Clap Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠘⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣾⣿⠉⠉⠙⠻⢿⣷⣦⣄⡀⠀⠹⣿⣄⠀⠀⠙⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠻⢿⣿⣦⣄⣀⠀⠀⠈⠉⠛⠿⣿⣶⣽⣿⣦⡀⠀⠈⠙⢿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣀⠀⠀⠀⠉⠛⠿⣿⣶⣤⣀⣀⡀⠀⠉⠙⠻⢿⣿⣦⣄⡀⠀⠉⠻⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣶⣤⣀⣴⣶⣦⣬⣿⡿⠛⢿⣷⣄⣀⠀⠀⠈⠉⠛⠛⠀⠀⠀⠀⠙⠿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠈⢹⣿⡏⠉⠙⢿⣿⣄⠀⠀⠙⢿⣿⣗⠀⠀⠀⢀⣴⣾⣿⣶⣄⠀⠀⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⣦⣤⣈⣿⣷⣄⠀⠀⠙⢿⣷⣄⠀⠀⠙⢿⣷⣄⠀⢸⣿⠁⠀⠹⣿⡄⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣴⡄⠀⠀⣴⣿⢿⣿⠟⠛⢿⣷⣄⠀⠀⠙⢿⣷⣄⠀⠀⠙⢿⣷⣼⣿⡆⠀⠀⢿⣷⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠐⠿⠿⠟⠛⠛⠋⠉⠉⠀⠀⠀⣿⣧⣸⣿⣄⠀⠀⠙⢿⣷⣄⠀⠀⠙⢿⣷⣄⠀⠀⠙⢿⣿⣿⡀⠀⠈⢿⣧⡀⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠈⠛⢿⣿⣿⣷⣄⠀⠀⠙⢿⣷⣄⠀⠀⠙⢿⣷⣄⠀⠀⠙⢿⣷⣄⠀⠈⢿⣷⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⡿⠿⠛⠁⠀⠀⠀⣿⡟⠉⠙⢿⣷⣄⠀⠀⠙⢿⣷⣄⠀⠀⠙⢿⡷⠀⠀⠀⠙⠿⠇⠀⠀⠻⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⣠⣄⠀⠀⢻⣷⣄⠀⠀⠙⢿⣷⣄⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⠙⢿⣷⣄⠀⠀⠙⢿⣷⣄⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠙⢿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⣀⠀⠀⠀⣀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⠲⣾⠃⠀⠀⡶⠒⠒⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠛⢲⡏⠀⢀⡇⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⢧⠀⢆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⣄⡾⠀⠀⣼⠀⠀⠀⣼⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⡆⠘⡆⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⢸⠃⠀⢠⠇⠀⠀⢠⡇⠀⠀⠀⠀⠈⠙⠲⢤⡀⠀⠀⠈⡆⠀⠀⠀⠀⠘⣄⠘⡄⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⡟⠀⠀⡼⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⡇⠀⠀⠀⠀⠀⠘⡆⠘⡄⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢰⠁⠀⢠⠇⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠸⡄⠘⡄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⡏⠀⠀⣼⠀⠀⠀⠀⡇⠀⠀⠀⠀⡆⠀⠀⠀⣀⡤⢤⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⢹⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢰⠃⠀⠀⡇⠀⠀⠀⢸⡃⠀⠀⠀⠀⡇⠀⢠⠞⠁⠀⠀⠇⠘⡇⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢀⡞⠀⠀⠘⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⣰⠋⠀⠀⠀⠘⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⢠⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠶⢤⡀
⠀⠀⠀⠀⠀⢸⠀⡘⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⢈⣿⣷⣤⡀
⠀⠀⠀⠀⠀⢸⠀⡇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⣠⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⢸⠀⡇⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠓⣤⡀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡰⠁⠈⠓⠲⠦⠤⢤⣀⡞⠁⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡰⠁⡜⠀⠀⠀⠀⠀⠀⢯⡀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⡔⢁⠜⠀⠀⠀⠀⠀⠀⠀⠀⠉⢲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⣀⣀⠀⣸⠁⠈⠉⠓⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⢀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⠀⠉⠙⠒⠦⢤⣀⠀⡐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⣾⠟⢿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠈⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⡿⠃
⠀⠀⠀⣸⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣴⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠁
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⢀⡴⠛⣶⠏⠀⣿⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢀⣴⡟⠳⣤⣟⡴⠺⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣠⠟⠉⠳⣾⡿⠋⠧⣤⡿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⡀⣼⢁⡴⠃⠀⠀⣰⠏⠀⠀⢀⣼⡟⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣁⠀⣷⣧⠏⠀⠀⢀⡾⠁⠀⠀⢠⠞⠀⢙⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠒⠒⠒⠂⠀⠀⢰⠿⠋⢸⣰⠟⠁⠀⠀⢠⠏⠀⠀⠀⡴⠋⠀⢀⡾⠯⣸⡇⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⣠⠟⠁⠀⠀⠀⠐⠁⠀⠀⠀⠞⠀⠀⢠⠞⠁⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠘⠒⠲⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⡏⠀⠀⠀⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢣⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡴⠲⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⣰⠋⠙⡻⣄⡀⠀⠉⠳⢤⡀⠀⠀⠀⠀⣠⠟⠁⠀⠀⡴⠋
⠀⠀⠀⠀⢠⡞⠑⣊⠡⠤⠀⠙⠲⣄⠀⠀⠙⠲⣄⢀⡞⠁⠀⠀⠀⣸⠁
⠀⠀⠀⣰⠋⠐⣉⠠⠄⠒⣉⠠⠤⠈⢙⠦⣄⡰⠋⢻⠉⠉⠙⠓⠒⢧
⠀⢀⡜⠁⢒⡩⠤⠐⣂⡁⠤⠐⠒⣈⡡⠄⠈⡓⢶⡿⠤⣤⣀⣀⣀⣾
⣠⠏⢀⡩⠤⠐⢂⡉⠤⠄⠒⣊⠩⠔⠒⣈⠥⠄⠂⣹⠆⠁⠐⢀⣈⠉⣽
⠉⠀⠠⠐⠂⢉⡠⠄⠒⢂⡉⠤⠒⠊⣁⠤⠖⠂⡴⢃⡠⠭⠉⠀⠐⢀⡇
⠀⠀⠀⠀⠈⠁⠀⠐⠂⣁⠤⠔⠒⢉⡠⠄⢠⠞⠑⠒⢒⣒⠨⠭⠁⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠐⠊⢉⡠⠄⡴⢃⣀⠈⠭⠐⠂⢐⣂⠉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⣁⢀⡞⠁⠐⠐⣒⠠⠬⠉⠀⡂⢰⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⣠⠟⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⠉⠙⢦⡀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⢀⡾⠁⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠒⠲⣇⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢸⡇⠀⢸⠀⠀⣀⠀⢿⡀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⠙⢦⣜⢧⣄⠀⠀⠀⠀⠀⠙⠳⣄⠈⠳⠴⢟⡴⠋⠉⠙⠺⣝⠉⠀⠀⠀⠀⣀⣠⡤⠖⠛⠉⠁⠈⣷
⠀⠀⠀⠀⢀⡤⠖⠲⢿⠀⠀⠀⠀⠀⠙⠳⣜⠳⣄⠀⠀⠀⠀⠀⠈⠳⣴⠶⢾⡇⠀⠀⠀⠀⠈⠳⣄⠀⢠⡟⠉⠀⠀⣀⣠⡤⠖⠛⠁
⠀⠀⠀⠀⡾⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠈⠳⣌⠳⣄⠀⠀⠀⠀⠀⠈⠳⣄⠳⣄⠀⠀⠀⠀⠀⠈⠳⣄⠳⠶⠚⠋⠉
⠀⠀⠀⠀⠻⣄⣠⡴⠶⠶⣌⠳⣄⠀⠀⠀⠀⠀⠈⠳⣌⠳⣄⡀⠀⠀⠀⠀⠈⠳⣮⡳⣦⡀⠀⠀⠀⠀⠈⠻⢦⡀
⠀⠀⠀⣀⣀⣸⠏⠀⠀⠀⠈⠳⣮⡳⣤⡀⠀⠀⠀⠀⠈⠛⢮⡛⢦⡀⠀⠀⠀⠀⠈⠙⢦⡙⢦⡀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⢠⠞⠁⠀⠘⢧⡀⠀⠀⠀⠀⠀⠙⢦⡙⢦⡀⠀⠀⠀⠀⠀⠙⢦⡙⢦⡀⠀⠀⠀⠀⠀⠙⢦⣝⢦⡀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⢸⡄⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠙⢦⡙⢦⡀⠀⠀⠀⠀⠀⠙⢦⣽⠆⠀⠀⠀⠀⠀⠀⠈⠙⠛⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠙⢦⡀⠀⢀⣀⣄⡙⢦⣀⠀⠀⠀⠀⠀⠙⢦⣝⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠙⣶⠋⠀⠀⠙⠷⣝⠷⣄⠀⠀⠀⠀⠀⠙⠳⣌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⣠⠖⠛⠛⣧⠀⠀⠀⠀⠀⠈⠳⣌⠳⣄⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⢰⡇⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠈⠳⣌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠳⣄⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠈⠳⣮⡳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠈⠳⣄⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠈⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠈⠙⠓⠶⢤⣤⣤⣀⣀⣀⣤⣤⢤⣶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠓⠚⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠘⢦⠀⠀⠸⡄⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠹⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⢀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⡤⣄⡤⠤⢤⡀⠈⠁⠀⠔⠋⠀⣀⡤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⢳⠞⠉⠙⢾⡀⠀⠀⠙⢦⡀⠀⠀⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡀⣘⣦⠀⠀⠀⠙⢦⡀⠀⠀⠙⢶⡲⡴⠚⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠈⡟⠁⠀⠙⢦⡀⠀⠀⠙⢦⡀⠀⠀⠙⢧⡀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠙⣄⠀⠀⠀⠙⢦⡀⠀⠀⠙⢦⠀⠀⠀⠱⣄⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⢹⠊⠉⠓⢄⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠘⣄⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠓⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠬⣝⣦⣄⣀⣀⣀⣀⣀⡤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠓⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠃
⠀⠀⠀⠀⠀⠀⢰⠂⡔⠠⣠⠐⡖⢠⡄⢰⡢⢀⠀⡔⠀⢠⡂⠐⡆⢰⢢⡠⠢⡄⣄⠄⡖
⣀⣀⣀⣀⣀⣀⣼⣤⣧⣴⣹⣀⣧⣏⣱⣼⣼⣶⣤⣧⣄⣠⣼⣀⣇⣼⣱⣱⣤⣣⣍⣦⣧⣄⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣾⣷⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⡿⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣯⠻⠿⠋⠉⡀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠿⣿⡟⠀⠀⠀⠈⠘⠟⠀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡏⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠂⢀⠇⠀⠀⢀⣤⠀⠀⡠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⠀⠤⣀⣀⣀⣠⠔⠃⠀⠀⠀⢸⠀⡏⢖⡡⢊⡽⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠛⠷⢦⣤⣬⣦⡀⠀⠀⠀⠀⡠⠞⢠⠇⠈⠀⠉⠴⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠈⠉⠚⢭⡁⠑⢄⡠⠔⢉⡤⠊⠁⠀⠀⠀⠀⣈⡻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡅⠀⠀⠀⠀⠀⠀⢠⡟⠢⠌⣧⠔⠁⠀⠀⠀⢀⡔⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⣄⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠑⠲⠤⢄⣿⣅⡀⠀⠀⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠛⠀⠀⠀⠀⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⣧⠀⠀⠀⠀⠀⢀⣠⡴⠞⠛⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠛⠉⠀⠀⠀⢸⡇⢀⣠⡴⠞⠋⠉⠀⠀⠀⠀⢸⣇⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⢀⣠⣼⠟⠻⢧⡀⣴⠟⠋⠙⢷⣤⡴⠟⠋⠁⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠀⠀⠀⠀⠀⢀⣠⡴⠞⢋⡿⠁⠀⠀⠀⣿⠋⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⡴⠞⠋⠁⠀⢀⡾⠁⠀⠀⠀⣰⠏⠀⠀⠀⢠⡿⠗⠲⢦⣤⡴⠾⣯⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⢀⡾⠁⠀⠀⠀⣰⠏⠀⠀⠀⢠⡟⠀⠀⠀⠀⣷⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⢠⡟⠈⠙⢷⣄⡾⠁⠀⠀⠀⣰⠏⠀⠀⠀⢀⡟⠀⠀⠀⠀⣼⠃⠀⣀⣤⠟
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢀⡿⠁⠀⠀⠀⣰⠏⠀⠀⠀⢠⡿⠀⠀⠀⠀⣼⣧⣴⡟⠉⠀⠀⠀⢀⣀⣠⣤⣴⣶⠆
⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢀⡾⠁⠀⠀⠀⣰⠏⠀⠀⠀⢀⡾⠁⠀⠀⠀⣼⠋⠁⠀⠙⣧⠀⠾⠿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢀⡾⠁⠀⠀⠀⣰⠏⠀⠀⠀⢀⡾⠁⠀⠀⠀⣼⠃⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⢠⡟⠀⠀⠀⢀⣾⠁⠀⠀⠀⠐⠋⠀⠀⠀⢀⡾⠁⠀⠀⠀⣼⠃⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢠⡟⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠁⠀⠀⠀⣰⠇⠀⠀⠀⢠⡟⠀⠀⠘⠿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⢠⡟⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⢻⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠶⠤⢤⠤⠴⠶⠞⠋⠁

⣿⡟⡛⡿⠿⠿⠿⠿⠿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢀⡾⡄⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡟⢧⡀⣀⠞⠀⠙⠢⠤⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠳⢤⣠⡼⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⢦⣀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠚⠋⣀⣀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⣤⣤⣄⣀⣀⣉⠙⠓⠢⠄⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣑⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢁⣀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣀⡠⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⣠⣀⠀⠀⠰⣏⠃⠈⠀⢸⠁⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡘⢦⠏⠳⢾⡉⠛⠿⢿⡀⢠⠀⢸⠀⢻⢫⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠛⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠹⣽⠦⠀⠉⠒⠄⠀⠉⠺⣄⣸⠀⢸⠈⠒⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣀⡀⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀⢀⡴⠛⢶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠾⣀⠀⠈⡷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠐⠁⠀⠱⡀⢠⠟⠉⠙⣾⠁⠀⠘⣌⠀⠑⢤⡀⠈⠀⢄⡀⠑⠂⠀⠀⠀⠁⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠏⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠉⠓⠲⠄⠤⣄⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠑⠦⣀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠊⠁⢸⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠤⠤⠤⠖⠚⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠰⡆⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⡶⠀⢠⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠢⠄⢀⣀⠠⠤⠒⠹⡀⠀⠀⠀⠀⠀⠠⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⠀⢲⠒⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⠤⠔⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⢀⣠⡶⡶⠛⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢀⣀⢀⣴⠟⠁⠊⢀⠞⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢹⡟⠁⡐⠁⠐⢁⠔⣿⡴⠖⢲⡄⠀⢀⣀⡀⠀⠀⠈⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠠⠋⠀⠊⢀⠊⠀⠀⢰⠋⢀⣠⠞⠁⣠⡟⠻⢻⡆⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠁⠀⠀⠀⠀⠠⠀⢠⠃⠐⠛⠷⠶⠞⠻⠈⠆⣿⠇⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢁⠴⡑⢤⠀⣰⠟⠀⠀⠀⢠⠀⠀⠀⠀⠐⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠠⠇⣸⡴⠋⠀⠀⠀⢀⡨⠧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⡁⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⣀⣀⣤⠶⠟⠁⠀⠀⠀⣠⠊⠁
⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⢶⡿⢏⠀⠀⠈⠐⢄⡠⢞⠁⣑⣴⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢀
⠀⠀⠀⠴⠚⠋⠉⠁⡠⠖⠁⠀⠀⠑⢄⠀⠀⡠⠃⣀⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⣀⣞⠀⠀⠀⠀⠀⣄⠙⠗
⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⠀⠀⣤⢈⡿⠗⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⢀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⢀⣀⠀⣠⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⣿⡁⠀⣿⠖⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⣠⢾⡋⢹⣶⣿⡞⠉⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢁⡼⠃⠀⢙⣿⠟⠀⠛⢶⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢳⣠⡟⣠⠟⠀⠀⢀⡾⠁⠀⠀⢠⠾⣏⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣯⣄⢸⣿⡾⠁⠀⠀⣠⠏⠀⠀⠀⣴⠋⠀⢈⣿⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⢀⡾⠛⠁⣿⡾⠋⠀⠀⠀⡴⠃⠀⠀⢠⡞⠁⠀⢀⡿⠓⢴⠇⠀⠀⠀⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢀⡼⠋⠀⠀⠀⠀⠈⠀⠀⠀⠀⠋⠀⠀⣠⠏⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠈⠙⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢻⠏⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣱⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⢉⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣠⠞⠺⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⢛⢧⣀⠀⠀⠙⠲⣄⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⡴⠛⠂⣉⠤⠀⠈⠓⢦⣀⠀⠈⠙⢦⡀⣠⡟⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⢀⡞⠁⠊⣁⠤⠔⠂⣁⠠⠄⠈⠳⢦⣀⠔⠉⣯⠉⠉⠛⠓⠺⣧
⠀⠀⠀⠀⣰⠋⠀⢂⡅⠤⢐⢈⡁⠤⠀⢒⡈⡁⠤⢛⠳⣼⡧⢤⣤⣀⣀⣀⣟
⠀⠀⢀⡼⠃⣈⠩⠀⠂⣋⠉⠤⠐⠀⡁⠈⠔⠂⡋⠩⠰⠈⣹⠀⠀⠀⠉⢉⠉⡿
⠀⠀⠘⠁⠀⠤⠒⠈⣁⠠⠄⠒⢈⡁⠤⠒⠈⣁⠤⠐⢊⡼⣁⡀⠩⠄⠀⠒⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⠈⣁⠤⠐⠊⢁⡀⠤⣠⠟⠤⠀⠒⣂⣀⠉⠅⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⠠⠔⠂⠉⣀⢀⡼⠁⢀⣀⠩⠤⠀⠒⠒⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠈⠁⢠⠞⠀⠤⠄⠀⣒⠂⠈⠭⠁⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠰⠋⠀⠒⠀⠀⠄⠀⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠗⠀⢳⣄⠀⠀⠿⠂⠀⢀⣿⣿⣇⠀⠀⠀⢀⣤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⣿⣿⣦⡀⠀⠀⣼⡟⢸⣿⠀⣠⣶⣿⡟⠀⠀⢴⡆⠀⠀⠐⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣆⡀⠀⠀⢸⣿⠙⢿⣦⣠⣿⠁⠘⣿⡿⠛⣽⡿⠀⠀⠀⣀⣀⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣿⣬⣿⠿⠃⠀⠀⢿⣇⠀⠉⠻⠇⠀⠀⠉⠀⣼⣿⠷⠿⢿⣿⡿⠋⠀⠀⠀⣰⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠃⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⣀⣤⣤⡀⠀⠀⢀⣴⡿⠋⠀⠀⣠⣴⣾⠟⠁⠛⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣶⠾⠿⠛⠃⠀⢀⣼⡿⠋⢹⣿⠀⠐⠻⢿⣦⣀⠀⠀⠀⠉⠛⣿⣦⣾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⡶⣶⣦⣠⣿⣯⡀⣠⣿⠋⠀⠀⣀⣀⣩⣿⣿⣦⣄⠀⠀⠈⢿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⣿⡇⢀⣿⡿⠉⠉⣴⣿⡁⠀⠀⣿⡟⠛⠋⠉⠉⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢹⣷⣾⠏⠀⠀⣼⡟⠙⠻⢷⣦⣿⡇⠀⠀⠀⢠⣾⣧⠀⠀⠀⢾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠆⠀⢸⣿⠛⠿⠆⣸⣿⠟⢿⣷⣀⣈⠙⠃⠀⠰⢾⣿⣏⣻⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣰⣿⠃⠀⢠⣿⠛⠻⣷⡀⠀⠀⠀⠙⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⢠⣿⠃⠀⢀⣾⠇⠀⢠⣿⠿⢿⣦⠀⠀⠈⠀⢠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⢠⣿⠇⠀⠀⣼⡟⠀⠀⣾⡏⠀⠀⣿⠇⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⠉⠀⠀⠐⠿⠁⠀⢰⣿⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠀⣤⣄⣤⡀⣀⣀⣀⡀⢀⣀⡀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡈⠉⠉⠁⠙⠛⠛⠃⠙⠛⠛⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⢷⣦⣤⣤⣤⣤⡄⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠉⠉⠉⠉⠁⠈⠛

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣢⣳⣸⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣼⣰⣣⡂
⠀⠀⠀⠀⠙⢿⣿⣷⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠈⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠀⠀⠀⠀⣰⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⣦⣄⠀⠀⣿⣿⣿⡏⠁⢀⣤⣶⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣶⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠀⠒⠀⠀⠀⠉⠒⠋⠂⠒⠀⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠏⠁⠀⢀⠀⢀⡀⠀⠄⠀⠀⠀⠠⢄⣈⠉⠙⡍⠀⢶⠀⠠⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⠤⠤⠤⠤⠀⠀⠀⠀⢸⠀⠀⠀⠠⠠⠛⠈⠉⠉⠉⠁⠉⠣⠀⠈⠳⡀⠌⢢⣈⠆⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠡⡀⠀⠀⠀⠀⠀⠀⠈⣤⢄⠈⡦⠆⠀⠠⠔⠒⠢⠀⠀⠀⠖⠉⠛⢍⠀⠀⠀⠙⠀⡌⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⠃⠀⠀⠀⠀⠀⠀⠀⡆⠘⣆⠇⠀⠀⣇⣤⡀⢀⠇⠀⠰⣴⡄⠀⡄⠀⠀⠀⠀⠶⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢂⠀⣀⣀⠀⣀⡠⡇⢀⠹⡳⠀⠀⠈⠛⠓⠁⡀⠀⠀⠉⠁⠉⠀⠀⠀⠀⢀⠠⠃⡜⠀⠈⠉⠐⠂⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠢⠈⢇⠀⠀⠀⠀⠀⠘⢄⠁⢣⡀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠀⠀⢀⡰⡃⠀⡤⠄⠊⠀⠀⠀⠀⠀⠀⠠⠀⠘⠒⠠⣀
⠀⠀⢀⠤⠒⠐⠂⠒⠂⠈⠉⠒⣄⠀⢡⢨⠀⠀⠀⠀⠀⠀⠀⠁⠈⠱⡀⠀⠀⠤⢀⣀⣀⡀⠠⠄⠒⠉⠠⠆⣘⣀⠀⠀⠤⠥⠤⠤⠌⠴⠦⠠⠤⠤⠤⠀⢡⡀
⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⢀⡤⠰⠆⠀⢣⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡂
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⢀⠀⠀⠉⠓⠷⡢⢄⢀⣀⡀⢤⠐⢈⡁⠤⠈⠢⢄⡀⠀⠀⠀⠀⣠⣔⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠰⣀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠉⠀⠒⢠⡅⠠⠁⠀⠀⠀⠙⠂⠒⠒⠒⠲⢄⡉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠉⠉⠑⠒⣒⣤⣤⣤⣀⣀⣀⣀⣀⠀⣀⡠⠎
⠀⠀⠀⠉⠉⠉⠐⠀⠀⠂⠀⠀⠀⠒⠀⠀⢰⠺⡗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⠂⠤⣀⠀⠀⠀⠀⠠⠀⠂⠉⠀⠤⠄⠀⠀⠀⠀⠀⠨⠉⠑⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠸⠁⠀⠘⠧⣀⡤⠤⠀⠰⠖⠋⠉⠉⠉⠀⠀⠀⢀⣀⡀⠈⠰⢦⣶⠶⠶⠶⠖⠒⠒⠚⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⣦⡀⠒⢈⡀⠀⠀⣀⣀⠀⠤⠄⠀⠂⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣤⣤⡤⠾⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⠨⡍⣁⣀⣀⡠⠤⠤⠤⠒⠒⠒⠈⠛⠉⠁⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

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


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠈⠙⢦⠀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠉⣹⠶⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠴⠚⠁⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠙⢆
⡖⠖⠂⠑⠤⠰⠊⠒⠁⠨⣀⢀⣤⠷⣄⡀⠀⠀⠀⠀⢀⣠⡟⢁⡀⠀⠀⠀⠀⠀⡖⠊⠉⠀⠀⠀⣠⠶⢦⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⡀⠀⡏⠰⠒⢤⡴
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠛⠒⠚⢻⣿⡿⠛⢻⠃⠀⣠⠤⣄⣠⠃⠀⠀⠀⠀⠀⠈⠀⠈⠁⠘⠒⡆⣠⠤⣀⠤⠙⠃⠌⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢⠀⢄⠀⠀⠀⠀⠀⠀⠈⠛⣷⢄⠸⡄⠀⡇⠀⠀⠁⠀⠀⠀⠀⠀⡶⡀⠀⠀⠀⢠⠏⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⡄
⣀⡀⠀⠀⠀⡴⠈⠠⠀⠁⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⢹⠈⣆⢳⡀⠉⠙⢳⠀⠀⠀⠀⠀⠀⡇⠘⠢⣄⡀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠒⣄
⠈⠉⠙⠓⠚⠓⠛⠛⠛⠓⠒⠒⠶⠤⠖⠒⠋⠉⠉⠓⠤⣌⣣⡘⡄⢳⡀⢀⡗⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠉⠁⣜⣰⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⢀⠠⣀⠀⠀⠀⠈⠉⠻⡄⢳⣾⣀⠀⠀⠀⠀⠀⠀⢀⣨⠷⠤⠤⠖⢿⠛⠛⣿⠒⢻⡉⣉⣉⣉⡉⢉⣉⣉⢉⠉⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢟⠅⢑⠀⣀⠒⠀⠀⠀⠀⠀⢱⠊⠙⢯⡇⠀⢠⠞⠛⠉⠁⢀⣀⣠⠤⠖⢋⣠⠤⠾⡿⠯⠭⠭⠭⠭⠭⠭⠭⠭⠭⢽⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⢰⣰⠃⡀⢓⣥⣄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠑⠦⠞⠉⠉⢗⠉⣉⡠⠤⠒⠋⠁⢀⣤⣖⣓⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡵⠷⢠⠟⠋⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⡴⠚⠉⠀⠀⠀⠀⠀⣀⣼⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣠⣇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣀⣯⣤⣭⣬⣭⣭⣬⣭⣭⣭⣭⣭⣭⣭⣭⣀⣀⣀
⠀⠀⠀⠀⡀⠤⣀⣠⣶⡶⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠳⣤⠖⠋⠁⠀⠈⠙⠒⠤⢄⣀⣸⢀⣀⠤⠔⣒⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠐⢕⠀⡛⠀⣛⢆⠢⡀⠀⠀⠀⠀⢐⣿⡴⢆⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣍⡠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⣠⣤⡌⢁⠈⡠⠗⡪⠁⠀⠀⠀⠀⠀⠉⠀⠈⠣⡘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠘⠛⡧⠾⠲⡀⠈⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠳⣜⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⡠⠤⠔⠒⠒⠉⠉⢁⣀⠤⠖⠚⠉⠁⠉⠓⠒⠤⣤⠤⢤⠔⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠤⠤⠖⠒⠒⠒⠉⠉⠁⠀⢀⣀⣠⡤⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠒⠒⠒⠒⠒⠒⠒⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠒⠒⠒⠊⠉⠉⠉⠉⢙⣄⣀⣹⠶⣲⠒⠢⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⣱⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⢿⡟⢢⡐⢐⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠢⠤⠤⠤⣀⣀⣀⣀⣀⣀⣀⣀⣀⡠⠤⠤⠴⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⡰⠃⡦⡭⡉⡥⠐⢪⡸⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠑⠪⠛⠃⣁⡀⢾⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⡜⠉⠁⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋
⣶⣶⣶⣶⣶⡾⢶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣿⣾⣶⣿⣿⣿⡷⠶⠿⠿⠾⢷⣾⡷⠶⠶⠶⢶⣾

⠀⠀⠀⢀⡀
⠀⠀⢀⠘⢀⡀⠀⠀⠀⠀⣠⢄⣀⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⣄⣀⣠⣬⠁⢀⣐⣣⣤⣨⣤⣄⡀⠀⠀⠀⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠖⠄⠀⠀⣯⠝⠈⠀⠐
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡁⡞⠀⢠⡆⣆⠀⠀⠀⠀⠀⣺⡞⠃⠀⠀⠀⠀⠀⠐⠀⠋⠀⠀⢸⣇⠰⣇⠀⢀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⢃⠀⠚⢠⣬⠀⠀⡤⠐⠯⠅⢂⣀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠉⠉⠀⠀⣠⠘⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠐⠾⠋⠀⢀⡼⠅⣀⣰⠖⠚⢋⠁⣾⡿⣦⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣤⠀⠀⠡⠂
⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣄⡀⠒⠁⣺⠀⠐⠈⣿⠋⠃⠉⣿⣾⣿⣷⣆⠈⠁⠀⠀⠀⠀⠀⠀⢸⣷⣶⠄⠐⣦⣤⠴
⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢨⡏⠀⢸⡷⠂⢠⠛⣿⠂⢀⣀⣽⣆⣧⠙⠟⠊⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠛⠉⢉⣴⠶
⣀⢺⣿⣿⣿⣿⣿⣿⣷⣿⡧⢾⣿⣧⡀⢸⡀⠀⠀⢐⡗⠀⢨⡉⠉⢹⣿⡀⢬⡂⡄⠠⠀⠀⠀⠀⢀⣴⣗⣢⣶⠇⣼⣿⣴
⢁⡌⢻⣿⣿⣿⡏⠻⢻⣿⣷⠀⢈⢹⣦⣾⠛⠃⠀⠈⠉⣄⣠⣧⠀⠈⡿⢷⡿⠃⠀⣠⣴⠶⢶⡄⣾⣿⣿⣩⡄⢀⡀⣿⣭
⡼⠀⢾⣿⣿⣿⠟⠻⣿⣿⣿⣯⣿⣿⣿⢏⠀⠀⠀⠀⠀⠙⣿⣯⣤⡴⢿⡟⠂⠀⠀⠸⢿⡗⡂⠁⠹⢿⡅⠙⠛⢻⣿⣏⠠
⡄⠴⠻⠞⠀⣩⠄⠀⢹⣿⡿⣿⣿⢿⣿⣾⣄⠀⠀⠀⠀⣀⣻⠈⠺⠧⠤⠀⠀⠀⠀⣶⣶⣍⣋⣠⣤⣼⡷⠶⠖⠾⡿⠛⠁
⣿⣿⣿⣇⣤⣀⡀⣀⣀⣽⠀⣨⠿⣟⣿⣷⣿⣿⣿⣿⣯⣿⡿⠓⠀⠀⠀⠀⠀⠀⠀⣀⠉⠛⠛⠛⠈⣿⣵⡫⢡⣶⡀
⢿⣿⣿⣿⠿⡿⣿⣿⡿⣿⣶⣶⣶⡿⠿⢷⣿⣟⠻⣿⡿⠟⠛⠂⠀⠀⠀⠀⠀⠀⣿⠈⣿⡶⢤⣀⠀⢽⣿⣿⣿⣿⠁
⣿⣿⣿⣿⣴⣧⠚⢻⣾⢻⣿⣿⣼⣧⠀⠀⠈⠋⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠘⣷⡆⢼⣹⣴⣴⣷⡄⠉⠁⠀⠀⢀
⣿⣿⣿⣿⣿⣿⡧⢾⣿⣼⣿⠃⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣧⠀⠈⠉⠋⢁⡈⠙⠛⠀⠀⠀⠀⠀⢸
⣿⣿⣿⣿⣿⣽⣯⣤⣭⣿⣿⣤⣤⣬⣿⣤⣤⣄⣀⣀⣠⣤⣤⣤⣄⣤⣤⣤⣼⣭⣽⣧⣀⣦⣴⣼⣿⣤⣤⣤⣠⣤⣤⣤⣴
⣿⣿⣉⣩⣍⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⡴⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢈⡟⠀⢰⠃⢀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢻⠀⢰⠃⠈⡇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢶⡇⠀⡼⢁⣤⠏⢠⡏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⣼⠀⢸⠀⢀⡏⠉⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⣸⠃⣼⠀⠀⡸⠀⡼⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢠⡇⢠⠏⠂⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡾⠀⢰⠃⢀⡇⠀⢀⠇⢰⠇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⣼⠁⡜⠀⠀⣼⠀⡼⢻
⠀⠀⠀⠀⠀⠀⢸⠁⠀⣸⠀⡼⠀⠀⢻⠀⡿⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⢠⡏⢀⡇⠀⢰⠃⢸⡇
⠀⠀⠀⠀⠀⠀⡏⠀⠀⡇⠀⣷⠀⠀⢸⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⢧⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢀⡾⣠⠋⠀⠀⣼⠀⡼⠃⢠
⠀⠀⠀⠀⠀⢸⠃⠀⠔⠓⠒⠛⠦⢄⣟⣾⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠘⡇⠀⠀⠀⠀⠀⣰⠗⠀⠀⣼⣣⡇⠀⠀⡼⠁⢰⠁⠀⢸
⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢺⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⠀⡼⠁⠀⠀⠀⠈⠉⠉⠉⠙⠣⢤⠏⠀⢀⡏
⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣠⠴⠶⣶⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣼⠁
⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢼⠃⠀⠀⠀⢀⡜⠁⠀⢠⠏⠀⠀⠀⣼⠀⠀⠤⠾⠤⠴⠿⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇
⠀⠀⠀⢠⡟⠀⠀⠀⠀⢀⡇⠀⠀⠀⢀⣀⣀⣀⣈⡇⠀⠀⡰⠋⠀⠀⢀⡟⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠀⠀⠀⠀⡴⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⠀⠀⠀⠀⠁⠀⠀⠀⠈⠑⢤⣾⠁⠀⠀⢠⠞⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⣾
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢰⡇
⠀⠀⠀⢨⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⣼⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣾⠋
⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⢿⠿⠿⢿⢟⡿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⣟⣻⣿⣿⣻⣿⣟⣿⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⢰⣿⠃⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠸⠟⠀⠀⣠⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡟⢀⣀⡀⠀⣠⣶⣄⢰⣿⣿⣿⡿⠛⣡⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠏⢀⣿⣿⡿⢠⣿⣿⡟⠘⠛⠋⣥⣶⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡄⣼⣿⣿⠃⣾⣿⣿⢁⣾⣿⣦⢹⣿⠟⣋⣥⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⢰⣿⣿⡟⢸⣿⣿⡏⣸⣿⣿⠇⣨⣴⣾⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠻⣿⣿⣿⣿⠃⣿⣿⣿⢁⣿⣿⡿⢠⣿⣿⡟⢠⣶⣦⡙⢛⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡈⣿⣿⡏⣸⣿⣿⡏⣼⣿⣿⠇⣾⣿⣿⢃⣿⣿⣿⢠⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⢸⣿⢁⣿⣿⣿⣠⣿⣿⡟⢸⣿⣿⡏⣼⣿⣿⠇⡼⠟⠉⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡈⠇⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢠⣿⣿⡿⠀⠀⠀⠀⠈⠛⠻⠿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠃⠀⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⣶⡀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢿⣧⠀⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠘⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⢿⣿⣿⠙⠿⠟⠿⠛⣿⣿⣿⣿⣿⡆⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⢸⣿⣿⣿⡿⢋⣤⣤⠤⠀⠀⠈⠉⠀⠀⠀⣠⡤⠲⢶⡶⠘⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠁⠈⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠁⠀⢸⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣼⣿⣿⣿⣇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⢀⣴⣿⣿⣿⣷⡄⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣆⣤⢀⡄⢠⡄⢠
⠀⠀⠀⠀⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⠁⠐⣆⠠⣸⠍⠉⠉⠉⣉⠃⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡧⠤⠀⡄⠠⠄⠠
⠀⠀⠀⠀⠀⠀⠉⠻⢿⢿⣿⣿⣿⣿⣿⣷⡀⠙⠆⠀⠀⠀⠉⠛⠿⠿⠛⠛⠁⠀⠀⠘⠃⡿⠿⠿⠿⣿⣿⣿⣿⠦⡄⠠⠄⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⡿⣷⡄⠀⠀⠀⠀⠓⠀⠀⠓⠲⠤⠀⣠⠖⠀⣾⣿⣿⣿⣿⣿⠿⠇⠺⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠠⠀⠠⠀⠉⡉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢠⣿⠿⠿⠟⠋⠄⠠⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣴⣆⠉⠀⠀⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣶⣤⣀⠙⠷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡉⠻⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡈⠙⢿⣷⡄⠀⠀⠀⠀⠀⢉
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣽⣧⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⠶⠶⠤⢤⣀⠀⠘⠁⠀⠀⠀⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠶⠤⣤⡀⠀⠀⠀⠀⠀⠀⢠⡇⠀⢀⡴⠒⠒⢦⡀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠶⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⡏⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠒⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⠀⣠⠤⡄⠀⣸⠀⢠⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠈⢧⡹⠴⠇⣠⠇⠀⢈⡇⠀⠀⠀⣼⠃⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠈⠙⠛⠛⠁⠀⠀⢸⠇⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⢀⠎⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⣀⡴⠋⠀⠀⠀⡸⠀⠀⠀⠀⠀⠐⠓⠲⠦⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡉⠉⠁⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠙⠲⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠚⠉⠁⠈⠳⣄⠀⠀⠀⣠⠀⠀⠀⣷⠤⠤⠤⠤⢴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠈⠓⣄⡴⠁⠀⠀⠀⣿⠉⠉⢉⣉⣹⠀⠀⠀⠀⠀⢀⡴⠚⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⣴⢛⣷⣄⠀⠀⠀⣿⣒⣒⣒⣒⣾⠀⠀⠀⢀⡴⠋⠀⠀⠀⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠈⠉⠉⠛⠪⢍⡐⢲⠇⠀⠀⣠⠀⢹⡄⠀⢠⡞⠀⠀⠀⠀⣼⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡬⠷⣄⣠⠖⢦⠴⠚⠉⡏⠀⢀⠞⢁⡄⠸⡇⣰⠋⠀⠀⠀⢀⡞⢹⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⠙⠒⠚⠣⢭⣉⣛⠙⢁⡴⠋⠀⢀⡟⠁⠀⠀⠀⣠⠋⠀⣹⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠙⠓⠦⣤⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠈⠉⠉⠀⠀⢀⣸⢧⣀⣠⣴⣮⣤⡤⠤⠿⠀⡇
⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠛⠓⠚⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠺⠦⠤⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢸⡗⠒⠚⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠛⣄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣠⠏⠀⠀⠈⠓⢦⡀⠀⢀⡴⠋⠉⠙⠲⣤⣀⣀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠞⠁⠀⠀⠀⠀⠀⠀⠙⠒⠋⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠰⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⠀⠀⠚⠀⠀⣠⠞⠁⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⡰⠞⠛⠋⠛⠛⢶⣄⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⣰⠎⠳⣆⠀⠀⠀⣠⠞⠙⣧⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⡟⠀⠀⠈⠳⣤⠞⠁⠀⠀⢸⡇⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⢻⣤⣤⣤⣤⣤⣾⠁⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣗⠲⠶⠤⢬⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⡁⠸⣏⣉⣛⣛⣺⡇⠀⢛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢁⡜⠁⠀⠻⣍⣉⣉⡽⠁⠀⢯⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢸⠀⠀⢠⡄⠈⠉⠉⠀⠀⠀⠈⣇⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠳⢤⣜⡧⠤⣤⣤⣀⡀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠉⢧⡀⠈⠓⢺⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠻⢤⡀⠀⠀⠀⢠⠇⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⡇⠀⢀⡴⠋⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⣀⡀⠀⠙⠚⢉⣀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠙⠨⠲⣄⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠚⢄⠀⠀⠀⠀⠀⠀⣤⠀⡄⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⢀⠤⠖⠂⠙⠒⠢⣄⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⡀⢀⠀⢀⠑⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠱⡀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠀⠀⠀⠀⠀⠀⠆⢄⠀⠠⡠⣀⠀⠀⠀⠢⠀⠀⢀⠂⠀⠀⠀⠀⠰⠆⠘⠃⠀⢀⠀⠀⠀⠁
⠀⠀⡀⠀⠀⠀⢃⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠑⠢⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠄
⠀⢠⠘⡄⠀⠀⠀⠑⠤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡳⢄⡀⠀⠀⠀⢀
⠀⠀⠑⢄⠀⠄⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠪⠍⡉⠉⠉
⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠑⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⢆⠀⠀⠀⠀⢀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠂
⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣷⣶⣷⣶⣿⣿⣶⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣤⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠶⠿⠟⠛⠿⠿⠶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄⠀⠀⠀⢰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⢸⡅⠀⠀⠀⢸⡇⠀⠀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⠇⠀⠀⠀⠸⠇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿
⠶⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠿⠿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠹⣷⡶⠾⠟⠛⠉⠁⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡶⣶⣶⣶⣶⡾⠿⠿⠿⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠁
⠀⣠⣤⣶⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠉
⣼⠟⠁⠀⠀⠀⠀⠉⠉⠛⠻⠷⢶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⠾⠛⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⣤⠀⣴⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⣤⣄⡀
⠀⠀⠀⢀⡘⣿⡙⠷⠟⢸⣧⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡾⠋⠀⠀⠀⠀⠉⠻⣆
⠀⠀⠀⣿⣙⠛⢡⡶⠶⣦⠉⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⣨⡾⠛⠛⠛⢷⣄⠀⠀⢹⣆⡀
⠀⠀⠀⣩⡽⠇⠸⣧⣤⠿⢀⣙⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⡇⠀⠀⢰⡏⠀⠀⠀⠀⠀⢹⡆⠀⠀⠈⠻⣆
⠀⠀⠀⠹⡷⠞⣷⢀⣴⣄⢻⣍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠁⠀⠀⠸⣧⠀⢤⣴⡄⠀⣼⠃⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠘⠻⠾⠃⠹⠛⠁⣶⠶⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⣿⢰⡞⠁⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠻⣦⣀⣿⠀⢀⣿⣠⡾⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⢰⡾⠷⠿⠾⣷⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠈⠉⠁⠀⠀⠉⠋⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣭⡛⢿⡄⠀⠀⠀⠘⠿⣾⠿⡷⠟⠀⣼⠛⠛⠉
⠀⠀⠀⠀⠀⢠⣤⣤⣴⠟⠀⢠⡾⠛⠛⢶⡄⠈⢿⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠀⣨⡗⠈⠻⢶⣤⡴⣦⣀⡀⠀⢀⣠⡾⠃
⠀⠀⠀⠀⠀⢸⣇⣀⣀⡀⠀⢿⡄⠀⠀⢸⡇⠀⢀⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣦⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠉⠉⣩⡷⠀⠈⠛⠶⠾⠋⠀⠀⣿⡉⠉⠉⠀⠀⣀⣀⣀⣀⡀⠀⠻⠶⠟
⠀⠀⠀⠀⠀⠀⠀⢾⣏⠀⣠⡶⣤⠀⠀⣴⢦⣄⠈⣻⡦⣠⡶⠛⠉⠉⠉⠉⠛⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠋⠀⣿⠀⢀⣿⠀⠙⠿⠋⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠰⠟⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣄⣠⣤⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⢠⡞⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣬⣥⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⣀⣤⠀⠀⠀⣠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠃⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⣄
⠀⠀⠀⠀⠀⢠⣄⢀⡤⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⢸⡇⠀⣀⣀⡀⣠⣤⡀⠀⠀⠀⣴⠶⠾⠋
⠀⠀⠀⠀⠀⢀⡭⢨⣄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⢸⡏⠉⠿⠋⢀⣿⠆⠀⠛
⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⣨⡿⠃⠀⠀⠘⣧⣀⡼⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠻⣦⡀⠀⠀⠀⠀⠉⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣷⠄⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠈⠻⣦⡀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢸⣧⣤⣤⣤⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣤⣤⣄⣼⡇⠀⠀⠀⠈⠻⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⡆⢰⠏⢱⡞⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⢀⠇⡎⠀⢸⠇⠀⣼⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢄⠀⢠⠎⠀⠀⡞⢰⠁⠀⡸⠀⠀⡏⠀⣧⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⢳⠁⠀⠀⠐⣲⠃⠀⣰⠁⠀⢸⠁⢸⠙⡦⠴⠓⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⡆⠀⠀⡰⠁⠀⠰⠃⠀⠀⡎⠀⡆⢠⣧⣤⣔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢼⠀⠀⠀⢣⢀⠜⠁⠀⠀⠀⠀⠀⠘⠀⠀⠁⣸⣀⡠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡜⠁⢸⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣋⣉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⡀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⡀⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⢀⣤⣀⣀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⣶⣦⣤⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣯⣿⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣯⣽⣿⣿⣭⣭⣭⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠁⢐⡄⡄⡀⢠⠀⠀⢀⡀⢆⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠉⠀⠀⠀⠜⠀⠀⠀⢃⠘⡈⠀⠈⠀⠀⠇⠁⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⢀⣇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣄⡀⠁⠈⡈⠂⠉⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⡔⠀⠃⣶⢀⡆⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢁⡀⠀⠀⠀⣴⣿⣴⡄⠀⠀⠀⠀⢸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡟⣇⠀⠀⠀⠟⣿⣿⠃⠀⠀⠀⠘⣦⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣛⣳⠀⣀⣠⣹⣻⣄⣀⣤⣦⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣷⣿⣿⣿⣿⣿⣿⣿⢟⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⣻⣿⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣽⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣚⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢹⣿⣿⡟⠉⢻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢋⣿⣿⠆⠀⣴⣿⣿⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⣿⣏⢿⣷⢠⣮⣿⣻⣷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠈⠻⠏⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡶⠿⠿⠿⠛⠿⠿⠿⢶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠉⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⡤⠊⠉⠉⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⢀⡞⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⢸⠀⠀⠀⢀⡴⠃⢀⠠⢶⠀⠶⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠈⠳⠶⠒⢋⢰⡇⢨⣘⡾⠀⣦⣹⣇⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⠞⠉⠙⠦⠎⠁⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠘⡀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡄⠀⠀⢀⠄⢺⠀⠀⠀⠋⠀⠀⠢⠄⢸⡏⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠘⢿⣄⢐⡁⠀⠸⠀⠀⠀⠀⠀⢀⣠⣶⠟⠁⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠉⠛⠷⠶⣦⣤⣴⣶⠶⠾⠛⠉⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠉⠙⠻⠶⣦⣤⣤⣤⡴⠶⠾⠛⠁⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣄⡀⠀⠀⠀⢀⣀⣀⣠⣤⠴⠞⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠉⠛⠛⠛⠛⠉⠉⠁⠀⠀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣤⣀⣀⣀⣠⣤⣶⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣏⠉⠉⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠁

⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⠶⠶⠶⣶⡶⠶⣶⡶⠶⢶⣶

⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⠀⠰⠄⣀
⣿⣿⣿⣷⡄⠀⠀⠀⠠⠤⠠⠤⢠⠄⠀⣄⠘⡁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⠘⠠⠼⠠
⣿⣿⣿⣿⣿⣦⡀⠀⢀⠀⠠⠀⠁⣠⠀⠛⠂⡂⠀⠀⣀⠀⠀⠀⠠⠀⣠⠀⠀⠀⠀⠀⠀⠀⠆⠀⢐⠎⡁
⠈⠙⠿⢿⣿⣿⠋⠀⠀⠀⠠⠂⠠⠀⠐⠀⠀⠈⠘⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⢰⠀⠀⠰⠂⠀⣴
⠀⠀⠀⠀⣿⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠳⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⡀⠀⢸⡀⢄⡘⠀⠀⢘
⠀⠀⠀⢹⣿⣇⠿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠂⠸⡿⠀⠀⠒⠀⠀⢀⣴⡾
⠀⠀⠀⠈⠉⠀⠀⢹⢁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠆⢀⢄⣀⢀⡀⣀⣠⡄⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠒⡒⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⠦⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠄⠀⠀⠀⠀⠀⠀⣴⣥⣯⣥⠀⠀⠀⢠⠀⠂⣆
⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠄⠀⢻⣟⣻⡿⠀⠀⠀⠀⠀⠀⠘⠀⠠
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⢀⡄⠀⠀⠀⠠
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡒⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠼⣆⡖⢀⡤⠀⡀
⠀⠀⠀⠀⢻⣷⢀⠘⠉⢨⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠙⢾⡁⡏⢰⠟⣡
⠀⡀⠀⢐⡀⠁⠈⠠⠦⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠚⠉⠳⠀⠀⠙⠧⣿⢰⡏
⡜⡤⠁⣀⠈⠠⣼⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣧
⠟⠃⠀⠉⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈
⣂⠰⠂⠀⠀⠀⠀⢻⡟⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⠄⠀⠀⠀⡠⢎⠁⠀⠀⠀⠀⠀⣠⡾⠃⠀⡈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣠⣾⠹⠂⣽⣻⠁⠐⡀⠀⠙⠀⠀⠀⠀⠀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣟⡵⣿⡽⠁⠀⠀⠀⠀⠀⠀⠀⢈⡀⢀⠀⡄⠑⠢⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠸⠇⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⠀⠀⠀⠀⠀⠀⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠛⠉⢧⠀⢀⣠⠴⠚⠉⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠉⠀⠀⢀⣠⡾⠶⢯⣡⠖⠓⢦⡤⠞⠋⠉⠙⡆
⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⢀⣠⡴⠞⢉⡟⠀⠀⢸⠏⠀⠀⣸⣁⡀⢀⣠⡴⠃
⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⣈⡁⠀⢀⡞⠀⠀⢠⠏⠀⠀⣰⠋⠀⠙⡏⠉⠹⡆
⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⡼⠁⠙⢦⡞⠀⠀⢠⠏⠀⠀⣰⠃⠀⠀⡼⣁⡤⠞⠁⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡼⠁⠀⢀⡞⠀⠀⢠⠏⠀⠀⣰⠃⠀⠀⡼⠛⠛⣆⠠⣴⠶⠾⠛⠋⠁
⠀⠀⠀⠀⢸⡀⠀⠀⠀⡼⠁⠀⢀⡞⠀⠀⢠⠏⠀⠀⣰⠃⠀⠀⡼⠁⠀⢀⡟
⠀⠀⠀⠀⠀⢧⠀⠀⡼⠁⠀⢀⡞⠀⠀⠀⠈⠀⠀⢰⠃⠀⠀⡼⠁⠀⢀⡞⠀⢴⣤⣀
⠀⠀⠀⠀⠀⠈⠳⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢀⣞⡀⠀⠀⠈⠙⠻⢶⣤
⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡞⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⣀⠀⠀⠀⣀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣤⣀⡀⣤⣄⠀⠤⣀⣀⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠀⠉⠀⠁⠉⠉⠁⠀⠁⠉⠁





⠀⠀⠀⠀⠀⠀⣄⢀
⠀⣓⣠⣤⡄⠀⠉⣥⣿⣾⠀⠀⠀⠀⡀⠀⡀
⠀⠆⠻⣷⣿⣿⣿⣿⣿⣿⣿⡯⣠⣶⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡿⠿⠿⢿⡀
⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⢸⡧
⠀⠀⠀⠰⠿⠋⣹⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢰⠀⠀⠘⡇
⠀⠀⠀⠀⠀⣸⠿⠿⢿⣿⣿⣿⣿⣿⣧⠀⠀⣾⣀⡀⢀⠁
⠀⠀⠀⠀⠀⡇⠀⢀⠀⢹⣿⣿⣿⣿⣿⣗⣷⣬⣿⣿⡇
⠀⠀⠀⠀⠀⠁⣀⣸⡄⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⠄
⠀⠀⠀⠀⢠⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠂
⠀⠀⠀⠀⠉⡿⣿⣿⣿⣿⣿⣿⢿⣇⢟⣿⣿⣿⣿⣿⣿⣿⣿⠉⣿⡁
⠀⠀⠀⠀⠀⠃⢹⢿⣿⣿⣿⡆⠈⠁⠀⠑⢿⣿⣿⢿⣿⣿⡇⠀⠿⠃
⠀⠀⠀⠀⠀⠀⠸⢸⣿⣿⣿⠁⠀⠀⠀⠀⢀⣿⡿⣼⣿⣿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⣠⣴⣶⡿⠿⠿⢿⣶⣦⣄⠀⠀⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠟⠉⠀⣀⡀⢀⠀⠀⠉⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⢰⡶⣛⣛⢿⣥⡀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⢰⣿⠁⠀⠀⢿⡗⣿⣿⢇⣿⡅⠀⠀⠀⠈⣿⡆⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠀⠀⢸⣿⠀⠀⢀⣜⣟⣶⡶⢿⢽⠞⣓⢷⡄⠀⣿⡇⠀⠀⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠠⡏⣶⢝⡇⣠⣤⣹⣮⣋⡼⠃⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⠙⠖⠛⠙⢿⣻⠇⠈⠁⠀⣰⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡷⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⢾⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠋⠀⠀⠀⠀⠀⠀⢸⣿⣶⣶⣶⣶⣶⣶⣿⠇⠀⠀⠀⠀⠀⠀⠙⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣿⣶⣶⣶⣶⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢽⣿⣿⣿⣿⡯⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⡉⠁⠀⠀⠀⠀⠈⠉⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡉⠉⠛⠛⠒⠒⠶⠶⠶⠶⠶⣶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣅⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⠉⠉⠛⠛⠛⠛⠛⠛⠉⣍⢿⡧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⣷⡈⠳⣤⡀
⠀⠀⠀⠀⠀⠰⣶⡖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢹⢡⠀⠀⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠈⡄⠆⠀⠀⠀⠀⠈⠛⠶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⢡⠘⡄⠀⠀⠀⠀⠀⣀⣀⣬⠋⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⣦⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠘⡄⢡⠀⠠⠖⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⡁⠀⠀⠇⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠖⠀⠀⢠⠀⠀⡇⠀⠀⢸⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⡏⠀⠀⠀⢸⡆⢸⡇⠀⠀⠀⡆⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡠⠞⠁⠀⡼⠀⠀⠀⠀⢸⡇⢸⠁⠀⠀⠀⢃⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠙⢻⣄⠀⠀⡴⠁⠀⢰⠀⠀⣼⠃⣾⠀⠀⠀⠀⢸⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠙⢧⡼⠁⠀⣰⠃⠀⣼⠃⠀⡿⠀⠀⠀⠀⠘⡄⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣠⠞⠀⠀⡴⠁⣠⡾⠁⠀⢀⡇⠀⠀⠀⠀⠀⡇⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡴⠃⠀⣠⠞⢦⡾⠋⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡇⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⠜⠁⡴⠋⠁⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⡇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⡴⠋⠀⠾⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡵⠂⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡎⠁⠠⠊⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣷⡱⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⢸⡆⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢀⠌⠁⡤⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⡴⠋⢰⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠂⢤⡊⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠈⠀⠀⣸
⠀⠀⠀⠀⠀⠀⣰⠃⠠⠔⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⡿⠀⠐⡇⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠏
⠀⠀⠀⠀⠀⢀⡁⠀⠀⣧⣠⠆⠀⠘⣷⠀⣴⠶⠶⡄⡀⢀⣤⣀⡀⢀⡀⣀⣀⢀⠀⣴⡄⡖⢀⣤⢀⣄⠀⠀⠀⡀⣀⡀
⠀⠀⠀⠀⠀⢸⠃⡤⢦⢾⡃⠀⠀⠀⠹⠀⠀⢀⣄⡿⣅⢿⣿⢿⣹⠦⡅⣭⠈⣯⡿⣯⡅⣽⡀⣧⢦⡼⠀⠘⣯⡯⣭⡄
⠀⠀⠀⠀⠀⠛⠀⠀⠀⠈⡇
⠀⠀⠀⠀⢰⠏⠀⠒⠒⠒⢲⡀⠀⠀⠀⠀⢤⢀⠤⣄⡀⣠⣤⡄⠀⢠⠤⢠⡤⣀⢀⣠⡴⡇⢠⣴⣤⡄⠀⠀⣰⣆⣀⡀
⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⢰⡌⠷⠏⠧⠻⠶⠇⠀⢰⡞⠰⠆⠹⠟⠤⠢⠧⠾⠿⠪⠽⠀⠀⠵⠾⠹⠇
⠀⠀⠀⣾⡁⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠈⠉⠓⠒⠲⠶⠶⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⣶⠰⡶⠀⡟⢠⣦⠐⠀⠠⣶⣆⠶⢰⣶⠆⠸⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⡏⠑⠷⠘⠿⠂⠳⠓⠿⠋⠒⠛⠿⠻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣀⠀⢠⢀⣀⣄⡀⢀⣀⡀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠙⠀⠀⠀⠁⠀⠉⠃⠑⠃⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠒⠒⠂⠤⡀⠀⠀⠠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠀⠀⠀⠀⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠈⢦⠘⠰⡞⠈⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⣀⣅⣀⠇⠀⠀⠀⠀⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠴⠶⠶⠒⠒⠒⠛⠒⠒⠶⠶⠦⣤⣄⣀
⠀⠀⠀⠀⠀⢀⣠⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣄
⠀⠀⠀⢠⣾⢛⠁⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⣿⠘⠈⡄⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⢿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇
⠠⠖⠃⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣤⣀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠈⠢⠀⢤⡄⠀⠀⢠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⣰⠆⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢻⡿⠛⠋
⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁
⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⢀⡀⠀⠀⠀⡈⣱⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢀⣤⠞⠋
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣸⣤⡴⠞⠋
⠀⠀⠀⠀⣿⣄⣄⣤⣤⣤⡤⠤⠤⠤⠴⠤⠴⠶⠖⠲⠒⠒⠒⠒⠚⠛⠛⠉⠉⠉⠉⠉⠉⠍⠉⠁⢹⡇
⠀⠀⠀⣴⢿⠀⠀⠀⠀⠀⠀⠒⠤⢀⡀⠀⠀⠀⠀⠀⠈⣤⠄⡜⠁⠀⠀⠀⠀⡠⠔⠀⠀⠀⠀⠀⢸⡇
⠀⢠⡞⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠄⡀⠀⠀⠇⠀⠠⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸⡇
⢰⡏⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠠⠀⠤⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠈⠛⢶⣄⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠈⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⠤⠤⠤⠤⠿
⠀⠀⠀⠀⠀⠓⠒⠒⠒⠒⠒⠚⠛⠛⠋⠉⠉⢹⡏⠉⠉⠉⠉⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣿⣄⡀⢀⣼⣷⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⠀⠀⠀⠀⠀⢰⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⣾⣿⡇
⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⠀⠀⢠⣿⣿
⠀⠸⢿⣿⣶⣤⣀⠀⠀⠀⠀⠘⣿⣿⡄⠀⢸⣿⡇
⠀⠀⠀⠉⠛⠿⣿⣿⣶⣤⡀⠀⠘⠿⠃⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠙⢿⣷⠀⠀⠀⠀⣀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⢨⣿⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠋⠉⠉⠙⣿⣿⣿⡿
⠀⠀⠀⠀⢀⣤⣤⣄⡀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⣰⣿⣿⣿⡿⠋⠀⠀⠀⠀⢀⣿⠿⠋⠁⣀⣤⣤⣄⡀
⠀⠀⠀⠀⣿⠁⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢠⣾⣿⣿⣿⠋⠀⠀⠀⠀⢀⣴⠟⣁⣤⣶⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⢰⣿⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⡏
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠁⠀⣀⡴⠋⠀⠀⠀⠀⠀⢠⣾⣿⣿⠟⠁⠀⠀⠀⠀⢠⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⣿⡿⠟⠋
⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡿⠋⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⠁⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀⢀⣼⡟⠀⢀⣀
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⠉⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⣠⣿⣯⣶⣿⣿⣿⣿
⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⢠⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⢻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠀⢀⣴⣿⡿⠟⠁⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⠿⠿⣿⣿⣿⡿
⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠋⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⠋⠀⠀⠀⢘⡟⠁
⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠋⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠉⠀⠀⠀⠀⢀⣼⡁
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠟⠁⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⡀
⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠋⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠇
⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⠟⠁⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠟⠋
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠿⠛⠉
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠟⠛⠉
⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠁
⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋
⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢦⣤⣀⣀⣀⣀⣠⣤⣴⠾⠟⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣿⣿⣿⣿⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⢁⠉⠉⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⡶⠶⠾⠛⠲⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣵⣶⣶⡶⠶⢶⣤⣀⠉⠻⣆⠀⠀⠹⣄⢀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣁⠀⠀⠀⠉⠻⠆⠈⠁⠀⠀⢻⣼⡆⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋⠁⠈⠻⢿⣿⣿⣿⣿⣿⣿⣷⣦⢻⣿⣦⡀⠀⠀⠀⣼⣿⡇⠀⢻⣦⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠿⣿⠀⢻⣿⣇⠀⠀⣠⣿⣿⠇⠀⣸⣿⣾⢷⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣤⣉⣡⣤⣾⣿⣿⡟⠀⣰⣿⣿⣿⣾⠛⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣋⣠⣾⣿⣿⣿⣟⣡⣤⡴⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⢴⣿⣿⠿⠟⠛⢻⣿⣷⣟⣛⣛⠛⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠋⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣶⣶⣤⣬⡍⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠻⣷⠀⠀⠀⠀⠀⠀⠐⠻⠟⠛⠉⠁⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠟⠋⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⣶⣦⣤⣀⡸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡤⠀⣹⣿⣿⣿⡀⠀⣰⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠋⣩⣻⣿⡁⣻⠀⠀⠀⢠⠀⠀⠀⣾⠿⠿⢷⣶⣤⡀⠀⠀⠀⠀⠀⢸⣷⢰⣿⣿⣿⣿⠿⢀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⣼⠇⠀⠙⠳⠿⠿⠙⠇⠀⠀⠀⠐⠀⠀⠞⢡⣾⣶⣆⣙⠿⠛⠀⠀⠀⠀⠀⠀⢿⣾⣿⣿⣿⠏⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣻⣷⣾⡏⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⢰⣆⡈⠻⢿⣿⣧⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⢻⠀⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣠⣄⠻⣿⡇⠀⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⣿⠀⠀⠀⠀⠘⠾⠷⠀⠰⣤⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣄⣉⣁⡀⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⣠⡴⠀⠀⠀⠀⠀⠀⠈⠁⠀⢲⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠀⠸⠛⠀⣤⣶⣦⣤⣴⣦⣤⣄⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⡟⢋⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡇⠀⠀⠈⢻⣏⣀⡀⠀⠉⠉⠛⠻⢦⣄⡈⠙⠷⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠳⣄⣫⣿⡟⣿⡋⠈⠉⣰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⣿⣿⣿⡄⢿⣿⣶⣿⣿⣿⣿⠏
⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⡀⠻⣿⣿⣿⠟⠁
⠘⣍⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠙⠷⣶⣶⣶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠘⢧⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠋⠁⠀⡄⠉⠙⢿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠙⢦⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠟⠋⠀⠀⠀⢸⡇⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠙⢆⠀⠙⣆⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⠈⣿⣶⣤⣤⣤⣤⣤⣤⣶⣤⣴⣶⣶⠏⠀⠀⠀⠀⠀⣠⣿⣿⣶⡄
⠀⠀⠀⣀⠴⠤⣈⣧⠀⠈⠳⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠋⠉⠀⠀⣀⣠⣤⡤⠰⠀⠉⠉⣭⡀
⠀⢀⣼⡧⠤⣄⡀⠈⠓⠦⢄⣹⣦⣀⣠⣤⡀⠀⠀⠀⠀⢸⣿⠁⠈⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠛⠉⠉⠀⠀⠀⠀⠀⠀⣿
⠀⢿⣾⣁⣀⣀⣈⣉⠑⠒⠢⡌⢿⣿⠋⠙⣧⠀⠀⠀⠀⢸⢻⡇⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⢸⣿⠉⠈⠁⠀⠀⠈⠀⠀⠀⢸⣿⡆⠀⢻⡄⠀⠀⠀⣿⢸⠀⠀⣀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠈⢻⠈⣷⢶⡀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠘⣧⠀⠀⠀⡿⠈⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠘⠦⣤⣈⣧⠀⠀⠀⠀⠀⠀⠉⣷⠀⠀⢻⡀⠀⢠⡷⠞⠉⠀⢀⣀⣤⡴⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⢻⠻⡄⠀⠀⠀⠀⠀⠀⢹⠀⠀⠸⣇⠀⣼⠀⠀⠐⠚⠋⠉⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠈⣧⣷⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠉⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡄⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦

⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠘⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣠⣴⣶⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠟⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠠⢤⣦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣦⣤⣿⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣠⣖⡀⠀⢠⣤⣴⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⠈⣉⠹⢿⣿⣧⣶⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣳⡾⢿⣿⣿⣷⣄⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡟⢃⣼⣿⣿⣶⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⢀⣾⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡸⣿⡿⣿⡟⠉⣿⣦⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣾⢿⡇⠀⢿⣿⣿⣿⣿⣿⣿⣟⣻⣭⣽⠿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣤⣷⡀⢀⣿⣿⣿⡿⣿⣿⣭⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣷⣤⣦⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡈⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠙⠛⠉⠀⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣙⠿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⡻⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠁⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣍
⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣅⣀⢀⢀⣀⣀⣀⣤⣤⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠏⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣋⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠒⠋⠉⠉⠉⠛⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣤⡴⠒⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣦⢀⡤⡾⠁⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠸⣅⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠀⢀⣠⠖⠚⠛⢳⢁⠞⠉⢻⠂⠀⢰⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠒⠒⠦⣄⡴⠋⠀⠀⠀⠀⣾⠋⠀⠀⣸⡄⠀⠸⠍⠉⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠶⡞⣁⠀⠀⠀⢀⡞⠁⠀⢠⠞⠁⠈⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⠤⠤⠤⠤⠤⠬⠽⠶⠖⠒⠙⣇⡹⠥⠤⢴⠋⠀⠀⠀⡇⢀⣀⡀⠀⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⡀⠀⠀⠀⢀⣀⣠⠞⠃⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣭⣭⡍⢳⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⣏⠁⠀⠀⠀⠀⠀⠀⠘⠉⡹⠓⠆⠀⢀⡴⠒⢶⣲⠤⠔⠋⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⢠⠎⠀⠀⠀⢀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠈⠀⠀⠀⢀⡟⠀⠀⠀⣰⡟⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢸⠳⢤⣠⠞⢡⣁⣀⠗⠒⠦⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣈⠑⢄⡀⠀⠀⠀⣸⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠠⠀⡜⡄⡟⡟⡌⢿⡄⠙⣦⡀⠀⢺⡴⢣⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠀⠇⡄⢳⠀⠈⡿⢺⠖⣬⠖⠉⣠⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠉⡟⠀⢠⠗⢋⠰⠃⠑⡊⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢀⠷⡄⢯⠀⣇⠀⣠⠞⠀⠀⡆⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⢂⠽⡌⢧⡟⢿⣥⡀⠀⡸⠁⠸⢶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠊⠁⠀⠸⡄⠳⠊⡴⣷⣠⠇⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⠞⠀⠈⠉⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣲⠒⡖⢲⠒⡖⢒⠚⡋⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⠀⠄⠨⠀⠄⠠⠀⢲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⣀⢐⡀⡃⠐⠰⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⣤⣤⣶⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⡤⠤⠏⣿⠉⠤⠤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠎⠁⠠⠤⠥⠤⠔⠛⠓⠒⠚⠣⠠⠤⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢉⠍⠀⣠⠴⣚⣻⣿⣿⣿⣿⣷⣄⠀⢶⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢠⡏⣔⢀⣴⣫⣿⣿⣿⢟⣿⣿⣿⣿⡃⠈⢄⠀⠀⠀⢀⡤⠴⠶⠦⢤⣀⣀⣠⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⡤⠤⣀⠀⠠⠊⠀⣾⣱⣼⣼⡿⠟⠋⠁⠀⠀⠀⠀⠈⠙⢯⣽⣿⣿⡆⠀⠂⠀⣰⠋⠀⠀⠀⠀⠀⠠⢴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⢄⠙⢿⡀⠀⠀⠙⢿⡟⢫⡂⣠⡴⢶⠿⠛⠋⠉⠻⣿⣿⢰⠪⢹⡟⠳⣶⣾⠕⡠⠶⢦⡤⠤⠴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡻⡌⢦⠀⢳⠀⠀⠀⠘⣦⣤⠞⡁⠀⠋⠿⠀⠀⠀⠀⠘⠿⠈⡗⢸⠇⠀⣿⡿⣾⣥⣭⠤⠷⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣽⣆⠣⠀⢣⡀⠀⠀⠘⣿⢫⠉⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⢠⡾⢶⣶⣿⡏⠀⠀⠀⠀⠀⠀⢄⡉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿⣦⠑⠀⢳⡀⠀⠀⣨⢦⡀⠀⡀⣠⠞⠈⠁⠀⠀⠀⠀⢀⠀⠀⠃⠈⠙⢿⣟⠛⠋⠉⠓⢦⣽⡄⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠷⠷⣼⠧⢤⡎⠁⠀⠳⣀⠉⠀⠀⢂⣰⣦⡀⠀⠀⢸⠀⠀⡆⠀⠀⡸⡏⠙⠒⠦⣄⡀⢟⢿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠥⣦⣤⡌⠁⠒⠛⠒⡴⢶⢿⡷⢄⠸⣿⠇⠀⡉⠀⠀⣾⠀⡸⠀⠀⠀⣽⡠⠂⢀⠤⠶⠿⠻⣄⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢝⣿⣆⠀⠀⣼⠁⢡⠏⠀⠨⠣⡈⠐⠁⠀⡠⠜⢻⡰⠁⠀⠀⢠⠋⠀⠔⣀⠤⠤⠄⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⢿⡷⢤⣇⠀⡌⠀⡀⠀⠀⠹⠶⣶⣟⠀⠀⢸⣿⣷⡀⠀⡞⠀⢈⠞⠁⠠⠶⠒⠒⠒⠆⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿⣆⠻⢴⡝⢼⡇⠀⠀⢂⠜⠛⠻⣄⠀⣼⠋⠀⠙⡴⠀⢠⠞⠀⠀⠀⠀⠒⠲⢶⡆⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢻⣦⠀⣉⠛⣇⢀⠀⠀⠀⠀⠀⠘⡶⠁⠀⠀⠀⠀⣤⠃⢀⠠⠤⢀⠀⠀⠀⠀⠙⢦⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⠾⢉⣙⠒⢧⣹⣿⡀⠀⠸⣄⣧⡀⢐⣌⠲⣤⠃⡀⠀⠀⠀⣢⠿⠤⠶⣒⠒⠀⠠⠤⠤⠤⠀⠀⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⣀⠀⠠⠀⠈⠁⠀⠙⣿⣷⡄⢰⡇⠀⠀⠀⣀⣽⠈⢰⣠⣴⣖⣛⣓⠢⢄⠀⠈⠉⠢⣄⠀⠂⢄⡐⢦⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢀⡀⠡⠀⠐⠢⠄⠀⠀⠈⠿⣿⣄⣟⣓⣘⣋⠁⠤⠴⠚⠛⠃⠀⠛⠙⢽⠢⠀⠀⠢⡀⠈⠳⣄⠐⠇⢈⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠀⠠⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠲⠤⠤⠤⠴⠷⡄⠀⠀⠙⡦⠀⢹⣮⣷⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠠⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⢱⠀⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠒⠒⠲⠶⠶⠺⢤⣄⣖⠠⠤⠤⠄⠀⠀⠀⠀⠀⠐⠒⢶⣶⢏⡄⠀⣸⡇⠘⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣌⣿⣿⣶⣶⣶⣶⣶⣶⣤⣶⣶⣻⡵⢋⣤⣾⣿⣡⣤⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠻⠿⠿⠿⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣄⠀⠀⠀⠀⠈⣿⡏⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣧⠀⠀⠀⠀⠻⠇⠀⠀⠀⠀⣰⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⣀⣤⣄⣀⠀⠀⠀⠙⠉
⠀⠀⠀⠀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣶⣦⠄⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢀⣠⣤⣤⣴⣾⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⢻⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⣠⣶⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢿⣿⣿⡏⠀⢀⣠⣶⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣿⣿⣷⣾⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⠿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠛⠛⠉⠁⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⣿⣿⡿⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇
⠀⠀⠀⠀⠘⠿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠈⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⠀⠀⠀⠈⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠃⠀⠘⠀⠀⠀⠀⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠆⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⢸⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠘⡇⠀⠀⠘⠀⠀⠀⡟⠀⠀⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠀⣀⡴⠖⠛⠛⠛⠓⠶⣄⡀⠠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄⡀⠀⣠⠞⠁⣀⡀⣰⡖⣶⡀⣀⡀⠙⢦⡀⠀⣀⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢰⠏⠀⠸⣏⠙⣩⠤⢬⡙⢉⡿⠀⠈⢷⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⣤⡀⣿⠀⢰⠞⠃⡞⠁⠀⠀⠙⡆⠓⢦⠀⢸⡇⣠⣤⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠘⠳⣆⠳⡀⠀⠀⡰⢃⡶⠋⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠘⣧⠀⠸⣧⡴⢬⠉⢩⡴⣤⡿⠀⢠⡟⠰⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣈⢳⡀⠀⠀⠘⠓⠛⠀⠀⠀⣴⢋⡀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢹⡄⠀⠀⠀⠀⠀⠀⣼⠁⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣛⣛⣛⣛⣛⣛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠤⠤⠤⠤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣛⣙⣛⣋⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣧⣤⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⣿⡏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⣀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣷⣿⣿⣿⣇⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠿⠟⣫⣭⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷⣶⣀⣀⡀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢀⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀
⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣾⣿⣿⣿⣿⡇⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀
⠀⠀⠀⢀⣤⣙⢿⣿⣿⣿⣿⣿⡏⢿⣿⣾⣿⣿⣿⣿⣿⡿⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣘⣿⡆⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⠀⠉⠉⠙⠛⢻⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣤⣦⣷⣶⣤⣶⣴⣯⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠀⠀⠀⠀⠉⠉⠙⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⡀⠀⢀⠀⠀⢠⡆⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣜⣠⠖⣹⣀⡴⢉⡇⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⠞⠉⣌⠃⠛⠁⠚⡉⢧⢀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠛⠁⠀⠸⠟⠀⠀⠀⢸⡟⠈⠛⣆⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣱⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⣀⡀⠀⠁⢀⣀⡴⠛⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣤⠤⠀⠀⠀⠀⣉⡽⠋⠉⠉⠻⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠃⠘⠁⠀⠀⠀⠀⣠⠞⠻⣄⣀⣀⣀⣤⠞⠉⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⣠⡀⣠⠔⠀⠀⠀⣰⠏⠀⠀⠀⠉⠉⠉⠀⠀⠀⡄⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⡴⠖⠿⣤⡇⠀⠀⠀⠀⣠⠤⠤⣀⡇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⢀⣿⡇⠀⠀⠀⢸⡁⠀⠀⡸⠆⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⡉⠉⣿⠃⠀⠀⠀⠘⣷⡒⠋⠁⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣿⠀⠀⠀⠀⠀⠈⠙⠲⠶⠛⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢧⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠐⢀⣠⡄⠀⢀⠤⣤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣼⣿⣦⣄⣀⣼⢠⠁⣠⠛⠒⠪⣕⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠸⣿⣿⣇⣿⣿⣿⣿⣿⣿⠀⠀⡆⠀⠀⢸⠹⡌⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢀⠐⣾⣿⣿⡯⠿⣿⣿⣿⣿⡟⠀⢤⠃⠀⠀⠚⢴⠃⠀⡿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⢰⣿⣿⣿⠀⠀⣿⣿⣿⣿⣧⠤⠼⠧⠀⠀⠀⢸⠀⠈⠹⡾⣆
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠳⠧⣀⣸⣿⣿⣿⠀⠀⣯⣿⡿⠛⡇⠀⠀⠀⠔⠚⠋⠉⠓⢄⠀⢷⢸⣇
⠀⠀⠀⠀⠀⠀⠀⣼⣷⣦⠄⠠⠬⣍⣛⡟⠀⠀⣿⣿⡇⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠘⢹⡄
⠀⠀⠀⠀⠀⠀⢀⣿⡿⠁⠀⠁⠙⠊⡌⠣⡀⢀⣿⣿⡇⢸⡷⠖⠒⠒⠮⠀⠀⡀⢀⡦⠴⠃⣰⠞⢳
⠀⠀⠀⠀⠀⠀⢸⣯⢁⠎⠀⠐⠄⠀⠀⠀⢘⡞⠛⢻⡇⢸⡇⠀⠀⠀⠀⠀⢀⡍⠉⠁⠀⠀⠻⠀⢸⡆
⠀⠀⠀⠀⠀⠀⢸⣿⠌⠙⢀⠔⠈⠀⠀⠀⠘⣷⠀⠈⡇⢸⡇⠀⠀⠀⢰⡴⠊⠀⠀⠴⠒⠢⡄⠀⢼⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢄⠤⠐⠀⠀⠀⠹⡄⠀⠃⢸⣷⠶⠶⠶⣏⠀⠀⠀⠀⢀⠀⠀⣿⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠸⣽⠀⠀⠀⠀⣤⣤⡇⢀⠄⠀⠁⠀⠀⢸⡇⠀⠀⢀⠈⠙⠒⠒⠒⠋⠀⣶⠋⣸⣸⠃
⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⣷⣷⡇⠈⠒⠀⢈⠀⠀⢸⡇⠀⠀⣸⠷⠤⠤⠾⠦⠤⠤⠻⣦⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠧⣍⡇⠀⠄⠀⢸⣴⣷⣼⡇⠀⣰⠏⠀⢰⣄⣠⠖⠒⢦⡀⢘⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢝⣦⢬⡑⣴⠁⣠⠂⢀⡏⢻⣿⣿⣧⠾⠯⡤⠔⠋⠈⣷⠀⠀⢀⣷⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⡙⣧⡰⢋⣴⣾⣷⣿⣿⣿⡇⠀⠀⢤⣄⣴⠾⠋⢀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⡿⣿⣿⣿⣿⠏⡷⠶⠛⡋⠉⢀⣆⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠋⠀⠘⠦⠶⠿⠖⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⣰⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢷⠄⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢦⠀⠀⠀⠀⠀⠀⣀⣤⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠘⡇⠀⣀⣤⠶⠛⠉⠀⠀⠀⢹⡆⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⣀⣴⠷⠻⢯⡀⡴⠛⠛⠳⣄⡤⠞⠋⠁⠈⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠀⠀⠀⠀⠀⣀⣤⠶⠛⣽⠃⠀⠀⠀⡿⠁⠀⠀⢀⡿⠀⠀⠀⠀⢀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠶⠛⠉⠀⠀⣼⠃⠀⠀⠀⡼⠁⠀⠀⢀⡾⠛⠛⢳⡴⠞⠻⢧⡀
⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⣠⠶⣄⡀⠀⣰⠃⠀⠀⠀⣼⠃⠀⠀⢀⡾⠁⠀⠀⢀⡗⠀⠀⢨⡇
⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠹⣶⠃⠀⠀⠀⣼⠃⠀⠀⢀⡾⠁⠀⠀⢀⡾⢀⣠⠴⠛⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⣸⠃⠀⠀⠀⣼⠃⠀⠀⠀⡾⠁⠀⠀⢀⡾⠛⠛⢦⡀⢀⣤⣴⣶⠾⠿⠛⠛⠁
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⣰⠃⠀⠀⠀⣼⠃⠀⠀⠀⡼⠁⠀⠀⢀⡾⠁⠀⠀⢸⡇⠈⠉
⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⣠⠏⠀⠀⠀⣰⠋⠀⠀⠀⠸⠃⠀⠀⠀⡼⠁⠀⠀⢀⡾⠁⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⢠⠏⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠼⠁⠀⠀⢀⡾⠁⠀⠀⢀⡞⠀⠀⠾⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢀⡞⠀⠀⠀⠀⠀⠉⠛⠿⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢀⡞⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⣤⣄⣀⣠⣤⠴⠖⠋⠁

⠀⠀⠔⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠈⠁⠀⠄⠀⢀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢌⠀⠀⠀⠀⢀⣠⡀
⠀⠀⢨⠁⠀⠀⠀⢀⣰⠈⠀⠀⠀⢡⣦⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠁⡎⡠⠀⠀⠦⠂⠠⠁⠀⠈⠀⡴⡰
⠀⡌⡄⠀⠁⠀⠀⠈⠟⠂⠄⡤⠀⠓⠟⠁⠀⠀⠀⢀⠀⠰⢆⢸⢠⡄⠂⠁⠈⠁⠀⠘⠀⠀⠃⠀⠀⠀⠑⠀⠁
⠀⠉⠀⠀⠄⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠐⠁⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⠀⠓⠀⠀⠀⠠⠀⠀⠀⣼⡀⠧⠀⠀⠀⠀⣠⠄⠐⠂
⠀⠀⣀⡰⡀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⣿⠃⠀⠀⠀⠀⠀⠙⠀⠀⠂⠀⠀⢈⣍⢩⠀⠀⠀⣭⢩⠁
⠀⠒⠀⠐⠆⠀⠃⠀⠘⠀⠀⠀⠀⠀⡇⠀⠂⠀⠀⣻⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⢿⠀⠀⠀⣿⣼
⠀⠀⠀⠀⠆⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠈⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠛⠋⠉⠁⠀⠀⠀⠀⠉⠛⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⢠⢞⣶⣴⣶⣶⣀⣠⣤⣠⣄⣤⣤⣂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⠀⢠⠁⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⢸⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠈⠀⠀⠀⠀⠀⠀⡟⠀⠀⠘⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⢀⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⢠⡀⠀⡇⠀⠀⣼⠁⠀⡼⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠈⣧⠀⠘⠀⢰⠇⠀⣰⠃⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠸⣆⠻⠿⠿⠃⢀⡟⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠹⡀⠀⠀⠀⣼⠁⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢧⠠⠀⣰⠏⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠸⡄⢀⡟⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢻⣼⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠸⣿⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣶⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣀⣀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⠿⠟⠉⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠟⠻⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣴⣦⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⠀⠀⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⣀⣀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⣠⠔⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣷⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⣿⠟⠛⠋⠉⠉⠙⠛⠻⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣶⠀⠀⠀⠀⠀⡇⠉⠒⢦⣤⣀⣤⠤⣴⣶⡤⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⣶⣶⣤⣤⡀⠀⠸⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⢰⠀⠀⠀⠀⢠⡟⠀⣴⢲⣶⣾⣤⡈⠻⣟⠻⠶⢤⣤⣀⣀⣀⠉⠉⠙⠻⠿⣿⣿⣷⠀⠆⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⠀⠀⠀⡈⠀⠀⠀⠀⠘⠇⠀⠈⠙⠿⠇⠘⠛⠃⢸⡇⠀⠀⠈⢉⣽⠿⠿⠷⠶⣦⣄⠉⠛⣿⡸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢠⣿⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⢠⡟⣁⡤⣶⣶⣬⡝⠏⠳⣄⠉⡃⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⢀⠁⢰⡎⠿⠀⠀⠛⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⣀⣤⠞⠀⠀⠀⠀⢸⠀⠀⠀⠙⠛⠁⠉⠀⠀⢸⠶⠷⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠠⡀⠈⠃⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢋⡉⠁⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢀⡾⠈⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⡖⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⠀⠀⠀⠀⠀⠀⠀⢀⠹⣦⣀⠀⠀⠀⣀⡴⠋⠀⠀⠀⢆⣀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠶⠟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠻⠶⠆⡀⠀⠀⠀⠀⠘⣧⠈⠙⠛⠛⠛⠉⠀⠈⠀⠀⠀⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⣿⠀⡤⠀⠒⠂⢿⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣧⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠂⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠐⠦⣄⣀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⠀⠀⣠⣤⣴⣾⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣆⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣶⣤⣄⡀⠀⣠⣿⣿⡿⠿⠿⠿⠿⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠰⡆⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⡶⠀⢠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠢⠄⢀⣀⠠⠤⠒⠹⡀⠀⠀⠀⠀⠀⠠⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠀⠀⢳⠒⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⠤⠔⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⢀⣠⡶⡶⠛⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⢀⣀⢀⣴⠟⠡⠊⢀⠎⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢹⡟⠁⡐⠁⡐⠁⠔⣿⡴⠖⢲⡄⠀⢀⣀⡀⠀⠀⠈⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠠⠋⠀⠊⢀⠊⠀⠀⢰⠋⢀⣠⠞⠁⣠⡟⠻⢻⡆⠀⠀⠀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠁⠀⠀⠀⠀⠠⠀⢠⠃⠐⠛⠷⠶⠞⠻⠈⠆⣾⠇⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢁⠔⡑⢤⠀⣰⠟⠀⠀⠀⢡⠀⠀⠀⠀⠐⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠠⠇⣸⡴⠋⠀⠀⠀⢀⡈⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⡁⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⣀⣀⣤⠶⠟⠁⠀⠀⠀⣠⠚⠁
⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⢶⡿⢏⠀⠀⠈⠐⢄⡠⢞⠁⣑⡴⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠴⠚⠋⠉⠁⡠⠔⠁⠀⠀⠑⢄⡀⠀⡠⠃⣀⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡤⣀⣞⠀⠀⠀⠀⠀⣄⠙⠓
⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⠀⠀⣤⢈⡿⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⢀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠑⠀⠚⠐⠊⠂⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠹⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣤⣀⠀⠀⠀⠈⠋⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⡆⠀⣀⣀⠀⢸⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣮⣻⠿⢋⣥⣬⡑⣤⠀⠀⠀⠀⠀⢰⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⠀⠀⠈⠛⢿⣿⡿⠿⠇⢸⣿⣿⣷⢰⣿⣿⣷⠀⠀⢸⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⣾⣿⣷⡎⣴⣿⣿⣎⣿⣿⣿⣏⣿⣿⣿⣇⢶⣄⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⠸⣿⣿⣿⡸⣿⣿⣿⣸⣿⣿⣿⡘⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡿⠿⠀⠀⠀⢈⣙⡁⢿⣿⣿⣧⢿⣿⣿⣧⢿⣿⣿⣧⢹⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⡞⣿⣿⣿⡞⣿⣿⣿⡞⣿⣿⣿⡆⣿⣿⡿⢟⣛⡻⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣷⢹⣿⣿⣿⢹⣿⣿⣿⢹⣿⣿⣷⠸⡟⣴⣿⣿⣿⡆⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣇⣿⣿⣿⣏⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⡿⢡⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⣿⣷⣶⣦⣼⣿⣇
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿
⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡰⣶⣄⠀⠀⢀⡄⠀⠀⠀⠀⠉
⠀⠀⣰⡆⠀⣠⣾⠋⣠⣶⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⣿⣿⣮⡻⣷⣄⢸⣿
⠀⠀⣿⣇⣼⣿⣡⣾⣿⣧⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⣡⡾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇
⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⡟⣱⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠙⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣷⣄
⣿⣿⣿⡿⢋⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢀⣾⢇⣾⣇⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⠀⣤⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣧⠈⠻⣿⣿⣿⣿⣿
⣿⡿⠋⢀⣾⣿⣿⣿⣿⠏⠀⠀⠀⣶⡄⢀⣾⣟⣾⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⢰⣧⢸⣿⣶⣿⣿⣆⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣧⡀⠈⢿⣿⣿⣿
⠋⠀⣠⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢸⣿⣼⣿⣿⣿⣾⣿⣿⣯⣿⣸⡆⠀⠀⠀⢻⡆⣿⣾⣿⣿⣿⠸⣿⡄⢀⣤⠀⠀⠈⢿⣿⣿⣿⣿⣷⣄⠀⠉⠻⣿
⢀⣼⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⡟⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣦⡀⠀⠈
⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣄
⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠏⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿
⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡟⠀⢠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿
⡿⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡿⠀⠀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿
⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣁⣀⣀⣿⣿⣿⣿⣿⣟⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⣿⣆⣻⣿⣿⣿⣿⣿⣆⣀⣀⣀⣀⣀⣀⣀⣀⣙⣿
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⢀⣈⢁⠈⡀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⠎⠘⠓⠆⠃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣶
⠀⠀⠀⢰⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉
⠀⠀⠀⠘⣷⣾⢻⢘⡢⡾⠁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡄⡄⣄⢤⠔⠂⡤⠰⡄
⠀⠀⠀⠀⠘⠃⠈⠈⠁⠁⡜⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣷⣦⣴⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣧⣻⣮⢻⣽⡟⣟⣸⣿⣟⣽⣧⣻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠙⠛⠛⠛⠻⠛⠋⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡼⢡
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠊⢐⡞⠀⡀
⠀⢸⡒⡆⢰⣄⠰⡔⡇⢙⢵⢴⡆⢠⡆⠀⠀⠀⠀⠀⠀⠸⣷⡿⠑⠂⠀⠀⠀⠀⠀⠀⠀⣄⡄⡄⡀⣠⢤⡀⡄⠲⢀⣤⣰⡀
⠀⠈⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠝⢓⠀⠄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠉⠉⠃⠉⠉⠀⠀⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣰⢶⠐⡠⢲⠂⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠉⠁⠁⠈⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣠⠞⢹⡾⠁⢈⣧⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⣠⣾⠋⢳⣼⣵⠚⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢁⡴⠃⠈⢳⡿⠋⠘⠦⣾⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠳⣄⡞⣠⠟⠀⠀⣠⠟⠁⠀⠀⡴⢏⣁⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⣰⣯⢤⢀⣿⡟⠁⠀⠀⡰⠋⠀⠀⢠⠞⠁⠀⣼⠷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⣰⠋⠁⣸⡾⠋⠀⠀⢀⠼⠁⠀⠀⡴⠋⠀⠀⡼⠛⢲⡇⠀⠀⠀⠲⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⢀⡴⠃⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⢠⠞⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢠⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠇⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢫⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⣠⡾⠁
⠀⠀⠀⠀⠀⠀⣰⠛⠶⣏⡀⠀⠉⠳⣄⡀⠀⠀⠀⠀⢠⠞⠋⠀⠀⣤⠉
⠀⠀⠀⠀⢠⠞⠑⢂⡨⠄⠙⠲⣄⡀⠀⠙⠢⣄⠀⡴⠋⠀⠀⠀⣴
⠀⠀⠀⣰⠋⠒⣉⠀⠄⢒⣉⠠⠄⠙⠢⣄⠠⠊⢻⠍⠛⠓⠒⠶⣧
⠀⢀⡞⠁⣒⠡⠤⠒⣈⠡⠄⠐⢂⡉⠤⠌⣛⢦⣿⠤⣤⣀⣀⣀⣿
⣠⠏⢀⡩⠄⠐⣈⠡⠄⠒⢂⡩⠄⠒⣂⠩⠄⠂⢨⠇⠁⠐⢀⣈⠉⡿
⠁⠀⠠⠒⠈⣁⠤⠐⠂⣉⠠⠐⠂⣉⠠⠐⠈⣱⠋⠠⠭⠀⠒⠂⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠈⡁⠤⠐⢊⣁⠠⠄⢢⠞⠑⣒⠀⠉⠠⠄⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠊⣁⠤⠄⣰⠋⠤⠅⠀⢒⣂⠉⠩⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠠⢀⡼⠁⢒⡀⠭⠉⠒⣀⠀⠌⠸⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣠⠖⠒⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠶⣤⣠⣿⠃⠀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⡀⠀⠀⣾⡏⠀⡴⢲⡆⢰⣶⢠⣶⡦⣠⡶⢲⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠿⠳⠅⠀⢠⣿⠃⣾⠧⣼⣇⣿⡿⠃⠙⢰⡿⠀⣼⡟⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠻⠴⠋⠸⡿⠁⠀⠀⢻⣧⠞⢿⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠯⠸⠟⠑⠢⠤⢤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⢶⡀⢠⡄⠀⠀⠸⠿⠆⠸⠿⠷⢳⠄⠀⠀⠀⠀⢀⣤⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡾⢧⣿⠷⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠴⣾⡟⣿⡟⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢻⣧⠀⣸⡏⢰⣷⠾⡟⣾⣫⢀⣿⢶⣿⠂⣴⠏⣡⣠⣿⢡⣿⢴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢨⣿⠀⣿⡰⣿⠃⠀⠸⣏⣠⣾⠏⢸⣇⢾⣏⣰⡟⣸⡇⣼⡏⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠉⠀⠁⠀⠀⠀⠈⠀⠈⢠⠀⠁⠀⢩⡿⠁⢿⣀⡌⠀⢿⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣴⠀⠀⠀⠀⠀⢀⣀⣀⠀⠘⢦⣤⡴⠟⠁⠀⠀⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⢈⣉⡀⡀⠀⠀⢰⡟⠁⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠃⠙⠀⠀⠘⣿⡀⠋⢀⡤⣤⠀⣤⢀⣤⡄⠀⣠⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⢹⣷⢀⡾⢣⣿⣼⡿⢡⡿⢁⣾⡏⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣠⣾⠟⠈⠳⠚⠁⠿⠁⠸⠷⠋⠿⠆⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠉⠙⠑⠒⠤⢀⡠⠀⠠⡄⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠀⠚⢡⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣠⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⣀⠀⠀⢀⣀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠲⣆⢀⣶⢸⣷⡖⡶⣶⠀⢰⡆⣆⡿⡇⠂⢰⡀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠉⠈⠉⠁⠉⠉⠀⠈⠀⠁⠁⠁⠁⠈⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠸⣡⠀⠘⡀
⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⡌⢁⠔⡐⢎⡅⢣⠀⠓⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣲⠀⢀⣀⠀⠀⣀
⠀⢠⢾⡈⢮⢄⢠⡀⠀⡐⢉⠠⢤⢀⠔⠠⡋⢸⠔⠛⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠸⡏⡖⠳⠹⠙⡁⣺⡾⣿⠉
⠀⢈⢎⠁⡈⢢⠡⡂⠀⡇⡎⠀⣁⡜⢖⠃⡏⢁⣀⠼⠁⠀⠀⡄⡶⠆⣴⣦⢦⠀⠀⠈⠑⠽⠒⠓⠓⠄⠓⠒⠃
⠀⠘⠂⢂⢫⠒⠓⠁⠰⡁⡐⢄⣈⣀⠬⠋⢠⠜⠀⠀⠀⢠⣦⠈⠈⠢⠘⠋⠀⢀⠀⠠⣶⣻⣿⢀⡀
⠀⠀⢀⢤⢥⡀⠀⠀⠀⠀⠑⣚⠒⠤⠔⠒⠉⠀⢀⢄⠸⣿⣿⠀⠀⡔⢖⠄⢿⡿⠀⠀⠈⢇⠈⠻⠁⣠⡀⢀⡀
⠀⠰⠹⠀⢨⡇⢀⠀⠀⠀⠀⢣⠑⣀⠀⠀⠀⠀⠈⢉⠤⠌⠋⣠⣄⠈⠋⢀⡀⡀⠀⠀⠀⣼⣶⣦⠀⠙⣋⣉⠁
⠀⠀⢆⠂⠈⠓⢡⠃⠀⠀⠀⡰⠀⠀⠑⢄⠀⠀⠀⢸⢠⢠⠀⠀⢁⣉⣁⣤⣀⡀⠀⠀⡾⡍⢹⡙⢄⠀⠈⠁
⠀⠀⠈⡄⠀⠀⡇⠀⠀⢀⣼⡓⢀⠀⡠⠊⠀⠀⠀⢸⣀⣉⣁⣀⠈⠉⠃⠉⢉⠃⠀⢸⡡⡁⢰⠁⢸
⠀⠀⠀⠿⠿⠿⠇⠀⢠⡿⠇⠈⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢉⠉⠉⠈⠉⠀⠀⡨⠀⠇⠈⠂
⠀⠀⢸⠀⠀⠈⠘⡄⠸⡑⠄⢀⠄⠂⢀⣶⣔⣼⡆⢀⠀⠀⡘⡇⢸⠀⠀⠀⠀⠀⠀⡇⠀⡄⠀⠃⠀⠅
⠀⠀⢰⠀⠀⠀⠀⡇⠀⠑⠠⠌⠀⠀⠘⡽⠹⠙⣧⢃⠃⠀⢀⠈⣩⠃⠀⠀⠀⠀⢐⠀⠀⡀⠀⠀⠀⡆
⠀⠀⡐⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢀⠃⠀⠀⢸⠛⣿⠀⠀⠀⠀⠀⢸⠤⣴⡴⢴⢶⡴⢷
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀
⠀⠀⠀⠀⡐⠀⠉⠉⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠁⢀⣀⠀⢀⣀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠙⡝⠳⠔⣫⠝⢸⣿⣿⣭⠇⣠⣖⢷⣆
⠀⠀⠀⠀⠀⢰⣈⣧⣽⢻⡾⡖⢲⡽⣶⠀⢀⠔⠂⠉⠀⡲⡂⠉⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣪⡽⡇⠀⢸⢸⣟⣧⠀⣬⣟⣾⢧
⠀⠀⠀⠀⠀⠸⠞⠳⡱⢺⢷⡳⢞⡔⢸⠀⠆⠀⠀⠀⠌⠀⢰⠀⠀⠈⠄⠀⢆⢀⣀⣀⠀⠀⠀⠀⠀⡉⣉⠁⠀⢩⣉⠉⠉⡁⠘⡛⠛⠁⢀
⠀⠀⠀⠀⠠⠈⠉⠀⠉⠁⠀⠀⠁⠀⠈⠀⣀⠀⠀⠐⠀⠀⢨⠀⠀⠀⠸⢄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⡏
⠀⠀⠀⠀⠀⠄⠀⠠⠠⣴⣤⠄⠀⠀⠀⠀⣀⠀⢀⣇⣀⡂⡈⠆⠀⠀⣘⡈⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠘⠀⠦⠧⣀⡀
⠀⠀⠀⠀⠐⠠⠄⢀⠀⠀⢸⠀⠀⠀⠀⡠⠀⠁⠒⠀⠤⠀⠃⠠⣀⠈⠀⠀⠀⠀⠀⠄⠊⠀⠀⠀⠀⢀⠠⠀⠀⣠⡀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠈⠩⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢸⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⠀⢀⣀⠄⠤⣀⠀⠀⠂⠀⠀⠀⠀⠠⠄⠂⡈⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢐⢱⠞⠉⢀⠀⠀⠀⠙⢦⡄⠀⠂⠀⢀⠂⠀⠀⠂⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⢹⡄⠀⠀⠀⠐⠤⣅⡇⣄⠀⠈⠀⠠⠅⣀⠠⠀⡀⠀⢣⡀⠀⠂⠀⠀⡂⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠁⠀⠀⢳⢟⡇⡀⠉⠂⡀⠁⠓⢯⠈⢩⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⢠⣀⠀⠊⠀⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⡣⠐⠀⠀⠀⠀⠀⠘⠀⢸⠀⠐⠉⠄⠀⠋⠀⠀⠀⠀⠈⡅⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠑⢄⠁⡠⠁⠀⠀⠄⠈⠄⠀⠀⠐⠀⠀⢰⠠⢀⠠⡀⢠⠀⠀⠈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⡀⠳⠀⠑⢄⡀⠄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⠀⠀⠀⠀⠠⠄⠀⡀⠀⠀⠀⠘⡄⢠⠀⠀⠤⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⡎⠀⠘⠀⠀⠂⠀⠀⠀⢀⠀⠀⡀⠀⠠⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢨⠀⠀⠀⠀⠀⠀⡇⠀⠀⡦⠀⠀⠂⠠⠀⠈⢦⢰⠐⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠠⠀⠀⡀⠀⠀⠜⡇⠀⠀⠹⣀⠊⠀⠄⠀⠀⠀⣿⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡀⠀⠈⠀⡇⠠⠀⢠⢣⠀⠈⠠⢀⠀⠀⢄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠂⠀⠀⠀⠀⠀⠯⣀⣀⠀⣀⣀⡱⠶⠤⡤⠤⠤⣢⠀⠐⠠⢄⣀⣠⡘⠑⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠈⠁⠀⠀⠂⠀⠀⠀⠀⠘⠒⠒⠐⠛⠁⠈⠨⠁⠄⠀⠐⠀⠂⠐⠠⠀⠀⠀⠈⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⠟⠛⠛⠛⠿⠿⢶⣶⣤⣀⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣠⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⢀⣀⣀⣀⣤⣤⡄
⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠈⠙⠛⠋⠉⠁
⠈⠉⠉⠙⠛⠛⠁⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣴⣶⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⢺⣿⣶⡿⠛⠉⣿⡆⠀⠀⠀⠀⣸⣿⠀⠀⠀⠐⠿⠶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⣴⣶⣄⣸⣿⠻⣿⡧⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⣿⡏
⠀⢀⣀⣀⣠⣤⡄⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠘⢿⣟⠛⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢰⣿⠃
⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⡀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⢸⣿⠀⠀⣸⣿⠀⠀⠀⠀⠀⠙⠿⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⠀⠀⠀⠙⢿⣄⠀⠀⠀⣸⣿⣶⡾⢿⠿⢿⣶⡀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⠀⠀⣻⣧⣶⡿⠟⠋⠁⠀⠀⢀⣼⣿⣅⡀
⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣙⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⢛⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠀⠀⠀⠀⠀⠀⢸⣿⣣⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠉⣿⡿⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠟⠀⠀⠀⢀⣠⣤⣶⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣤⣤⣴⡾⠿⣿⣿⣿⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢀⣀⣀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⣄⠀⢺⡇⠀⢹⡀⢸⠏⠀⢹⡇⢸⡏⠉⠉⠁⠀⣿⠛⠳⣦⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠻⠀⢸⡇⠀⢸⠇⢸⣦⣠⡼⠃⢸⡗⠛⠃⠀⢴⣯⣤⡴⠟⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡉⣛⡦⠀⠳⠤⠞⠀⠘⠇⠀⠀⠀⠈⠳⠶⠒⠂⠸⠇⠈⠳⡄⠀⣘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⠤⠒⣩⡆⣀⠀⠀⠀⠀⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⣹⢀⠤⠒⠋⣀⠶⠚⣁⡤⢚⠄⠀⠀⠑⣄⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⣠⠖⠋⠀⠀⠶⢋⡠⠚⢉⡠⢶⠉⠀⠀⠀⠀⠘⡆⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⡇⠀⠀⢀⣠⠶⣿⠠⠖⢉⣴⣫⠤⠒⠋⣩⣧⣄⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢀⡴⠚⢉⣠⠾⠷⠒⠚⠋⠉⣀⡠⠔⠋⣠⠴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⣴⠋⠀⢠⠋⠀⠀⠀⠀⠀⠐⠉⣁⡠⠖⠋⣡⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣠⠖⢋⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⣀⣤⠴⠖⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣄⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣿⣿⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⡆⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣯⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠝⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣷⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡆⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⢸
⠀⠀⠄⣡⠆⠐⢄⠠⠀⠀⠀⠀⠄⡥⠂⣄⣀⡀⠀⠀⠠⢀⡴⠶⢦⡅⠄⠀⠀⠀⠠⢀⢔⠀⡢⡀⠄⠀⠀⠀⠰⢉⠞⠒⣷⣈⠂⠀⢸
⠀⠀⠐⡃⠀⠀⢀⠀⠂⠀⠀⠐⠀⡀⠀⢈⣿⠁⠀⠀⠂⢸⡁⠀⢀⡂⠐⠀⠀⠀⠂⢀⢆⡋⡠⡀⠐⠀⠀⠰⣈⢀⠀⠀⠀⡇⣁⠆⢸
⠀⠀⠀⠑⣀⣠⠃⠀⠀⠀⠀⠀⠀⠱⣀⠟⠉⠁⠀⠀⠀⠀⢩⣙⡙⠁⠀⠀⠀⠀⠀⠀⢃⣿⡘⠀⠀⠀⠀⠀⢠⡀⢂⣀⡜⣀⡆⠀⢸
⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⢸
⣿⣿⠟⠿⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁⠉⠁⠉⠛⠛⢻⣿⣿⠋⠁⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡍⢻⣿⣿⣿⣿⡊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠯⠌⠉⠉⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠉⠁
⣿⣿⣿⣿⣯⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣤⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠻⠿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠻⠿⢿
⠿⠛⠻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢲⣾⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⣦⠀⠀⠹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⣿
⣿⣧⡀⠀⠹⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠈⢿⣿⣤⣶⠀⠀⠀⠀⠀⣼⣷⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⡿
⣿⣥⣷⡄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣶⣿⣿⣿⣷⣄⣀⣰⡎⢿⣿⣿⡇⠀⠀⣠⣤⣿⠿⠁⠀⠀⣤⡄⢀⣄⡀⣤⣤⣄⣀⣀⣿⣿⣿⠃
⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠞⣿⣿⣷⣶⣶⣿⣿⣿⣶⣶⣶⣶⣿⣿⣾⣿⣇⣹⣿⣿⣿⣿⣿⣿⣿⣞
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣧⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠋⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⠀⠀⠀⠀⠀⡇⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠣⣈⠉⠁⠼⠃⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣦⣼⡆⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠚⠛⠋⠉⠉⠉⠉⠉⠉⠙⠛⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⣁⠐⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢀⡴⠾⣉⣛⠲⣄⠀⠀⠀⠀⡰⠛⠁⢠⣤⣌⠙⢦⡀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⣏⣶⣴⣿⣿⡇⠈⢻⡄⠀⣾⢡⣷⣤⣾⣿⢿⠀⠈⣷⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⡈⢿⣿⠿⠟⠀⠀⢸⠀⠀⣇⠘⢿⣯⣟⠽⠋⠀⠀⣿⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⠈⠧⣀⠀⠀⠀⢀⣠⡿⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⢙⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢁⡎⠀⠀⠈⠙⠒⠚⠋⠁⡎⠀⠀⠀⠈⠓⠦⠤⠤⠶⠚⠁⠀⠀⠀⠀⢈⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆
⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣀⣼⡇⣠⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⢰⣧⠨⠄⣿⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀

⠀⠀⡟⠶⢢⡌⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⣅⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢋⣧
⠀⠀⣿⡀⣾⠀⠀⠀⠀⠀⠀⠀⢠⠟⢦⣄⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⡤⠔⠂⠀⠉⠉⠁⢀⠴⠊⠙⣆
⠀⠀⠈⣧⢸⡆⠀⠀⠀⠀⠀⡴⠛⠳⢤⣉⠙⠛⠒⠒⠒⠋⠉⠉⢳⡶⣶⠚⠉⠀⠀⠀⠀⠀⡠⠂⠁⠀⠀⠀⠘⢧
⠀⠀⠀⢹⠀⡅⠀⠀⠀⠀⡴⠛⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⢸⠃⠸⣆⠀⠀⢀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠈⡇⣿⠀⢀⡤⠼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠶⢿⣄⣤⣿⠖⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⢹⢸⣄⡞⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡋⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠘⡏⠻⠃⠀⣀⣤⡇⠀⠀⠀⠠⠾⠀⠀⠀⠀⠀⠀⠀⠀⢸⡡⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⣷⢀⣴⠟⠉⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠸⠞⠁⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⢀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠞⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣧⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣷⢹⠀⠀⠀⡇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣹⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣄⣀⣀⣀⣹⣇⣀⣀⣀⣀⣀⣀⣀⣀⣿⣼⣀⣀⣰⣁⣀
⣿⠿⣿⠿⠿⠿⠟⠻⠿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠛⠛⣿⠻⣿⡟⠿⠿⣿⠿⠿⠿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐
⠀⠀⡠⠠⠄⠈⢀⠡⠤⠄⢸⠀⠀⠀⠀⠂⡀⠃⣀⠀⢀⠀⢀⠀⠠⠀⠁⠠⠀⠀⠀⢸⠇⠀⠀⠀⢠⠀⣘⠀⢨⠙⡆
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠊⠀⠀⠀⠀⠀⡄⠀⣿⠀⢼⠂⠈⠃⢀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⢺⣈⢸⠃⠘⢁⡟
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠨⢀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣲⠀⠀⢰⠀⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠐⠢⡀⠉⠀⠀⠑⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠈⠢⠄⣀⠀⠠⠀⠂⠁
⠀⠀⠀⠤⢄⠀⠤⠀⠶⠀⡄⢀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⡁⠀⠙⠐⠀⠣⠤⠃⠀⠀⠀⠈⠀⠀⡀⠄⠀⠀⠠⠀⠀⠀⣀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠚⠁⡀
⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠈⠁⠈⠀⠀⣤⠀⢠⠀⠀⡀⢠⡄⠀⣠⠄⠀⢀⢀⠀⣀⠀⣀⠀⡄⠉⠆
⠀⠀⠐⠀⠐⠒⠂⠀⠀⠐⠒⠋⠉⠁⠀⠀⠀⠠⠀⠀⢨⣻⠅⢸⡖⣿⠁⣾⠃⠀⢨⣀⠀⢿⡀⠀⣿⠛⠛⠰⡟⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠌⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠁⠀⣀⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠇
⠀⠀⣀⣀⣀⣀⣀⣑⣁⣀⡀⡀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠒⡐⠒⠂⠶⠁⠄
⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠛⢦⠀⢀⠄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠈⠈⠐⣄⣀
⠀⠀⠀⠸⣆⠀⣴⣒⠀⠸⢝⠀⠀⠈⡆⠀⠂⠀⠀⠀⠀⢀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠈⠁
⠠⠀⠀⠀⡛⠀⠿⠤⠀⠠⠞⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠑⡄⠸⠀⠀⣀⠢⠀⠀⠀⠀⠀⠠⠊⠀⢀⣀⣤⡀⠀⢱
⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣴⡒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠂⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠘⠛⠿⠟⠉⠀⢸
⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣈⣃⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⣠⠞
⠀⡔⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠑⠤⠖⠪⠀⠤⠤⠚⠁
⠀⢠⠀⠀⠀⠀⠒⣦⠔⠒⣶⠀⡀⠀⠀⢸⡆⠀⠀⠀⠠⠂⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠒
⠀⠀⠆⠀⠀⠄⠀⠘⢀⡼⠟⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂
⠀⠀⠘⡄⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠘⠳⣶⡄⠀⠀⠠⣤⣿⣤⠄⢀⣀⡀⠀⠀⠀⠀⠀⠄⠀⠐⠂⠐⠋⠀⡀⠀⡀
⠀⠀⠀⠘⢄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠸⠛⠇⠀⠉⠉⠀⠀⠀⠒⠒⠂⠀⠀⠀⠚⠀⠀⠀⠀⠤⠂
⠀⠀⠀⠀⠁⠈⠁⠐

⠀⠀⠀⢀⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⠄
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢄⢀⠀⠀⡀⡏⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡄⢧⠱⡐⣀⣇⢧⡀
⠀⠀⠀⡀⣨⡷⡀⠀⠀⠀⠂⠙⠀⡀⠀⠈⢆
⠀⢄⡐⠰⡁⡗⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢒⡄⠀⠀⠀⠀⠀⠀⠴⣂
⠀⠀⠀⠀⠣⠡⠀⡀⠀⠀⠉⠢⢀⠀⠀⠀⠀⠰⠀⠄⠀⠀⠀⢂⡰⢌⢌⢞⠀⠀⠀⠠⡀⠴⣀⠃⠃
⠀⡤⠦⠀⠀⠂⠀⠑⠀⠀⠀⠀⠀⠑⠂⡤⠄⢚⣷⢂⠀⠀⠀⠀⠸⡘⡌⡍⠀⠀⠀⠀⡀
⠀⠈⠐⢄⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⢀⣀⠀⠁⠁⠀⠀⠀⠀⠀⢄⠀⠀⠀⠃
⠀⠀⠀⠀⣷⣄⣀⠠⠛⡀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡀⠀⠘⠪⡁⠀⠀⠀⠀⠀⠀⠀⠀⢱⣄
⠀⠀⠀⢀⡯⢣⣤⣤⣾⣿⣄⠀⠀⠀⣸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠋⣳⠤⠔⠚⡄⠀⠀⠀⡰⢼⡆⠤⢳
⠀⠀⠀⣸⡶⣻⡇⠈⠩⠻⢞⣧⠀⠀⣿⣿⣿⣿⣿⣿⣧⠀⠀⢰⠀⠡⠟⠉⠉⢱⠀⠀⠀⠂⠈⠒⠒⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣻⡶⢦⣽⠿⣭⣹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠉⠉⣿⠃⠀⠀⡿⠻⢦⡹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢠⠏⠀⠀⣸⠁⠀⢸⣇⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣣⠞⠛⠻⣄⣠⠴⣇⠀⢀⡿⠛⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣦⣄⠀⠀⠀⠀⢀⣰⠟⠁⠀⠀⣠⠟⠁⠀⠈⣇⡸⠁⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⡟⠉⠉⠹⡟⠛⢳⣄⣠⠞⠁⠀⠀⡠⠚⠁⠀⠀⡠⠊⠉⢳⡀⢠⡏⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡼⠀⠀⠀⢀⡇⠀⢠⠟⠁⠀⠀⣠⠀⠀⠀⠀⡠⠊⠀⠀⣠⠞⠀⣼⣷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢇⡇⠀⠀⠀⡼⢀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠳⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡼⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡴⠃⠀⢀⡼⣿⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡬⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⢀⡴⠋⣰⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⢠⣯⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⣠⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⢾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠌⠶⣿⡂⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⡀⠙⢷⢄⠀⠀⠀⠀⠀⠀⡀⠔⠋⠉⠁⠲⠦⣤⣾⣷⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⡀⠱⣵⣄⠀⡀⣐⡭⠚⠉⠶⣶⣤⣄⣀⣰⠏⢈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡻⣦⡈⡳⢩⠞⠉⠀⠀⠐⠤⢍⠛⡿⠟⠛⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠎⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠉⡴⠢⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⢦⡖⠢⡀⠀⡖⢄
⠀⠀⠀⠀⠀⠀⠀⠐⣂⢀⣘⠙⣄⠑⣀⠳⡀⡞⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢼⠓⢄⠙⢦⡈⠢⣧⠈⢆
⠀⠀⠀⠀⠀⠀⠀⣸⣌⠻⣄⠑⢆⢸⡈⢧⠹⣇⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⠀⢨⠳⠄⠑⢄⠙⠂⢸⠇⠈⣆
⠀⠀⠀⠀⠀⠀⠀⢣⡈⠳⣌⠳⣄⠙⢧⠈⢧⠘⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠈⠱⣏⠓⠲⠤⣄⡀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢫⡙⠢⡈⠓⠀⠀⠀⠀⠈⡆⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠒⠒⠒⠛⠒⠀⠀⠉⠳⢄⣘⣂⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡀⠀⠀⠀⠀⠀⠀⢷⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡚⠛⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠈⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⡀⠀⠀⠀⣨⠗⢮⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣉⣉⣉⣉⣉⠀⠀⠀⠀⠀⢀⣀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣤⠞⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠤⠤⠤⠤⠖⠒⠋⠉⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⣄⣀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⠈⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣒⣦⡤⣄⠀⠈⠉⠒⠶⢾⠉⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡹⠊⣡⠟⢹⢀⠀⢠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⢋⣉⣡⠤⠄⡰⠦⣴⠲⣄⠀⣸⢢⡸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠠⠊⣠⠞⢁⠔⢙⡎⠳⣼⡄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣉⣁⡤⠤⠖⢠⡛⠢⡈⠳⣌⠳⢼⡀⠳⡁
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠈⠁⠔⢁⡴⠫⡈⠳⠈⢻⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⢴⠒⢚⡁⡽⢦⡈⠢⡈⠓⠀⠓⠀⢱
⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠴⠟⠒⣱⠏⠀⠀⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡉⠀⠙⢦⡙⠆⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⢠⡊⠛⣄⠀⠀⠀⠀⣀⣀⠤⠖⠉⢤⡀⠀⠀⠀⠀⠀⠱⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠰⠄⠙⢦⡀⠀⠀⠀⠀⠀⢳⣀
⠀⠀⠀⠀⠙⢦⡈⢳⡞⠉⠉⠁⠀⠀⠀⠀⠀⠉⠲⠤⣀⠀⢀⠔⠉⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⠀⡠⠊⢀⡵
⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠁⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣀⡴⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠉⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⡏
⠀⠀⠀⠀⠀⠀⣠⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⣢
⠀⠀⠀⠀⠀⠀⠱⡄⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢆⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠀⠀⠀⠀⠀⠀⠀⠸⡁⢀⡇⠀⠀⠀⠀⠀⠀⢀⠄⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⢀⣈⣉⣀⠀⠀⠀⠀⠀⠀⠈⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠚⠉⠉⠉⠀⠀⠉⠉⠉⠛⠒⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢠⣾⠿⠂⠀⠀⠀⠀⠐⠻⢷⡀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠘⡡⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⡠⠂⠑
⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⢲⠁⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢀⠜⠀⢀⡴
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣺⡆⠀⠈⠄⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⡴⠾⢀⡔⠉⢱
⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠈⠁⠀⢰⠆⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠘⣇⠀⠠⠠⡔⠉
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠠⡂⠀⠀⠈⠂⠤⠤⠔⠁⠀⠈⠀⠈⠀⠀⠀⡠⠂⠀⠀⠀⢠⡟⠀⠀⠀⢸⣥⣠⠤⠝⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠱⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⠀⠀⠀⢠⠏⠀⠀⠀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠈⠒⠀⢀⡀⠀⢀⡠⠠⠄⠀⠁⠀⠀⠀⠀⠀⢠⠏⢀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⡀⡇⠀⢀⡂⠀⠀⡆⠀⣀⠀⠀⠀⠀⠀⠀⢀⣿⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠹⡍⠉⠉⠉⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣆⠀⠈⠢⣀⠀⡀⠀⠤⠓⣂⠠⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠁⠸⡆⠀⠀⠈⠉⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣿⡀
⠀⠀⠀⣀⠤⠰⠖⣾⠁⠀⠀⠀⠀⠀⢘⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⢀⣀⣀⣀⡅
⡠⠴⠚⠁⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠸⠓⠒⠒⠒⠒⠚⠛⠛⠋⠉⠉⠉⠉⠉⢀⣀⣱
⠓⡲⠃⠀⠀⡴⠒⢄⡈⡱⠀⠀⠀⠀⠈⠗⠒⠒⠒⠒⠒⠒⠒⠒⠛⠋⠉⠉⠉⠉⠉⢹
⠀⠣⠔⢆⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⣶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣩⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣄⣀⣀⣀⡤⠶⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢳⡀⠀⠀⠀⠀⠀⠀⣰⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠙⠳⠶⣢⣤⣄⠲⠿⠃⠀⠀⠛⢦⣄⣄⣀⣴⠾⠃⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⢟⠢⡀⣀⣀⢀⣠⣤⣾⠁
⠀⣄⣀⣀⣀⡠⣤⣄⡲⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠚⠋⠉⢁⣕⠃
⠀⠈⠚⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢽
⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡼⡄
⠀⠀⠀⠀⠨⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠙⠪⣖⣄⡀
⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⣿⠿⠒
⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠟⠁
⢀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⡀⠀⠴⠄⠀⠼⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢨⢴⠁
⠛⠛⠑⠐⠭⢖⢦⡀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⣆
⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⡶⠂⠀⠀⠀⠀⠀⠀⠀⠔⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣻⣷⣤⣀
⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⣠⣺⠕⠋⠉⠉⠁⠉
⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠈⠀⠀⠈⠂⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡇
⠀⠀⠀⠀⠀⠾⣧⢂⣦⢄⠀⠀⠀⠀⠐⠈⠀⠀⠀⢰⡀⠐⡐⡁⠀⠀⠀⢠⠁⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⢿⣧
⠀⠀⠀⠀⠞⠁⠀⠀⠈⠳⣵⠀⠀⠀⠀⠀⠀⠀⠀⠺⠐⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣐⠿⠛⠛⠛⠛⠛⢺⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡇⢀⢀⣀⣐⢄⡀⠀⠸⠀⠀⠘⠀⠀⢐⡢⠀⡀⡀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡻⠟⠋⠁⠉⠀⡏⡟⢙⠀⣀⣛⠩⢤⣿⠀⠉⠉⠛⠳⣦⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠠⣛⣙⡉⠀⣀⣭⠄⢠⡶⠀⠀⠀⠀⠀⠈⠙⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢋⠉⡋⠀⢀⣨⡄⢠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢉⣙⠁⠀⡥⠄⠴⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣭⣭⣀⣠⠤⠦⣲⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⣶⣶⡶⠞⠁⠀⠀⢀⣀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡰⠊⠑⣀⡀⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠤⡿⠁⢨⠇⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⣀⣰⠁⠀⡌⠀⠀⢸⠀⠀⠀⣀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡆⠰⡀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⡏⠀⢰⠁⠀⠀⡇⠀⠀⠀⠀⠉⠒⠤⣀⠀⠈⡀⠀⠀⠀⠈⡄⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢸⠀⠀⡎⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡄⠀⠀⠀⠀⠘⡄⠰
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡇⠀⢰⠁⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡇⠀⠀⠀⠀⠀⠸⡀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢸⠁⠀⡞⠀⠀⠀⡏⠀⠀⠀⢸⠀⢀⡴⠋⠉⠡⠸⡄⠀⠀⠀⠀⠀⠀⢣⠈
⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠎⠀⠀⠃⠀⠀⠀⠁⠀⠀⠀⠈⢠⠏⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠖⠤⣀⡀
⠀⠀⠀⠀⢰⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⢀⣼⣿⣷⣦⣀
⠀⠀⠀⠀⠸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢆⡀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠁⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠈⠑⠲⠀⠤⢄⡴⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡠⠁⠀⠀⠀⠀⠘⢄⡀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⡰⠻⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢊⠐⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⣶⣶⣴⣅⣀⠀⠀⠉⠙⠒⠤⢤⣀⠀⠀⠀⠁⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⣸⡿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠉⠓⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡿⠁
⠀⠀⢠⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟
⠀⠀⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⠀⠀⢀⣀⡀⠀⠀⢀⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡸⣧⣰⡏⠀⢹⣇⣠⠞⣡⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡌⠁⠁⠀⠙⢋⣥⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣄⠀⠀⢀⣀⠀⢠⡇⠀⡀⠀⠀⣾⠃⠀⠀⠀⢶⡘⣧⡀⣴⠒⠲⣄⠀⣠⠟⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡹⣦⣼⠋⠉⣿⢀⡥⢞⣵⠏⠀⣿⠀⠀⠀⠀⠈⠳⣌⠻⠟⠂⠐⠛⠛⣡⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠹⡄⠀⢀⣤⣤⡀⠀⢀⡾⣰⠆⠀⠀⠈⠳⣄⠀⠀⠀⠉⣡⡶⢋⣥⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡙⠦⠺⠁⢠⣿⠴⣫⡾⠃⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⡿⢠⡾⢻⣇⠀⣿⡄⡀⢀⠀⢀⣀⣀⠻⢀⡆⣤⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⣾⠁⢀⢀⡄⠀⣀⣀⠸⠇⣠⣀⠀⠀⣷⠙⠁⠀⢻⡄⠸⣧⢳⡈⠳⠿⠀⢸⠷⢋⡼⣃⡀⠘⣷
⠀⠀⠀⠀⢀⡄⣶⠀⢀⣀⣀⢸⡇⣠⢀⠀⠀⣿⠀⠘⣆⠻⠼⠇⠨⠧⢞⡵⠋⠀⠀⣿⡀⠀⠀⠀⠛⠂⠛⠀⠙⣦⠀⠀⠀⢠⡟⠀⡿⣷⡀⠹⣇
⠀⠀⠀⠀⠈⢷⡘⣧⠿⠁⢸⡧⢞⣡⢟⣄⠀⢻⡄⠀⠈⢧⡀⠀⠀⢀⡞⢲⡄⢠⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠸⣧⣸⠇⠈⢷⡀⢻⡄
⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⢰⡏⢀⡾⠙⣆⠈⣧⠀⠀⢸⡇⢀⡀⠸⡇⠈⣷⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣸⢿⡄⢿⡄⠀⠀⠈⠳⠀⠛
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠼⠃⠀⠘⣆⠘⣆⠀⣼⠁⡾⢿⡀⣿⠀⢹⡆⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⡟⠈⢳⡈⣷⡀
⠀⠀⠀⠀⠀⠀⠿⣤⠀⣀⠀⣤⠟⠀⠀⠀⠀⠘⠆⠘⢠⠏⠼⠁⠈⢷⠹⠆⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠀⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⢠⡟⣰⠿⣆⢹⡄
⠀⠀⠀⠀⠀⠀⠛⠰⠋⠀⠻⠜⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠶⠿⠿⠿⠿⠷⠶⢶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⢀⣤⠀⠀⠀⣿⠉⠉⠉⣿⠀⠀⢀⣤⡀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⢀⣴⠟⠙⢿⡶⠿⠛⠀⠀⠀⠛⠿⣶⡿⠋⠻⣦⡀⠀⠀⠀⠀⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⣠⣼⠟⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⢀⣴⠿⠛⠛⠛⠿⣦⡀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⣾⡟⠛⠛⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠛⠛⢻⡇⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠙⠛⠻⣷⡀⠀⠀⢻⣦⡀⠀⠀⠀⢀⣴⠟⠀⠀⢀⣿⠛⠛⠃⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡷⠀⠀⠀⠉⠛⠷⠶⠿⠛⠁⠀⠀⠀⢾⣇⡀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⡀⠀⣀⣄⡀⠀⠀⠀⠀⠀⢀⣠⡀⠀⢀⣽⠗⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⠟⠙⠛⣷⠀⠀⠀⣿⠛⠉⠻⣶⠟⠁⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠐⠿⢷⣦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣶⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟
⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠁
⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠘⠛⠿⠶⢶⣶⣶⠶⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⠇

⠀⠀⠀⢀⠀⠢⠀⠀⠀⠀⠀⠀⠠⣤⠠⠈⡀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠈⠢⠀⣀⡄⠀⠀⠀⠀⠈⢄⠀⠁⣀⡤⠒⠀⠒⢌⣲⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠈⢶⡤⣀⠀⠈⠫⡁⠀⠀⠀⠀⠠⠈⠀⢙⡿⠄⠀⣁⠀⠀⠉⢧⡀⠘⠄
⠀⠀⢸⠃⠀⡿⣄⠀⠃⠀⠀⠀⠄⣠⣴⣿⣞⡅⣈⠀⠀⠁⢄⠀⠀⡘⠆⢸⡄⠀⠀⡀⡠⣀⠀⠀⠀⠀⣠⠖⠁
⠀⠀⠂⠀⠀⢷⠟⠿⣄⠂⠀⠀⢰⠡⠋⣿⢀⡤⠂⢈⠑⠂⠄⠁⠀⢣⢀⢾⠁⠊⣉⠀⠙⠂⢧⡠⠐⠊⠁
⠀⠀⠀⠀⠀⠓⢈⠀⢋⡇⠀⢀⡄⠀⢰⠇⢀⡴⠾⠉⢿⣿⣦⣅⠲⣼⣾⡾⠃⠀⠠⡀⠀⠀⠏
⠐⣀⡉⠷⠀⠀⠀⠃⠈⠀⠀⡈⡇⠀⣾⠴⠋⠀⠔⠐⠀⠉⠉⠛⣧⠟⣋⠇⡄⠀⠈⠉⠉⠀⠒⠁
⠀⠈⢠⣤⡄⠀⠀⡀⠀⠀⠀⠅⠀⢰⣿⡀⠀⠀⣠⣤⣤⡀⠀⠀⣸⠛⠛⠋⠱⠁
⠀⠈⠀⠉⠛⠹⠉⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠹⡋⠁⢈⠇⠀⣰⡿⠀⠀⠀⢸⡓⠒
⠀⠀⠀⠀⠀⠀⢀⡀⠰⠀⠀⠆⡀⠀⣿⡟⣦⡀⠙⠈⠀⢀⡶⠉⡰⠀⠀⠀⠀⡇⠠⡀
⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⢐⠰⡇⠀⠛⢳⡈⢷⣷⣴⢾⡟⢀⡴⠃⠀⠀⠀⠀⠟⣄⣩⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠇⠀⢠⠀⠳⠈⠄⠈⠑⠻⣿⡆⠀⠀⠀⠀⠀⢸⡟⠀⠦⣀⠈⠁⠒⠆⠤⢄⣀
⠀⠀⠀⠀⠀⣀⣠⠖⠒⠀⣰⠃⠀⠀⠘⡀⢘⠀⠀⠂⠀⠀⠀⠙⠃⡀⠀⠈⠀⣏⢀⣠⣤⣸⡇⢢⡀
⠀⠀⠠⠴⠖⠋⠁⠀⡠⠚⠁⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⢠⣤⡀⠀⠘⢦⣾⣄⠑⠘⣀⢈⠝⠀⠀⠙⢆
⠁⠀⠀⠀⠀⠀⢰⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣰⡔⠃⠁⢧⠀⠀⠀⠙⠄⡉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠐⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡟⠁⠀⠀⠠⢊⠀⠀⠀⠀⠀⠘⠓⢀
⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠑⣤⡀⡀⠴⠁⠡⡀⠀⠀⠀⠀⠀⠀⠐⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⢀⠎⠀⠀⠀⢀⠀⠀⠰⣄⠠⠀⠀⢠⠀⠀⠀⠀⡄⠀⠀⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⢀⡎⠀⠀⠀⠀⠈⠆⠀⠀⠀⠳⠰⣟⣷⡀⠁⠢⠄⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠑⠀⠀⠀⠀⠤⠀⠉⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⣶⠀⠀⢀⣠⠀⠀⠀⠀⢀⡀⠀⠀⣀⣤⣤⣄⡀
⠀⠀⠀⣠⠎⠙⣆⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣀⣤⠶⠛⣿⠀⠀⠀⠀⠈⢳⡄⠀⣿⠁⠀⣽⠛⢶⣄
⠀⠀⣰⠿⢶⣄⠘⣦⠀⠀⢸⡏⠀⠀⠀⠀⠰⢾⣏⡀⠀⠀⣿⠀⠀⠀⠀⠀⠘⣷⠀⠉⠛⠛⠁⣠⡴⠟⠃
⠀⠀⣿⡀⢀⣿⠀⠸⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣿⠀⠀⠀⠀⠀⢀⣿⠀⢀⣠⡶⠛⠉
⠀⠀⠈⠛⠛⠁⠀⠀⠘⠃⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⣸⠇⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋