊⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⡇⠀⢀⠞⡡⠊⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠙⠒⠒⠂⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⣇⡴⢫⠎⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠦⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⣠⢏⡔⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠇
⠀⠀⠀⢀⡔⣡⢊⡄⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⢀⠔⠈⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⡌
⠀⠀⢠⠎⡔⡡⠊⢻⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⣴⠃⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⡴⠃
⠀⣰⢃⡾⠊⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⡼⠁⠎⠀⣾
⣰⡷⠋⠀⠀⠀⠀⠀⡸⠈⠳⣄⠀⠀⠀⠀⠀⠀⠘⢦⣤⠼⠁⠀⠀⡀⣼
⠉⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⠊⠑⢄⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠁⠀⠀⠀⠉⠓⠦⠤⣄⣀⠀⠀⠀⠀⠀⠀⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⡀⠀⠐⠠⢱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⡈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢌⡑⠓⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣤⣤⣴⡲⢄⠀⢀⣀⣠⢤⢤⠤⠤⠤⠤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠓⠲⠭⣝⢦⡙⣆⡽⠖⢋⠙⡀⠀⠈⡀⡇⠀⠀⢀⣴⣶⣦⡁⠁⠒⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⡒⠉⠛⠳⢄⡨⠛⢋⡔⠅⠄⣼⣆⠁⠀⠀⠀⡇⠀⠀⢸⡃⣇⣀⣿⠀⠀⠀⣸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠭⠬⣭⡉⢢⣔⠁⣂⠵⠫⢊⣤⢞⠁⢹⡄⠀⠀⢀⡁⠀⠀⠈⠓⠶⠟⠁⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠒⠒⠒⠦⣼⠏⠀⠉⣁⣤⠶⠋⢕⠅⡡⢸⡇⠀⢠⠞⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⢠⠗⣛⣉⣉⣩⡏⠁⠈⢘⡩⠿⣷⣄⠀⠅⠊⠔⣼⣷⣄⠡⠀⠀⠀⠙⢦⠀⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⢸⣋⠁⠤⣴⣏⠀⠀⠈⠈⠀⡐⠀⠻⣦⡀⢐⡴⢻⠏⡍⢳⠀⠀⠀⠀⢸⡆⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠉⠉⠭⠛⠶⢦⣄⡀⠀⠛⣧⠞⢔⢁⠄⠀⠀⣇⡴⠚⠀⣰⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠈⢻⡏⠣⡄⠘⡖⡠⢂⢄⣠⠴⡿⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⣤⣤⡶⣴⠦⠄⣀⢿⠀⡘⡆⡇⢠⠖⠋⠀⠀⡇⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠘⠁⠈⠙⢦⠀⠀⢀⠙⡆⠡⢻⡷⠁⠀⠀⠀⠀⠻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠈⢇⠀⠀⠀⢸⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣴⠶⠾⠓⣻⠶⣤⠀⣾⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢁⣾⣿⠿⣤⡛⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣼⢻⣿⢿⡶⣽⣷⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⡎⣧⠹⡀⠹⣟⢿⡫⢍⡙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠃⢹⠀⡇⠀⠘⣧⠙⢄⠉⠢⡀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡞⠀⡄⢀⡤⢼⣧⠀⠑⠤⣈⣑⢨⣑⣦⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⡼⠁⠀⠃⡸⠀⠀⠈⠑⠦⠤⠤⠤⠌⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣟⡜⠁⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢐⠞⡠⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢞⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠊

⠀⠀⠀⠀⠀⠀⣠⢤⠀⠀⠀⠀⠀⣀⡄⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣦⡄
⢻⣿⢽⢽⢽⣿⠃⠀⠀⠀⠀⠀⢴⣙⡿⢷⣷⣿⠀⠀⠀⠀⠀⠀⣿⡆⣿⢸⡇⠀⠀⠀⠀⠀⣸⡟⠟⠿⡟⣿⡀⠀⠀⠀⠀⣀⣰⣶⣶⣶⣶
⠈⢭⣭⡭⣭⠟⠀⠀⠀⠀⠀⠀⢠⣟⠋⠿⠶⠾⠃⠀⠀⠀⠀⠀⠋⠁⠉⠈⠃⠀⠀⠀⠀⠀⠘⣷⣾⣶⣷⡟⠀⠀⠀⠀⣾⣤⣿⣿⣿⣿⣿⠨⠄
⠀⠘⠃⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠃⠁⠀⠀⠀⠀⠀⠀⠀⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠀⠀⠀⠀⠀⠙⠛⠉⠉⠉⠛⠉


⠀⢴⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⠀⠀⠀⠀⠀⡔⣫⠕⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢤⣀
⠀⡶⠳⠶⣶⣼⠃⠀⠀⠀⠀⠀⣿⣿⡏⢦⣹⣿⣧⠀⠀⠀⠈⢦⡘⣃⢜⠞⣷⣆⠀⠀⠀⢠⣶⣾⣷⣶⣮⣙⡳⠀⠀⠀⠀⠶⠶⠶⠶⢶⡾⠇
⣰⣷⣶⣶⣿⣿⣦⠀⠀⠀⠀⠀⢹⣿⣿⡿⠿⠛⠓⠀⠀⠀⠀⠀⠈⠀⢿⣧⣾⠟⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠠⠭⠥⠘⠋⣠


⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⢀⡜⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠛⠢⠀⠀⠀⠀⠀⠀⢠⣞⣽⡿⢙⣶⠀⠀⠀⠀⠀⠀⢤⣥⣧⣥⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣄
⢿⣻⣟⣿⣻⣟⡿⠀⠀⠀⠀⠀⣾⡛⠛⠛⣛⠻⡇⠀⠀⠀⠀⢸⣿⣷⣴⡿⣿⠃⠀⠀⠀⠀⢸⣿⡷⠰⣿⣿⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⢳⠄
⠸⣽⣧⣿⣼⣯⠇⠀⠀⠀⠀⠀⠻⣴⣾⣧⣽⣶⠇⠀⠀⠀⠀⠀⠙⠷⠷⠟⠁⠀⠀⠀⠀⠀⠸⣿⡧⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠈⠫⠔⠋


⠀⠀⡴⠑⠵⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡦⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡃
⠀⣿⡿⠿⣿⣿⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⡆⠀⠀⠀⠠⣶⣂⣸⣿⣏⣹⡷⠀⠀⠀⠠⣶⣂⣙⣟⣉⣹⠷⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⡆
⠀⣿⡐⢒⣽⣿⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠶⠿⠟⠋⣈⣿⡇
⠀⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠒⠚⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠈⠳⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠂⠀⠀⠀⠀⠀⠀⠺⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣻⠇⡠⠖⠉⠀⢀⣀⣀⡀⠈⠑⠢⡀⢷⡻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⠏⠊⣀⡴⢾⢯⠛⢳⠋⢫⢿⡶⣄⡈⠈⢷⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠏⢠⢪⣿⡟⢃⢸⣆⣼⣄⣾⢠⠛⣝⣯⢢⠈⢿⣿⣿
⠀⠀⠀⠀⢶⡒⠶⢄⡀⠀⠀⠀⠀⢸⣿⡟⠀⢡⣟⢢⣴⣾⣻⣿⣿⣟⣟⣻⣾⣤⢛⣧⠁⠈⣯⣿⠀⠀⠀⠀⠀⣀⠴⠖⣲⠄
⠀⠀⠀⠀⠀⠙⢦⡀⠉⠢⣴⣄⠀⢸⣿⠁⠀⣾⢬⣿⡿⣟⣯⣯⣟⣯⣯⣟⣟⣿⣯⢸⡆⠀⢸⣿⠀⢀⣴⡤⠊⠁⣠⠞⠁
⠀⠀⠀⠀⠻⣍⠓⢭⡳⣄⠘⠎⣇⣼⠇⠀⢠⣿⣻⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣾⢿⣿⣧⠀⠀⣿⣆⡏⠞⢀⡴⣫⠕⢋⡽⠃
⠀⡤⠖⠲⠦⢬⣙⠢⢝⢮⢳⡀⠘⣿⠀⢰⢸⣿⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣻⣏⣿⢰⠀⢸⡟⠀⣠⢫⠞⣡⠖⣋⡤⠶⠶⢦⡄
⠀⠳⢤⣄⣀⡀⠈⠓⠦⠇⠑⠟⠀⡟⠀⡎⢸⠻⢿⡟⣋⢉⠉⠛⠟⠛⠉⣉⢉⣛⣿⢾⣿⠈⣆⢸⣇⡸⠗⣁⣾⡴⢋⣁⣀⣠⣤⠴⠃
⢀⣠⣤⣤⣌⣉⠙⠲⠦⣄⡀⠀⠀⡇⠰⡇⢻⡧⣅⡟⣹⢹⠟⡟⣆⠟⡟⣯⢹⣙⡇⢤⡧⠀⠼⠸⡿⠛⠯⣫⣵⠶⠛⣋⣩⣥⣤⣤⣄
⣏⠀⠀⠀⠀⠉⠙⠓⠦⢤⣍⣳⠀⣧⠀⠳⣄⠙⠲⢭⣝⣋⠲⠦⠞⠤⠷⣋⣛⣭⠷⠋⢀⡰⠃⢰⡟⢰⣋⣩⠴⠖⠛⠉⠉⠀⠉⠁⢙
⠈⠙⠛⠛⠛⠛⠓⠒⠒⠲⢦⡄⠀⠘⢧⡀⢌⡙⠲⠄⠀⠉⠉⠙⠛⠛⠉⠉⠁⠀⠀⠚⢉⣠⣾⡟⠁⢀⣤⠶⠒⠒⠒⠛⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠠⣞⣋⣩⡭⠿⢛⡦⠀⠀⠀⠉⠓⠿⣶⣦⣤⣀⣀⡀⠀⠀⠀⢀⣀⣠⣤⣶⠿⠛⠁⠀⠀⠠⣞⠻⠯⢭⣉⣛⡦
⠀⠀⠀⠀⣠⠴⠖⠒⠚⠉⠉⢀⣠⠴⠖⠒⢦⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⢠⠖⠒⠶⢤⣀⠈⠉⠙⠒⠒⠶⢤⡀
⠀⠀⠀⠸⣅⣀⢀⣀⣠⡴⠞⠉⠀⢀⡴⠚⢉⡤⢶⠆⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⣠⣌⠙⠲⣄⠀⠈⠙⠲⢤⣀⣀⢀⣀⡽
⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠻⠤⠖⠋⢰⠏⠀⠀⠀⢀⣠⠾⠋⠀⠈⠳⢦⣤⠇⠈⠓⠦⠼⠃⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣒⣦⣠⡄
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠜⠁⠀⠀⢀⣀⣤⣾⣿⣷⡚⠓⠂⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢈⡤⠊⠁⢈⠂⠀⠀⠙⠒⢲⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⣴⡧
⠀⠀⠀⢀⠀⠉⠘⠒⠤⠀⡤⠀⡀⠴⠦⠀⠀⠀⠀⠀⠀⠸⣄⠀⡇⠀⠀⠈⠳⡄⠀⣀⡴⠋⠀⠀⠀⢀⠀⠀⠘⢛⣟⠃⠟⠙⠛⠛⢻⣿⣦⣄⣀⣀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠷⠶⠶⠶⠓⠚⠉⠀⠀⠀⠀⠚⠰⣦⠀⠀⢹⡶⣤⣀⣀⢢⣄⣮⣵⣿⣷⠶⠶⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⣀⣀⣠⣀⣾⣿⣾⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠉⠛⠆
⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⢿⣿⣯⡉
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢠⣇⢁⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠌⢻⢠⣏⠂⡴⢐⢸⡇⣴⠀⡇⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡤⠤⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠴⠋⠀⠙⠊⠋⠉⠉⣇⠘⢺⡗⠊⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡾⠋⠡⠊⡀⠀⢸⠙⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠁⠀⠀⠀⠘⢷⣶⣆⡘⠁⠀⠸⠀⠈⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠙⠻⢿⣤⣴⣿⣾⣶⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢤⣰⡄⡀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣒⣂⣩⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠘⠶⠚⠙
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⢿⢻⣽⣿⣿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⢀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠐⣀
⠑⠃⠀⡰⠁⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⢸⡞⠋⠁⡢
⠀⠀⣸⡇⠀⠀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠀⠀⢰⡞⠂
⠀⠀⢿⡇⠀⡞⠀⢀⡔⠀⠀⢠⡄⠀⢡⠀⣧⠀⢠⠰⡟⣁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧
⠁⠀⣻⡇⢠⡇⢀⡿⠁⠀⠀⠀⠀⠘⡉⣇⣻⠀⡆⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢹⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠄⠀⣿⣇⡼⠁⣼⠇⠀⠀⠀⠀⠀⠀⢹⣿⡟⣸⣏⣴⣿⢃⡀⠀⠀⣀⣀⡤⠘⢿⣼⣸⠟⠶⣶⣶⣦⣤⣀⠐
⠀⢠⣿⡟⢁⣼⠇⠀⠄⠀⠀⠒⠀⠀⠀⠙⠷⠟⠿⠿⠛⠚⣠⣴⣾⣷⣶⣶⣆⣀⣿⡗⠇⢤⣼⡾⡿⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⣠⣤⣀
⠀⣸⠟⡴⠟⢁⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⡏⢀⣹⣧⡷⣀⢷⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⣰⠟⣭⣷⣦⣽⣧
⢰⣿⣫⠔⠚⠋⠉⠀⠈⠉⠙⢶⡀⠀⡀⠉⠉⠉⠉⠁⠀⠀⠈⠉⠛⠒⣶⣿⣶⣿⡿⠙⢿⣮⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣿⣘⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⡖⠔⡄⠀⠀⠐⠄⠀⠀⠀⠈⠀⠀⠐⠀⠀⠠⠀⣾⣿⣿⠟⠫⠁⠈⠲⡟⢿⣿⣷⡄⠀⠀⡄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠿⠿⠋⠈⠉⠁⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⢀⣀⣀⡀⠀⢤⢀⣀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡁⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣀⠐⠀⠀⢀⣀⠤⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣛⣋⣭⣹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠀⠙⠻⣭⠭⠿⠿⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⢠⣿⡟⠿⠿⠃⠀⠀⠀⢹⣿⡟⠁⠀⠀⢸⣿⠉⠉⣠⠞⠃⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⣰⣾⣷⠀⠀⠀⢰⣿⣠⠞⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠸⠿⠿⠿⠇⠀⠀⠀⠀⠀⠿⠟⠿⠆⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠿⠿⠿⠿⠿⠇


⠀⠀⠀⠀⠀⢀⣻⣿⣿⡀⠀⠀⠀⠀⢠⣶⡀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⠀⠀⢀⣿⡀⠀⠀⢸⣿⣿⣿⠀⠀⠀⢠⣤⣤⣶⣶⡆
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⣠⣬⣿⣥⣄⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⢸⣿⡇⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠈⢹⡏⠁
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⢰⣿⣿⣿⣿⣿⡄⠀⠀⠼⠿⠿⠟⠿⠿⠄⠀⠈⣿⠁⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢀⣴⣷⡄
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣷⣶⣄⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠻⣿⣿⠟⠁⠀⠀⠀⣤⣾⠤⠄⢼⣦⡄⠀⢠⣿⣿⣿⣿⣿⣿⡄⠀⢀⣿⣿⣿⣿⣿⣇⠀⠀⢸⣿⣿⣶⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠻⣿⣿⣿⣿⡟⠀⠀⠈⠻⠿⠿⠿⠿⠋⠀⠀⠸⠿⠻⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠀⠀⠀⢀⣶⡀⠀⠀⠀⣴⣶⣤⣶⣦⠀⠀⠀⠰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠆⠀⠀⠐⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣷⡄⠀⠀⠈⣿⣿⡟⠁⠀⠀⠀⣠⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠔⢿⣿⡟⠆⠀⠀⢠⣿⣼⣷⠀⠀⠀⣀⣠⣀⣀⠀⠀⠀⣶⡆⠀⠀⠈⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠛⠉⠛⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠉⠁⠀⠀⠀⠘

⠀⠀⠀⠀⣀⣀⣀
⠀⠀⢠⠞⠻⢭⡉⠛⠷⣤⡀
⠀⢠⡏⠀⠀⠀⠙⣄⠀⠈⠙⢷⣄
⠀⢸⢃⠀⠀⠀⠀⡈⢦⠀⠀⠀⠙⢷⣄
⠀⣿⢿⠀⠀⠀⠀⢿⠈⢳⡀⠀⠀⠘⠛⠛⠛⠛⠳⢶⡄
⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⡙⢲⣶⢒⣲⠆⢻⣦⡀
⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠻⢯⡁⠀⠈⠀⠙⣦⣀⣀⣀
⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠘⣿⣭⣭⣉⣛⣛⠲⠦⣤⣀
⠀⠀⠈⢷⣤⣀⣀⣀⣠⡤⢶⠒⢺⠓⣶⣦⣀⠀⠀⠈⣧⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠉⠐⠛⠙⠲⢤⡀
⠀⠀⠀⠀⢻⡈⣯⢡⠿⣀⣾⣠⣿⣴⣇⡜⣻⣧⠀⠀⢹⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⣠⡴⠶⠚⠛⠉⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠙⠋⠋⠈⠋⢺⢹⣿⣿⣿⣿⣷⣿⡃⠀⢸⡆⠀⠀⠀⠈⢿⡀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿
⠀⠀⠀⠀⠀⣰⢻⡴⢻⣴⣾⣼⡿⠿⠿⣿⣿⣿⣧⠀⠀⡇⠀⠀⠀⠀⠈⢿⡄⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⡇
⠀⠀⠀⢠⡶⠛⠛⠳⠾⣥⣃⣾⠊⣇⣤⠉⠉⠉⢻⡀⢠⡇⠀⠀⠀⣆⠀⠈⢻⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠹⡄
⠀⠀⠀⠘⣧⣀⠀⠠⢀⡀⠉⠓⢤⣏⣼⢻⢶⣆⣸⡇⠸⡇⠀⠀⢠⡇⡄⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢻⡄
⠀⠀⠀⠀⠈⠙⣧⡀⠀⠉⠓⢦⡀⠉⠻⣿⠾⢽⣹⠇⠀⡇⠀⢀⡾⢡⡇⡄⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠻⡄
⠀⠀⠀⠀⠀⢀⣼⢷⡄⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⣸⡇⢠⠟⣡⢟⡼⠃⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⣿
⠀⠀⠀⠀⣰⠟⠁⠈⠻⣦⡀⠀⠀⠀⠀⠀⠒⠐⠒⠚⠉⣇⠀⠀⣁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣤⣤⣀⣀⣠⡤⠿⠃⣠⠘⣧
⠀⠀⢀⡼⠃⠀⠀⢀⣀⣬⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⣴⠾⣇⠀⠈⢷⡀
⠀⠀⣼⠁⣠⡴⠟⠛⠉⠁⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⣏⣀⡀⠈⠳⣄⡀⠙⢦⡀
⠀⠰⣷⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⣀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⣀⣠⠤⣴⣾⠿⠿⠥⠴⠞⠋⠀⠀⠀⠈⠙⠓⠶⠽⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣬⣿⠀⠀⠀⠀⠀⠀⣿⡉⣉⣉⣭⡤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⣿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣿⠿⠿⠿⡿⢟⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣻⣛⣿⣿⣿⣿⣟⣿⣿

⠀⠀⠀⠀⠀⢠⠐⠀⢀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣶⡂⣄⠀⠀⣸⠀⡈⠁⠀⠁⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡟⠁⠀⠀⣀⠀⠀⠀⢀⡶⠀⠀⡄
⣀⡄⠈⣿⠀⠀⠀⠀⠀⠀⠤⠀⡰⣄⠀⠸⠇⣀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠒⠀⠈⠐⢶⠗⠊⠁⠀⠀⢸⠀⠀⠀⠀⠀⢀⡀⠀⠰
⠶⠦⠛⠉⠹⣋⢛⣴⣦⣤⡆⠄⣐⠀⢣⠰⠛⠁⠀⠀⢠⠁⠀⠀⠀⠀⠀⠔⠊⢁⠀⠀⡀⠀⠀⠈⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋
⠀⠀⠀⠀⠀⠙⠂⠘⠊⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠮⠡⡀⠀⠀⠈⠉⠉⠻⠂⠀⢠⣄
⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠢⠄⣀⣀⡄⠔⠂⠈⠀⠂⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⣀⢀⣀⡀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠁⠉⠑⠖⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢰⡦⠙⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠠⠠⡀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡎
⠰⠿⡓⠡⠆⠂⠤⣥⣖⡂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠑⠦⡖⠀⠀⠀⠀⠀⠀⠀⠃⠐⢠⡼⠉⢝⠲⠀⢀⣶⠠⠔⠀⠁⠀⠀⠆⠈⠁
⠀⠀⢠⢤⡤⣶⢏⡌⠈⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⢲⠱⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠒⠙⢤⠤⣶⢺⡛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠂⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⢄⠚⣶⡄⠀⠀⠀⣆⡁⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠙⢤⡆⡀
⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⣀⠌⠠⠋⠀⠉⠀⠀⣰⢃⡃⠀⠀⠁⠀⠀⠀⠁⠀⡀⠀⠀⠀⠠⠀⠀⠀⠘
⣤⣤⣦⣜⣀⡛⠀⠈⠈⠀⠐⢀⠊⠀⠀⠀⢰⡾⠞⠁⠎⠀⠀⠐⠀⠀⠀⡆⠐⠀⠈⠐⠁⠒⠀⠉⠀⢀⣠⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠤
⠈⠁⡉⠀⠐⠃⡤⠀⠤⠠⠞⠁⠀⠀⠀⠀⠛⠁⠈⠂⠀⠀⠀⠀⠀⠀⠍⠘⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠉⣀
⠠⠐⢀⠄⠀⠀⡡⠂⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⣠⡀⢄⠀⠠⠁⠀⠀⠀⠀⠀⡦⠀⠀⠀⠀⢰⡆⡀⠀⠘⠿⠃⠂⠀⢈
⠟⠀⢁⠀⠐⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠈⠀⠈⠀⠀⠀⠀⠈⡴⠀⢀⡀⠀⠀⠀⠀⠀⠲⣀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⢀⡀⠢⠠⠈⠓⠠
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣹⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⡄⠀⠀⢀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⢰⡄⠀⡀⢄⠀⠀⠀⠀⠀⠀⡂⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⢡⠆⠀⠀⠀⠀⠀⠘⡂⠀⠀⠠⢾⡿⠈
⠀⠀⠀⠀⡨⠣⠄⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⢣⠹⠌⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠁⠈⠀⠀⣠
⠀⠀⠀⠘⠀⠀⠂⠀⠄⠀⠀⠀⢀⣰⠆⠀⠀⠀⣀⠀⠀⢀⡀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠄⢀⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁⣀⡔⠁
⠈⠀⠀⠀⠀⠄⠤⠊⠈⠀⢣⡀⠠⠁⡆⣀⠖⠉⠀⠁⠀⠈⢋⡋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠔⠈⠀⢀
⠀⠈⠐⣄⠀⠀⠀⠀⠀⢈⠄⠈⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⢰⡵⠂⠉
⠺⠃⠀⠁⠐⠀⠂⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠒⠠⠀⠉⠊⠉⢳⠂⠀⢄⡰⢾⠀⠀⠚
⢂⠒⠀⠀⠀⠀⠀⡈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠈⠺⠻⠖
⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡀
⠀⠀⠀⠀⠀⢸⣏⣉⣩⠩⠃⠀⠀⢸⣿⣿⣿⣿⣆⣠⡀⠀⠀⠀⠀⠀⡈⣄⣀⡄⠀⠀⠀⢠⣶⣿⣾⣶⣆⠀⠀⠀⢰⡭⣌⠱⣘⡆
⠀⠀⠀⠀⠀⠈⢻⡗⠓⣶⠂⠀⠀⠘⠻⠛⠛⠛⠛⠻⠋⠀⠀⠀⠀⠀⠁⠋⠉⠃⠀⠀⠀⠘⡿⣿⣾⣿⠗⠀⠀⠀⠈⢷⣤⡢⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠚⠓⠂

⠀⠀⠀⠀⠀⠀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠐⠑⡀⠀⠀⠀⢀⡤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⣴⣿⣿⣶⣷⡄⠀⠀⠀⡢⠕⢚⡉⠀⢠⠀⠀⠀⠸⡈⠇⡨⠰⣦⡀⠀⠀⠠⢖⣋⣵⣾⡆⠀⠀⠀⠰⣶⣄⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡆⠀⠀⠀⠧⠀⠸⠇⠀⠰⠀⠀⠀⠀⠈⠉⢾⣧⣽⠇⠀⠀⠀⣿⣿⣿⡧⣾⠀⠀⠀⠀⢸⡏⠓⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠐⠶⣶⠞⠀⠀⠀⠀⠀⠀⠀⡀⠚⠢⡀⠀⠀⠀⠀⢀⣀⣛⣢⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⢛⣿⣌⣹⣿⡃⠀⠀⠀⠛⠚⣟⠚⠣⠀⠀⠀⠀⠀⣿⢿⢿⣿⢿⡇⠀⠀⠀⣿⣿⣿⢿⣿⡇⠀⠀⠀⠀⣼⢋⣠⡝⣇
⠀⠀⠀⠀⠀⠸⠿⠿⠼⠼⠁⠀⠀⠀⠀⠀⠧⠀⠐⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠇⠀⠀⠀⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠙⢤⣁⡴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⣶⣶⣾⣿⣿⣿⠀⠀⠀⠀⠠⣿⣧⠄⠀⠀⠀⠀⠀⠀⢺⣿⠓⠀⠀⠀⠀⠀⠀⢤⣿⡧⠀⠀⠀⠀⠀⠀⠐⢺⣿⠂
⠀⠀⠀⠀⠀⣿⣿⠉⠀⠀⢹⠀⠀⠀⢰⣶⣦⣴⣶⡆⠀⠀⠀⠀⣶⣶⣭⣶⣶⠀⠀⠀⠀⣶⣶⣤⣶⣶⡆⠀⠀⠀⣠⣶⣬⣵⣶⣄
⠀⠀⠀⠀⠀⣿⣿⣶⣤⣴⣿⠀⠀⠀⠸⠿⣿⣿⣿⠇⠀⠀⠀⠀⠿⣿⣿⣿⡿⠀⠀⠀⠀⠿⢿⣿⣿⠿⠁⠀⠀⠀⠸⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣀⠀⠀⠀⢰⠛⠿⠿⠛⠆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⠀⠀⢠⣤⡾⠃
⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⠁⠀⠀⠀⠸⠄⠀⠈⠋


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐


⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠸⡀⠀⠉⠻⠗⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠈⠲⠄⠀⢀⠀⠈⠛⠦⠀⠀⠀⢀⣀⣀⣀⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠢⡄
⠀⠀⠀⠀⠀⠈⠳⠦⠤⠤⠶⢦⣄⡀⢀⣀⡀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠰⣄⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⣿⣿⣿⣿⣿⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠠⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠰⢦⣄⣀⣛⣙⣢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣠⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣭⣶⣶⣦⣤⡄⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⢸⣿⣿⣟⡽⠚⠋⠉⠀⠈⠁⠀⠀⠀⠠⣄⠀⠰⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣸⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣇⣠⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣶⣶⣶⣶⣶⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠐⢠⣀⠀⠀⠀⠀⠀⡎⠀⠐⠒⢀⠐⠀⠀⠑⠤⠀⠁⠠⠘⠁⠀⠀⠠⠀⠒⠩⠀⠀⠀⡀
⠠⠀⠸⠍⢴⠀⠀⠀⠀⡇⢀⠤⢀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⡀⠀⠀⠀⠀⠠⠄⠒⠁⠀⠀⠀⢤⠀⣀⠀⠀⡀⠠
⠂⠊⣈⠓⠚⠀⠀⠀⠀⡇⠈⠈⠀⠁⠀⠀⠀⠀⠐⠀⠀⡠⣠⠜⠁⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠊⠀⠀⠐⠒⢛⢌⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠈⠀⣀⠀⠀⠀⠀⠫⠋⠛⠛⠛⠛⠛⠛⠀⠀⠀⢀⢀⠀⢀⠀⠀⠀⢤⣤⡤
⠀⡤⠀⠀⠁⠀⠁⠀⠀⠈⠳⠤⠤⠤⠴⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⢻⢛⠛⡟⠀⠀⠀⠀⠀⠀⢦⠠⢠
⡸⠁⠀⠂⠰⢰⠂⠀⠦⢰⠒⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⢰⣹⡇⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⢉⣈⣀
⠆⠀⢰⠀⡀⣿⠀⢸⠀⡀⠁⠀⠀⠀⠀⠠⡤⠂⠀⠀⠀⢀⣤⠀⠀⠀⠀⠹⠀⠀⠀⠴⠀⠀⠐⠀⠀⠀⠀⠀⠲⠂
⠀⢀⠀⠁⠁⠍⠉⣉⢀⢡⠉⡠⠀⠀⠀⠀⠀⠀⢳⠀⣠⡾⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⢀⠄⠒⠂⠀⢄
⠀⠈⠀⠒⠀⢀⣀⢀⠘⡇⢰⠀⠀⠀⠀⡄⠀⢀⣬⣾⠏⠀⠀⠀⠀⠀⠈⣁⠀⢲⠀⠀⠀⠬⠀⠀⣰⠃⠀⠀⠠
⠀⠀⠚⠀⠀⠊⠃⠘⠀⠓⠘⠐⠂⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⡀⠀⠻⠟⠉⠓⢤⡀⠀⠀⠀⢻⠀⠀⠐⠦⠄
⠀⠀⠀⠀⠀⣠⠤⢄⣀⠀⠀⠀⠀⠀⠀⣸⡲⠀⡀⠀⡤⠔⠂⢀⡠⠦⠤⣠⣤⠆⡀⠀⠈⠂⠀⠀⠈⠷⣄⣈⣉⣠⠔
⠤⠀⠤⣤⠚⠁⡠⠀⠈⠃⠀⠀⠀⠠⡄⠈⠁⠀⠀⡸⠁⠀⠀⠀⠙⠒⠐⠐⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠉⠋⠉⠉⢧⠀⣀⣀⢔⠄⠀⢠⣄⡀⠀⠀⠀⠀⣰⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠙⠒⠒⠋⠀⠀⠀⠀⠉⠑⠢⢥⢫⢳⡄⠀⠀⠀⢀⠈⠀⠀⠁⠂⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⡀
⢀⡰⠤⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣤⠄⠀⠀⠉⠉⠀⠀⠀⢴⡏⠀⠤⠄⠀⢨⣦⡀⢢⠀⠀⠀⠀⠐⠒⠰
⡁⠀⠀⠀⣉⠲⢀⠀⠀⠀⠈⠐⠐⠒⠒⠐⠄⠀⠀⠀⠀⠈⠀⠐⢠⠄⡄⣄⠀⠀⠅⠀⠀⡄⠀⠀⠀⠀⠀⠀⠄⠀⠰
⠀⢙⡖⠉⠀⠀⠂⠀⢂⡀⠐⡀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠰⠤⠤⠬⠤⠤⠤⠤⠤⠀⠁
⠈⠁⡇⠀⢀⠠⠀⠀⠀⠀⠈⢃⠄⠒⠐⢠⡎⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡄⠀⡀
⠀⠁⠂⠘⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠤⠀⠄⡄⣀⡄⣀⠄⠠⠀⠄⡄⠀⠀⠀⠀⠀⠛⠁⠀⣹⠁⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡑⢋⠑⢫⠂⠰⠂⠀⡁⠀⠀⠀⢀⣤⣶⡤⠴⣧⡀⠀⠀⣤⡀⠀⠀⠈⠑⠢⡄⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⣀⠀⠀⠀⠀⠀⠀⡈⠀⢰⡆⠀⢸⡇⠀⠂⠀⠈⠐⢤⠔⠊⠁⠄⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣛⣿⣭⣭⣭⣭⣿⣿⣦⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⡿⣟⣿⠿⣛⣽⢿⣻⣽⢞⣻⣽⠶⣛⣭⡶⢟⣯⣵⢾⣻⣽⡿⢟⣿⣿⣿⣟⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⢿⣻⡿⣛⣽⠞⠫⠵⠟⠋⠒⠛⠉⠈⠉⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠉⠁⠈⠛⠛⠿⢿⣷
⢀⣀⣀⣤⣤⣤⣤⣤⣤⣴⣾⡿⢛⠽⠯⠗⠛⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⢻⣽⠿⠷⠶⠀⣾⡏⠀⠀⠀⣀⣤⣤⣶⣶⣿
⠈⠻⢿⣿⣿⣿⢿⣏⡙⣿⣿⣄⣀⣤⣤⣶⣶⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣼⣿⣦⣶⣾⣿⣿⠿⠟⠛⠁
⠀⠀⠀⠙⢿⣿⣿⡽⣷⣘⣿⣿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣽⣿⣿⣛⣻⣿⣿⠿⠻⠿⠿⠛⠛⠛⠛⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⢻⣿⣞⣟⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠘⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⣿⠟⠁





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀
⠀⢀⡶⢰⡆⢲⡄⠀⢀⣰⣁⣑⣄⠀⠀⠐⡦⣤⣤⣤⠀⠀⢠⣮⣤⡷⠀⠀⢀⣚⣊⣑⣓⡂⠀⠀⣤⠄⢠⡆
⠀⠀⣟⡟⢻⣛⡇⠀⠘⣿⣿⣽⣾⠁⠀⠀⠘⡟⢛⠛⠀⠀⢸⣿⣿⣿⠀⠀⠀⣾⣾⣷⣿⡇⠀⠀⠁⠠⡄
⠀⠀⠉⠁⠈⠉⠁⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠁⠈⠁⠀⠀⠈⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈
⠀⠀⠀⢀⡄⠀⠀⠀⢠⢠⣄⡄⣤⡄⠀⠀⠾⠥⣤⣤⠄⠀⠀⠀⠴⡗⣄⠀⠰⠖⢀⣄⠒⠆⠀⠀⠀⣠⡄
⠀⠀⣸⣹⣿⣿⡀⠀⢸⢸⣿⡇⣿⡇⠀⣾⣿⣿⣿⡆⠀⠀⣿⣿⣿⡿⣇⠀⠰⠆⠈⠊⣄⡀⠀⢠⣾⣷⣿⣧⡀
⠀⠘⠝⠿⠛⠟⠇⠀⠘⠈⠀⠁⠉⠃⠀⠛⠛⠛⠛⠃⠀⠀⠛⠛⠛⠛⠃⠀⠀⠀⠘⠇⠛⠁⠀⠈⠉⠉⠋⠙⠁
⠀⢀⣤⠤⠤⠤⡄⠀⠀⣠⠀⢀⢀⠀⠀⠀⢀⣤⣄⠀⠀⠀⢀⣤⢤⣤⠀⠀⠀⠀⠀⡀
⠀⢸⠀⠻⠗⠀⡇⠀⠸⣯⠁⠚⡞⠀⠀⠀⢧⢀⣽⠀⠀⠀⢸⠢⣤⢼⠀⠀⢰⡿⣿⢿⢿⡇⠀⠀⢀⡄⢀⡀
⠀⠈⠉⣹⣿⡉⠁⠀⠀⠙⢷⣶⡄⠀⠀⢰⣶⣝⣴⣦⠀⠀⢸⣦⣠⣼⠀⠀⠈⠻⠟⠛⠛⠁⠀⠀⠠⡜⠭⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣠⢚⡟⢢⠀⠀⢰⣾⣶⣾⣷⡄⠀⠀⢀⣷⣆⠀⠀⠀⣀⢠⣾⣁⡀⠀⠀⣶⣶⣶⢰⡆⠀⠀⡟⢻⣿⣿
⠀⠀⣷⣀⣃⢴⡇⠀⠈⢿⣿⣿⠟⠀⠀⠀⣾⠿⣿⠄⠀⠀⣿⢸⣿⣿⡇⠀⠀⠻⢿⡿⠘⠃⠀⠀⣯⣭⣭⣿
⠀⠀⠙⠛⠛⠋⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠉⠁⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⢀⠤⣤⠤⢀⠀⠀⡤⢠⠄⣶⡆⠀⠀⣤⣤⠆⠤⡀⠀⠀⣤⣄⣀
⠀⢸⣯⣻⣿⣆⣄⠀⠀⠀⢿⣿⡇⠀⠀⠏⠉⠛⠁⢹⠀⠀⠃⢘⠀⣘⡀⠀⠀⣿⣟⠂⢁⠃⠀⠀⡌⣄⡄⡄
⠀⠈⠛⠉⠉⠑⠉⠀⠀⠀⠿⠏⠁⠀⠀⠣⠁⠩⠩⠽⠀⠀⠱⠋⠀⠉⠁⠀⠀⠈⠻⠄⠃⠀⠀⠀⠂⠐⠒
⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠊⣁⡀⡙⡄⠀⢠⢋⣀⢈⠑⠀⠀⢀⣰⢿⣻⣷⠀⠀⢀⣴⡿⣹⡦⠀⢀⣠⣈⣁⣂⡀⠀⢀⣔⣈⣁⣀
⠀⠀⠦⣀⣀⡠⠃⠀⠘⢄⣀⣀⠴⠀⠀⣾⣯⣾⠟⠁⠀⠀⣿⣯⡾⠋⠀⠀⢸⣿⣭⣭⣽⡇⠀⢸⣿⣯⣭⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⡶⠶⠟⠛⠛⠳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⡟⠋⠉⠀⠀⠀⠘⠁⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠟⠛⠁⠉⠀⣀⣀⣀⣀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⣶⠦⣤⣠⣶⣿⣿⠿⠋⠀⠀⢀⣠⣶⣿⣽⣼⣼⣩⠟⣦⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⣤⣶⣿⣿⣻⣻⢿⣿⣿⣿⣿⡜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣧⠀⠀⠀⠀⠉⠁⠀⠀⠉⠙⡻⣞⡽⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢦⡈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠣⣄⠉⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⣡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢠⠿⠿⠿⠿⠿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⣿⡻⣿⡀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠈⠙⠇⠀⣀⣴⣾⣿⠟⠁
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠛⠉⠁⠙⠻⣆⠀⠀⠀⢀⡌⣧⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⣻⠟⠁
⠀⠀⠀⠀⠀⣼⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠈⠙⠦⣀⠈⠀⠘⢿⣶⣶⣶⣧⣴⣿⣿⣟⣵⠏
⠀⠀⠀⠀⢀⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠄
⠀⠀⢀⠐⠀⠠⢀⢘⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠒⠀⠀⠀⠀⢧⠴⡣
⠀⠀⠘⡀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣈⠳⠄⠀⠽
⠀⢄⠀⢡⢁⠀⠀⠀⣂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠟⠦⠀⢀
⢀⠈⠁⠄⠈⠀⠐⠇⢷⠀⠀⠀⠒⡒⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠀⠀⠀⠀⠈⢠⠐⢀⠄
⠀⠐⠉⠀⠡⠀⢾⠓⡋⠀⠉⢠⢀⠂⠀⠀⢀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠄⢸
⠀⠀⠀⠀⠀⠀⠈⠞⠻⠄⢀⠄⠀⠀⢀⡀⠁⠐⢠⣶⣑⡁⠀⠀⠀⠀⠀⢀⣰⣤⡀⠀⠀⠘⠃⠀⠀⢀⡌
⠀⠀⠀⠀⠀⠀⠀⢠⣄⢔⠂⠀⠀⠀⠀⢀⠀⠀⠀⢏⠴⡀⠀⠐⠲⠔⠄⠀⢀⠀⠻⡄⠂⠥⠂⠀⠀⠸⠁⠘
⠀⣀⠀⠀⠀⠀⠀⠀⡍⠀⠀⠀⠀⠀⠀⠀⠀⠾⠖⠁⠀⡉⠤⠀⠙⡞⠀⠀⡽⣷⠀⠀⠀⠀⠀⠀⢀⠁⢰
⠀⠈⠓⠂⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢈⠒⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢈⡀⢰
⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⣀⠉⠀⠀⠀⢀⠈⠄⠀⠀⠀⠀⠀⠀⢀⠀⠙⢀⠘⠂⠈
⡈⠀⠊⢠⠀⠀⠀⠀⢀⠁⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠘⠀⠠
⠀⠐⠦⠆⠀⠀⠀⢀⡸⠤⠠⠔⠂⠁⠀⠀⠀⠀⠒⡀⠀⠀⠀⠀⠂⢀⠀⢀⠀⠀⠀⠀⠐⢼⠧⠂⠀⠀⠀⠈⠣

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠟⠋⠉⠉⠉⠉⠛⠿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⣀⡀⠀⠀⣀⡀⠀⠈⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠔⢩⣀⣦⣼⣤⣆⣨⠑⢄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡆⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡇
⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠈⣿⣧⡀⠀⠀⠀⠀⢷⣤⣾⣿⣿⣧⠀⠀⠉⠛⠏⣹⣿⣿⣿⡿⣟⡿⠁
⠀⠀⠀⠀⠀⢻⣿⣷⣀⣠⣤⣴⣿⣿⣿⣿⣿⣿⠁⠀⠉⠉⠃⠉⠘⠈⠀⠉⠉⠁⠀⢁⣀⡀
⠀⠀⠀⠀⠀⣾⣿⠆⠉⠉⠙⠛⢻⡿⠟⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠳⣄
⠀⠀⠀⠀⠼⠛⠁⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠



⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀
⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠐⠀⠀⠀⠀⠀⠀⢀⠐⠀⠠⠄⠂⠐⢖⠂⠠⠐⠶⡂⢄⢰⡶⠀⢰⣬⣠
⠀⠀⠂⠘⡆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⡀⠀⠐⠀⠀⠀⠀⠀⢸⠐⠂⠀⠀⠐⠊⠘⠁⠃⠠⡶⠀⠈⣛⣀⡠⢌⡡⠤⢄
⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠘⢆⠂⢀⠀⠀⠀⡀⠀⠟⠒⢶⠃⠀⣿⠂⡐⢆⠀⠐⢲⠂⠈⠁⠈⠀⠈⠁
⡀⢠⠄⠀⠀⠀⠈⠤⠄⠀⠀⢀⣀⠀⠀⠀⢘⡀⠐⣀⡦⢀⡎⠀⠉⠉⠀⠾⢶⣿⠚⠥⡌⡙⢠⠉⡂⠍⢂⠑
⣀⣀⢀⣀⡀⠀⠀⠘⠛⠂⠀⢉⠀⠀⠀⠀⣬⡤⠄⠉⠁⠀⠀⠀⠄⡀⠀⠀⠀⣀⡉⠆⠦⡈⣹⣦⣍⠱⠄
⠻⣧⣄⣡⣄⡦⠀⠀⠀⢀⣀⡀⣀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠂⠁⠠⠀⠀⠀⠀⠀⠛⠷⠦⢤⣴⣄⡀⠀⠀⠀⢀
⠀⠈⠉⠉⠀⠀⠀⠀⠀⠈⠉⢙⡁⠀⠀⠀⠀⠀⠀⠀⢀⡤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠛

⠀⢀⡀⠀⣀⠀⠀⠀⠠⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠈⠀⠀⠈⠀⠀⠀⠀⠈⠠⠠⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⠈⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠠⡀⠁⠀⢀⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⠀⠀⠁
⠁⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠆⠀⠢⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠤⠤⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠄
⠀⣀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⡀⠐⢀⡀⠉⠈⠀⠀⠠⠀⠐⢂⡀
⠆⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⣀⠔⠠⠀⠀⠀⡆⠂⠒⠀⠒
⠰⠀⠀⠀⠀⠱⠀⠀⠀⢀⢀⢀⡀⠀⠀⠀⠠⠀⠃⠀⠀⠁⢤⠀⠀⣄⠀⠀⠀⠮⠔⠀⠀⢹⠨⠅⠏⠭⢨⠁⠀⢁⠀⠀⠉⠀⠀⠁⠀⠀⠇⠀⠰⠀⠄
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠈⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠊⠀⠀⠀⡇
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠂
⣀⠀⠀⠠⠄⢀⡀⠀⠀⠀⠄⠀⠀⠠⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢤⡀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⢀⠀⠀⠀⠀⡀
⠁⠘⠁⠐⠀⠀⠀⠀⠀⣀⡀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⢡⡀⠀⠀⠀⠀⠀⠀⢄⠐⠄⠀⠅⠀⠀⠀⠀⠀⠃⠀⠠⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⡀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠈⠁⠀⠀⠒⢾⠀⠁⢸⠁⠀⠀⠀⠀⠀⠀⠊⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠰⡒
⠀⠀⠀⠂⠀⠀⠀⠀⠈⠏⠉⠉⠉⠉⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠠⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⣀⣀⡀⠀⠀⢀⢀⣤⠀⡀⠀⠀⠠⣄⠀⠀⠀⢀
⡆⠀⠐⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠠⠀⠀⠀⠋⠉⠉⠉⠉⠉⠃⠀⠐⠁⠉⠐⠉⡈⠀⠀⠀⠀⢄⠀⠠⠂
⠓⠀⠚⠀⠀⢀⡀⠀⠀⠀⠈⡶⠒⢐⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠖⠶⠀⠀⢀⠈⠁⢙⠀⠃⠃⠀⠀⠀⠀⢰
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠳⠊⠁⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠰⠆⠀⠘⠀⠀⠈⠉⠭⠉⠍⠈⠀⠀⠀⠑⠛⠾⠛⠂⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠉⠅⠀⠀⠀⠀⠈⠀⠀⢡⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠀⢁⡀⠀⠀⢀⡀⠀⠠⠠⠤
⠀⠲⠐⠀⠀⠄⠀⠀⠀⠀⠀⢸⡤⢤⡀⠀⠀⠐⠐⠂⠒⠐⠀⠀⠀⠀⠠⠤⠀⠸⡂⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⢠⠗⠰⠋⠀⠀⠀⠀⡇
⠀⠀⠤⠀⠀⠀⠀⠀⢘⠐⣶⠈⡃⠀⠁⠀⠀⠀⠠⠓⠁⠠⠀⠀⠀⠄⠀⠀⠀⠄⠰⠀⠀⠢⠄⠠⠰⠤⠅⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠠⠧⠀⠀⠀⠠
⣀⣀⣀⣀⡀⠀⠀⠀⢀⠀⡀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⡿⠀⠀⠀⠷⢠⠄⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡀⠀⠀⢲⢲⠀⠀⠀⠀⠈⠉⡄⢀⠀⠀⠀⠀⠀⠀⠨⠄⡀
⠀⡆⡆⣰⠸⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡁⠁⠀⠀⠀⠀⠀⠅⠀⠀⠀⠠⠀⠀⢰⠀⡄⠀⡇⠀⠀⠀⠀⠀⠢⡀⠀⠂
⢄⠃⠃⠘⠈⠈⠀⠀⢀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⡂⠰⠆⠐⠀⠀⠀⠀⠘⠀⠃⡀⠃⠐⠀⠀⠈⠀⠀⠈⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⣀⣠⣤⣶⣶⣶⣶⣦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣀⣶⣾⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣷⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⣾⣿⣯⣿⣹⣯⣹⣇⣼⡏⣹⠟⣿⠿⡿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣾⣴⣹⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⢛⣥⣶⠀⠀⠀⠀⠀⠀⠙⢿⣷⣯⣏⣟⣻⢻⡟⢿⢿⡿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⢋⠄⣾⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⠿⠿⠶⠷⣷⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⢿⠰⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣺⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⣟⢷⡘⢮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣷⠙⢷⣽⣦⣙⢿⣿⡟⠛⠛⠛⠛⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠋⢿⣄⠀⠀⠀⠉⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣷⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⢱⣎⠿⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣟⠾⣍⣀⣁⠐⠒⠤⠤⠤⢤⣴⣶⣾⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣾⣭⣯⣭⢄⣲⣮⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠟⠉⢿⣿⣿⣿⣯⡙⠛⠛⠛⠉⣤⣴⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⣀⣴⣾⣿⡿⠛⠁⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⣀
⠀⢀⣠⣴⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠙⠛⠻⠿⣿⣿⣧⣄⡀
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⣴⣿⣿⠉⠛⠛⠷⠶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠈⠉⠙⢿⣿⢿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠙⠿⠉⠙⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠠⠱⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⡔⡂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⢠⡶⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠸⠋⠃⠀⠠
⠀⠂⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠂⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⠄⣀
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢧
⠀⠀⠀⠀⠀⢣⣥⡆⠀⠀⠀⠀⠀⠀⠄⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⠀⠈⠀⠲⠀⠀⠀⠀⠀⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠘⡃⡔⠀⠀⢸⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠄⠀⠈⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠃⠢⢞⠄⠐⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠤⠘⠁⢐⠀⠀⠀⠀⠀⠀⢀⠈⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡀⠁⠐⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢁⡀⢀⠀⠀⠀⡀⠀⠐⠋⠘⠀⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠀⠠⠀⠀⠀⠀⠀⠀⠊⠉⠑⠀⠀⠈⠃⠀⠀⠀⠈⠁⡀⠀⠀⠀⠀⠖⢰⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠰⠀⢀⡂⠀⠀⠀⣀⣀⠔⢠⠀⠀⠀⠀⠀⠀⠀⠀⣅⠉⠀⢀⠛⡔⠀⠁⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⣾⣶⣌⣠⠌⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠘⠃⢋⡄⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠄⠂⠀⠀⢠⢷⡾⠋⠁⠄⠸⡷⠆⠀⠐⠃⠀⠰⠆⠈⠁⠀⣄⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⣀⡀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⢠⠒⠉⠉⠑⢄⠀⢠⠒⠉⠑⢆⠀⠠⠠⣶⡆⠀⠀⠀⠀⠠⡀
⠀⠀⠛⠑⠒⠈⠁⢀⠀⠀⠀⡀⠀⠀⠆⠀⠀⠄⠀⢈⠀⠸⡀⠀⢁⡜⠀⡒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⡀⠄⠘⠤⣀⣀⡠⠊⠀⠀⠈⠉⠉⠀⠀⠀⢀⠀⠀⠀⠐⠀⠈⠀⠄⠑
⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠐⡀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣂⠀⣠⡀
⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠁
⠀⠀⢠⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠘⠀⠐⠦⠄
⠀⠀⠀⠐⠐⠁⠀⡀⠀⠀⣀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠐⠗⠀⠀⠆⠀⠃
⠀⠀⠀⢀⠀⠀⠘⠟⢄⠠⠛⠁⠀⠠⠀⠀⠀⠀⢀⠼⣗⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠄
⠀⠀⠐⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⠀⠀⠈⠁⠈⣉⢿⡷⢒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠉⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⠀⠀⡃⡀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠶⠎⠛
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠙⠑⠠⠂⠁⠀⠀⠀⠀⠈⢤⣀⣀⣄⣼⠗⠀⠀⠀⠀⣭⠑
⠀⠀⠀⠀⠀⠈⠛⠢⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠿⠸⡅⠁⠂⠈⢄⡀⠀⠁⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠁⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤
⠀⠀⠀⠀⠀⢀⢀⠀⠀⢀⣀⣀⡀⠀⡀⢠⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠁⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡆⠘⠛⠛⠛⠛⠛⠃⢰⡆
⠀⠀⠀⢰⢶⣦⣒⣠⡄⣂⣤⣤⣀⣤⣠⣖⣠⣤⢴⢄⣂⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠛⠇⣀⣀⣀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠘⠘⠛⠛⠃⠘⠛⠃⠃⠋⠒⠛⠛⠘⠛⠘⠒⠋⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣼⣿⣿⣿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⢀⣀⠀⠀⢀⡀⣀⡀⣀⣀⠀⣀⡀⢀⣀⢀⡀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡀⣀⠀⠀⣰⣿⣿⣿⣆
⠀⠀⠀⠻⠯⠈⠁⠧⠜⠧⠟⠏⠏⠻⠹⠹⠻⠯⠛⠘⠥⠸⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠿⠿⠉⠉⠉⠉⠉⠉⠉⠻⣿⠟⠉
⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⢸⠿⠿⢇⡇⣿⡍⢏⢸⠱⣏⡇⢯⢹⢾⣹⢾⢹⢸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣠⣿⣷⠀⠀⠀⠀⠀⠀⣀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⡄
⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇⠸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣤⣀⣀⠀⣠⡴⢶⣟⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣾⢱⣿⡭⣿⡿⣛⣽⣿⣯⣶⣿⣿⣿⣿⠇
⠀⠀⠀⠀⢀⣤⣤⣼⢧⣿⣿⣿⣫⠞⠉⠀⠉⢻⣿⡿⣿⣻⣿⡀
⠀⠀⠀⢠⣿⣾⣻⣯⣾⣿⣿⡿⠃⠀⢴⡿⣿⣿⡂⠀⢸⠛⣿⣿⣄
⠀⠀⣴⢟⣵⣿⠿⠟⣿⡿⠋⠀⠀⠀⠀⢷⠐⢍⠙⡄⠈⠐⢃⡿⣾⣷⡄
⢠⣾⠵⠛⠉⠀⠀⠚⠋⠀⠀⠀⠀⠀⠀⣼⢀⡨⠇⢹⠀⠀⠠⣶⣾⣿⣿⣄
⢻⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢘⡄⣸⠀⠀⠀⠈⢻⣿⣭⣙⡳⣦⡀
⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃⠈⡫⠅⣰⠇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣦⡹⣦
⠀⠀⠀⠈⠙⠛⠶⠶⠶⠶⠶⣿⡧⣤⣼⣃⡤⢞⣡⠞⠀⠀⠀⠀⠀⢸⣿⣿⠛⠿⢿⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣶⠟⠋⠉⢳⡄⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠈⠻⠄
⠀⠀⠀⠀⢠⣤⣤⣤⣀⡀⠀⠀⠀⠘⣿⠃⠀⠀⠀⠈⣧⠀⠀⠀⢀⣿⠏⠀⢠⠖⣒⠦⣀⣀⣀⡤⠒⠒⢒⡶⠂
⠀⠀⠀⠀⠀⠈⢿⣾⣿⣟⡷⣄⡀⠀⠁⠀⠀⠀⠀⣰⠇⠀⠀⢠⡾⠋⢀⣀⡏⢸⣯⠟⠁⠀⠙⠒⢦⣀⡾
⠀⠀⠀⠀⠀⠀⠈⠿⢿⣿⣿⣾⣝⣷⣦⣤⣤⣶⠞⠋⠀⣠⡴⠋⠀⣜⠉⠙⠀⠸⠃⠀⢠⣴⣶⡄⠈⠆⣟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠋⠉⠁⠀⣀⡴⠞⠉⠀⣠⠞⠁⠀⢀⡀⠀⠀⠀⠀⢁⠈⡙⡄⠀⠐⠂⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠠⢶⡶⠛⠉⠀⠀⠀⢰⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠰⣅⡇⠀⠈⢤⠐⠻⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⢀⡠⠚⡐⠞⡹⣃⠀⠀⠀⣧⣄⣀⠙⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠻⢿⣻⣙⡭⠾⡅⠀⠀⠀⠈⣸⠉⠙⠳
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡥⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⣷⠋⠀⠀⢹⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠙⠲⣄⡀⠀⢀⣠⠞⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⡄⠀⠉⠉⠉⢁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢲⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡧⠖⠁

⠀⢀⠄⠀⠉⠉⠁⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⣀⡀
⠠⠁⠀⠀⠀⠀⠀⣀⡀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠉⠲⣄⠀⠀⢀⡴⠊⠉⠓⢄⠀⠀⢀⠔⣡⣲⣆⠀⢠⠀⠁⠈⠀⢘
⠀⠈⢯⠇⣀⣀⠸⣿⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠈⡆⠀⢸⠀⠀⠂⠖⢈⡇⢠⣁⠁⠈⠛⠃⠀⠈⠀⠠⠀⠄⠌⠓⠀⠠
⠐⡀⠀⠀⠈⠉⠀⠀⠀⣠⠄⠒⠀⠀⠢⠄⡀⠀⢸⡀⠀⠀⠉⠀⠀⢀⡏⠀⠘⢦⣀⣀⣠⠞⠀⠀⡤⠀⠀⠀⠀⡀⠀⢠⠀⠠⡀⠀⠀⢀⠲⠄⠠⠐⢈
⠀⠀⠠⢀⠀⠀⠀⠀⠘⡁⠀⠁⠀⠁⠀⢄⡈⠄⠀⠑⢤⣀⡀⣀⡠⠞⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⢄⡀⠠⠊⠀⠄⠨⠠⠈⠁⠀⡤⣀⣋⣁
⠀⠀⠀⠀⠀⠑⢀⠀⠀⠂⢈⠂⠀⠂⠔⠈⠑⢠⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠘⠓⠛⠓⢃⠠⠈⠈⠀⠀⠀⠀⠈⠂⠂
⠀⠀⠀⠀⠀⠀⠂⠀⠀⡦⢉⠀⠀⠀⠐⠠⠐⢠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠂
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠐⠀⠀⠳⠠⠊⠈⠀⠊⢥⡀⠀⠀⠀⣀⡀⠐⠃⠀⠐⠄⣀⡀⠀⠀⠀⠀⠂⠀⠤⢀⠀⠠⠎
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠘⢂⠀⠀⠀⠀⠈⠂⠀⢆⠀⠀⣀⡀⠀⣀⡀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠆⠀⠀⠀⠁⠀⠀⠀⠀⢸⠀⠀⠑⠄⠉⠁⠐⠉⠁⠔⠀⠀⠀⠀⠐⠀⠀⠖⠐⡄⠀⠀⠀⠀⠀⠈⠐⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⢀⠀⠀⢀⠄⡀⠀⢠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠰⣦⠀⣾⡶⠀⠀⠀⠀⠄
⠀⠀⠀⠠⠊⢁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠈⠑⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀
⠀⠀⢠⠁⠀⠀⠀⠀⢠⠀⠀⠀⠃⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠤⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⢨⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠁⠀⠀⠈⠁⠢⡀⠀⠀⠀⠀⠈⠢⡀⠀⡀⠀⢥⠀⠀⡬⠐⢠⣉
⠀⠀⠀⢄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠈⠉⠀⡀⠊⠀⠈⠀⠠⠀⢎⢣
⠀⠀⠀⠀⠓⠉⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘⠁⠁⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠈⠀⣀⡀⣶⠄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⢠⠁⠐⠈⠃
⠀⠀⡠⠀⠐⠀⠀⠀⢿⡿⠀⠀⡘⢿⠇⠀⠀⢙⡂⢄⠀⠀⠀⠀⠀⣰⣿⠦⢀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⡀⠊⢀⠠⢊⡘⠀⠀⠀⠀⢁⠂
⠀⠀⠈⠀⠊⡀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⡌⢋⠁⠀⠀⢀⠤⠜⠁⡽⢷⣦⣄⣁⣰⠒⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁⢀⠊⠱⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡁⠁⠀⢄⡀⠀⠀⠀⠀⠀⡀⠔⠢⡉⢎⠀⠀⠀⠀⠀⠀⠀⢀⡾⡻⣞⡅⡀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠃⠀⠀⠀⣰
⠀⠀⠀⠀⠑⠁⠀⠀⠀⡉⠀⠀⠈⠁⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠘⠃⠁⠘⠀⠇⠀⠂⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⡀⢄⠀⠀⠐⠀⠰⡀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣶⠀⠀⠀⣶⣶⠀⠀⠠⠔⠆⠀⠀⠀⠄⠀⠰⠀⠀⢁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠢⠀⠀⠀⠀⠀⠀⠈⠁⠘⠛⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠰
⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣤⣄⠢⡈⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠑⠆⠀⠀⡀
⢆⠀⠄⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣠⠀⠀⠀⠀⢷⠟⣀⠀⡨⠛⠋⠀⠠⠀⠀⠁⠐⡄⠀⠀⠀⠀⠀⢒⣟⣴⠀⠀⠀⠀⠠⠔⠠⠄⠈⠆
⠀⡀⠀⠀⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠘⠀⠳⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⡸⠓⡆⢶⢴⡲⣏⠎⠀⡢⠀⠀⢈⠀⣞⠓⣀⡀⠁
⠀⡡⠂⠀⠀⠀⠀⠈⠙⠣⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠅⢠⡝⡊⠿⡅⠀⠁⠀⠈⢅⢀⠈⠀⡈⠉⠉⢀⡠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠆⠈⠉⠉⠛⠛⠛⠛⠛⠓⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠘⠀⠲⠠⡞⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠉
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⠿⠟⠛⢛⣛⣋⣙⣛⡛⠛⠻⠿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⢋⣡⣴⠶⠛⠛⠉⠉⠉⠉⠉⠉⠛⠛⠶⣦⣌⡙⠻⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⢋⣠⣾⡟⢋⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡙⢻⣷⣄⡙⠿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⢃⣴⣿⣿⣿⣾⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣀⣤⣿⣦⡈⢿⣿⣿⣦
⠀⠀⠀⠀⠀⣼⢳⡿⠂⣠⣿⣿⣿⣿⣿⡿⠻⠻⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⣼⣿⣿⣿⣿⣿⣄⠙⣯⣜⣧
⠀⠀⠀⠀⡘⠂⠅⣧⣴⣿⣿⣿⣿⣿⣿⣷⠀⣶⣶⡆⢰⣶⣶⠀⢰⣶⡆⢀⣶⣶⠆⢰⣿⣿⣿⣿⣿⣿⣿⣦⣤⠈⠐⢆
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⣉⣁⠀⣉⣉⠀⢈⣉⡁⢀⣉⡉⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠿⠿⠀⠿⠿⠀⠹⠿⠃⠸⠿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠠⣶⡄⢠⣶⠀⢠⣦⠀⣴⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠉⢁⣈⣉⣀⣈⣉⡀⠉⣁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢁⣴⣤⠙⢿⣿⣿⠏⢠⣤⡌⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⣠⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡈⠻⠟⢀⣾⣿⣿⣆⠘⠿⠋⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄
⠀⠀⠀⢰⣾⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⣿⣷⣄
⠀⠀⠀⠘⣿⣿⣿⡌⢿⣿⣿⡟⣛⣿⣿⠟⣛⡿⣛⠻⡟⢻⡟⢻⠟⢿⠛⣿⢛⣻⠛⠛⡿⢛⣻⢛⣻⣿⣿⡿⢡⣿⣿⣿⠃
⠀⠀⠀⠀⠘⣿⣿⣿⡄⠻⣿⡇⠲⣯⣭⣘⠻⣆⠻⢃⡇⣄⣰⣸⣀⣀⡄⣿⠰⢾⢠⡔⣇⠻⢿⡀⢾⣿⠟⢠⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣴⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠹⢿⡿⠷⣄⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠚⠛⠛⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠱⠂⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⢿⣿⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⣿⡿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁




⣶⣾⡶⠶⡶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠈⠅⠂
⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⣤⣰⡶⠶⢶⣶⣦⣦⣤⣤⣶⣶⡶⡶⣶⣶⣦⣤⣤⣀⡀
⠀⠀⠀⢀⠄⢀⡞⠁⡔⠁⡠⠼⣛⣓⣚⣻⣿⣿⣿⡿⣟⢋⠿⠳⠎⢁⡁⢸⡿⡟⠈⢘⡿⣿⣷⣤
⠀⠀⢀⡎⢀⡞⠀⡜⢠⣞⠩⠭⣒⣲⣾⣿⠿⣿⣙⡿⢧⠃⡅⡠⢀⡏⠀⠀⠉⠀⠀⠀⣁⣴⣿⣿⠆
⠀⠀⡸⠀⣸⠀⠘⢀⡿⣒⠩⢥⣴⣿⣿⣿⣿⣺⡭⠑⡃⠀⣾⠀⢸⠃⠀⠀⠰⠦⢶⢟⣵⣿⡿⠃
⠀⠀⠇⠀⡇⠀⠀⣸⢇⡂⢭⣿⣿⣿⠿⣹⣻⠙⠀⢁⣀⡠⣿⠀⠘⣇⢃⠀⠀⠀⠈⠲⠭⣛⣿⠔
⠀⢀⣾⡀⠀⠀⢐⣿⢒⢪⣿⣿⣿⠬⠡⢁⠄⢡⣶⠋⡁⢠⠟⠳⠃⢈⡤⠤⠤⠤⠖⠚⠉
⠀⠘⣧⠇⡀⠀⠐⣿⡲⣼⣿⣿⡳⣍⠐⡈⠄⠷⣧⣾⣷⠏⣠⠴⠚⠉
⠀⠀⠈⠀⡇⡆⠈⠙⠩⣿⣿⣟⠮⢖⠑⡌⠢⠀⠀⠀⡴⠋
⠀⠀⠀⠀⡇⢱⠀⠀⠠⣿⣟⣉⡫⠐⢀⡈⠀⠀⡠⠞⠁
⠀⠀⠀⠀⢱⠀⠆⠀⠀⣿⣿⡐⠔⢎⠁⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶
⠀⠀⠀⠀⠈⢇⢶⡀⠀⣿⡦⣃⡱⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡆
⠀⠀⠀⠀⠀⠈⠹⣹⠀⠸⣿⡷⠀⡄⠀⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠹⣿⣀⠀⠀⣿⣾⡀⠀⠀⠀⠀⣀⣴⢟⢟⣽⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠈⠓⠙⠷⠒⠚⠋⠙⠕⡵⡿⡫⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⠶⠦⠦⠤⠤⠴⠒⠒⠚⠿⠿⠿⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠐⠾⠇⠀⠀⠀⠀⡀⢡⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣆⠀⠀⠀⠀⢀⡀
⠀⠀⠀⣀⡀⠀⠀⠬⠁⠀⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣿⢀⠇⡀⠀⠀⢀⠀⠀⠀⠙⠀⢴⣤⠀⡀⠀⠀⠈⠁⠀⠀⠠
⠀⠀⠀⠈⠁⢸⡇⡀⠀⠀⠀⢠⡀⢋⣀⢄⡂⠀⢸⡇⠀⣿⡠⣧⣿⣏⢠⠃⡐⢀⢦⢀⣀⡀⠀⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠲⠄⠓
⠀⠀⣴⠀⣴⠏⢰⡇⡄⡀⢀⡎⣿⣿⠟⣇⡆⡍⢹⡇⢸⡟⠁⠈⠁⠙⠘⢤⣵⣯⠞⡄⠋⣷⡦⠀⠀⠀⠨⣀⠀⠀⡄
⠀⠀⢿⣆⢼⡇⢻⡆⢣⣽⢴⡄⢫⡟⢳⣿⡏⠁⡌⢳⣼⠀⠀⠀⢀⠁⠀⠘⣿⠛⠛⠃⠘⣧⣿⣻⡄⠀⠀⠀⠀⣇⢱⠀⡄
⠀⢀⣠⣻⣦⣷⣾⣶⣄⠙⡎⣿⢎⡟⣾⡟⠀⠀⣿⣿⣿⣧⣀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⣮⣿⣤⣶⣄⠀⢀⣇⣞⣼⣁⣦⣠⣆⠁
⣴⣿⣿⣿⡟⢻⣿⣿⣷⡀⢦⠙⢈⡼⢟⣿⠀⠀⠙⠁⣿⠛⠉⠀⡀⠀⠀⠄⠀⠰⢶⡄⠀⠀⡼⠋⡻⠻⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣶
⣿⡟⢿⣿⠀⢠⡿⢙⠳⠀⠈⠀⢸⠇⢟⣿⣷⠀⠀⠀⠃⠀⠶⠟⠃⠀⠀⠀⠀⠆⠀⠀⢀⡄⡸⠞⣻⣤⠿⣿⣿⣿⣿⣿⠁⠨⣿⡿⣿
⣩⡇⠀⠁⠀⡾⠃⠀⣅⡀⠀⠀⣀⢾⡿⣿⣿⡂⠀⠀⣿⣶⣤⠀⠀⠀⣤⢀⢀⠀⠴⠀⠙⣧⣷⡄⠉⠡⠤⡄⢻⣍⣬⣭⠀⠘⡻⠃
⡷⠶⠀⠀⠀⠃⣀⠐⢀⡛⠀⠀⠴⢫⣾⣿⠿⠻⠃⣸⣿⣿⣿⣄⠘⣆⠈⠐⣿⣶⡆⠀⠀⢸⣿⣧⠀⠁⣶⣶⡸⣿⡆⢴⡀⢘⡅⢠⣆
⠀⣾⡀⠀⠀⠀⢼⣧⠀⢤⡀⠀⣶⡄⠀⠁⠀⠀⠺⠿⣿⣛⠿⠟⢀⡏⣸⣦⣴⣶⠀⠀⠀⠀⠀⣿⠀⢀⣿⠶⣷⣬⣅⠈⠁⠘⠇⣸⡏
⠀⠉⠉⠀⠘⠀⠘⠛⠀⠘⠀⠀⣽⠟⠀⠀⠈⠀⣀⣘⣺⣿⣿⡿⣿⣧⣻⡿⠿⠷⠀⠀⠀⠀⠚⠛⠀⠈⠉⠀⠀⠀⠉⠀⠀⠻⠆⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠒⠀⠀⠀⢸⠈⢉⡁⠉⡉⡀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠂⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⢀⢠⠄⠐⠶⠀⠈⢈⡠⠊⠁⠀⠐⠃⠸⠃⠦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠶⢟⠏⠉⠀⠈
⠀⠀⢰⢁⡾⠀⠀⠀⣀⡼⠈⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠰⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠂⡔
⠀⠀⠈⠠⢤⣀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠋⠀⠀⠀⠀⢠⠄⠁⠀⠶⠘⢲⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⡤⠀⠀⠀⠶⠁⢀⡴⡁⠈⠀⠉⠀⠀⠈⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢶⣶⢶⢲⠒⡆
⠀⠀⠠⠀⠀⠆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠐⡷⣮⡏⠿⠘⢰⠃⠈
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠀⢤⠀⡀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⣤⣴⡖⡖⡆⠀⠀⠀⠚⠳⠧⠆⠎
⠀⠀⠀⠾⠀⢠⠆⠀⠀⠰⣄⠀⢸⣴⡇⠀⠀⠀⠀⠤⠔⠀⠀⠀⢲⣾⡏⡇⠀⡇
⠀⠀⡀⠀⠰⠈⠀⠀⠀⠐⢂⢼⣿⣷⠯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⣰⡾⣠⠀⠀⠀⠀⡤⣡⠻⡟⠻⡕⠀⠀⠀⠀⢠⢿⣷⠀⣠⡤⣶⣶⡶⠀⠀⠀⣄⠒⣄⠀⢠⠀⠀⡆⠂
⢠⠀⠀⢐⣿⠁⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⠩⠬⠱⡰⠉⠁⠀⠀⠀⠀⠈⠁⠘⢀
⢸⡄⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⡽⣆⠁⠀⠀⠀⠑⣃⠀⠀⠀⠀⠀⠀⣀⡝⠀⠄⠀⣤
⠀⢳⡄⢰⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⢸⣿⠁⠝⠀⠠⠄⠀⠄⡑⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠰⠃
⠇⣺⡄⣾⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠀⡄⠚⠃⠀⠈⠠⠢⠁⡀⠒⠬⣆⠀⠄⠀⠀⠀⠶⠄⠀⠁⠈
⣇⣟⣼⠃⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡇⠈⠀⠀⠀⠀⠀⠸⠾⠛⠋⠈⠙⠀⣆⠀⠀⠀⠀⠀⡀
⠘⠋⠁⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣺⡇⠀⠀⠈⠢
⣤⠶⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⠴⠀⠀⠀⠀⠈⣆⠘⡇⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢄⡀⠀⠀⠀⠘⣀⠀⠀⠀⠀⠀⠨⡇⠠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡯⣰⠏
⠀⠀⠀⠀⠀⠀⠈⢆⣰⡂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡄⢀⠀⢀⠄⠀⠀⢸⠀⠀⠀⠀⠀⢰⠏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣠⠄⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠘⢀⡃

⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⢀⠔⠋⠉⠉⠑⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠⡀⠀⠀⠀⠀⢀⡠⣀
⠀⠀⠀⠀⠈⠀⢤⠀⣢⠠⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢐⡂⡆⢒⢢⣄⣀⠀⠀⢀⠔⡈⠐⠀⠘⠀⠀⢀⣴⠏⠑⠎⠉⠖⠓
⠀⠀⠀⠀⠠⠀⠉⠀⠤⠀⢀⠀⠐⡂⢱⠀⠀⠀⠀⠀⡀⠞⢿⣩⢝⡱⣣⣞⡴⡯⣯⢕⣷⣮⡄⠀⠀⢸⠀⠀⡮⠛⢄⠀⢡⢠⠀⢠⠆
⠀⠠⠏⠢⢀⡱⡀⠀⡀⢀⠀⢁⣈⡀⠌⠀⠀⠀⢀⠌⢰⣦⠈⣗⣩⢟⣳⣳⣯⣭⢽⣹⡟⠯⢁⠀⠀⢘⠄⠀⠳⣄⠀⠡⣌⣜⠀⠜
⠀⠀⠀⠈⠒⠞⣵⢃⠣⠘⡁⠂⢡⠀⠀⠀⠀⠀⠘⠽⠀⠀⠀⢹⣾⣿⣿⣾⢿⠭⠋⠁⠈⠐⠠⢁⣀⣠⠆⠀⠀⠀⠁⠂⠬⠥⠊
⠀⠀⠀⠀⢸⣠⠁⢸⠀⠁⡀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⠖⠿⠛⠋
⠀⠀⠀⠀⠈⠁⠈⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠙⢫⠥
⠀⠀⠀⠀⠀⢀⣤⠐⠖⠀⠐⠖⠀⢀⠀⠀⠀⠀⡀⡜⠡⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡼⣁⠁⠀⢸⢶⠁
⠀⠀⠀⠀⡼⡁⠀⠀⠑⠂⠀⣀⠀⠈⠓⢄⠀⠌⣀⣡⠷⡚⡀⠀⠀⠀⢀⣨⠛⡒⠤⢤⣡⡶⠢⢄⢣⠀⠀⠀⢈⡟⢠⡟⣦⣢
⠀⠀⠀⢰⠀⠀⠰⡟⣆⠀⠀⠀⠀⠠⠄⠀⠓⠀⢄⣀⠤⠃⢰⠀⠀⣠⣙⠆⢧⣤⠂⢨⢽⢃⡇⣼⡜⠀⠀⢠⠋⡀⠀⢿⢅⢨
⠀⠀⠀⠘⠀⠀⠀⢉⠁⠀⠀⠈⠀⠀⠀⠠⠄⠀⠀⠀⠀⢀⠎⠀⠀⠈⠢⠄⣦⣮⡶⠁⣬⣿⢫⠏⣰⡄⠀⠘⢄⢱⠀⢸⡟⠉
⠀⠀⠀⠀⠰⡖⠒⠉⠀⡠⡤⢖⠖⡲⡲⠲⢶⣶⡶⠶⠒⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⣿⠣⣣⡮⠚⠁⠀⢰⠲⢈⠇⣼
⠀⠀⠀⠀⠀⠈⠐⠐⠯⠮⠰⠅⠾⠚⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠴⠗⠚⠁⠀⠀⠀⠘⠦⠥⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⠄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⡀⠀⠀⠀⢀⠎⣀⠀⡦⠀⡃
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣰⠖⢂⠀⢀⣰⣤⣤⣀⡔⠉⡄⠔⣀⠀⠡⡂⠀⠀⠨⡀⠙⠀⠂⢔⢩⣴⡀
⠀⠀⠀⢃⠘⣢⠄⠐⣶⠀⠀⠀⠀⣴⡊⠀⠩⣥⠀⠒⠀⠐⠖⢒⣒⣻⣿⣾⣿⠤⠤⣀⠀⡴⠀⠀⠀⠈⠒⣀⠰⣞⠣⡙⢿⣦
⠀⠀⢀⠔⠲⢓⠄⠐⣇⠀⠀⠀⣌⠈⠋⠀⠀⠺⠀⠐⣊⣩⡭⢟⡻⠛⠁⠃⡅⠀⢄⠈⠠⠂⠀⠀⠀⠀⠈⠑⢄⠂⢹⣟⡿⣿⡷⣄
⠀⠀⠃⠄⠂⡀⣸⠂⠘⠀⠀⠀⠀⠐⠠⠀⣀⣘⡇⠩⠤⠐⠊⠁⠀⠀⠈⠁⢤⢘⠘⢀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣿⣌⢮⡙⠊
⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠎⠓⠁