Headset Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣟⣯⣿⣿⣿⣿⣿⣿⣶⣭⡙⠲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢟⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠛⠛⢿⣦⡀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⣾⣟⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣆⣠⣄⣌⢧
⠀⠀⠀⠀⠀⠀⣼⡿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣾⣿⣿⣯⣇
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢣
⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢸
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡇⡇
⠀⠀⠀⠀⠀⢻⣿⠀⠉⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⣄⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠘⣿⣇⠀⣀⣠⣷⣶⣿⠷⠶⢤⡀⠀⠀⣠⠖⢋⣀⣴⠞⢋⣩⣿⣿⣿⣿⣿⣹
⠀⠀⠀⠀⠀⠀⢿⣿⣿⢿⣿⣿⠋⣠⣶⣶⣄⡋⢦⡰⠉⢤⣤⠉⣠⣾⣿⠋⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⡏⢸⠇⣿⣿⣿⢀⣿⣿⣿⣿⣷⣾⢓⣿⡾⠀⣴⣿⠟⢠⣾⣿⣿⣷⣾⣿⡾⡇
⠀⠀⠀⠀⠀⢸⠁⣾⣀⣿⣽⣿⡄⢿⣿⣿⣿⣿⣏⣻⣿⣥⣼⣿⠋⣰⣿⣿⢻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣠⣿⣿⣿⣟⢿⣿⣌⠻⣿⣿⣿⣟⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⡟⣿⣿⣿⣏⡇
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣾⠻⣿⣷⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⡿⡜
⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⣿⣙⠷⣾⣛⡿⣿⣟⣿⢯⣿⠻⣿⣿⢻⣿⣿⣿⣿⣿⣧⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠪⠽⠷⠾⠿⠟⠛⠋⠀⠀⠙⠓⠼⣿⣷⣽⣿⣿⣿⡿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣁⣴⣤⣶⣶⣷⣞⣿⣷⣶⣠⣤⣤⣀⣤⡀⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢿⣿⣿⠿⣛⣿⣿⣯⣿⣿⣯⣻⡿⢻⣿⣿⣿⣾⣶⣤⣀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠠⠦⣤⣴⣿⠋⡁⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⢿⣷⣶⡈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣋⣶⡾⠟⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠛⠻⢿⣿⣿⣃⡀⠉⠻⢿⣿⣿⣧
⠀⠀⠀⠀⠀⣴⣤⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣶⣦⣾⣿⣧⠈⢷
⠀⠀⠀⠀⢀⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣷⣿⣇
⠀⠀⠀⠀⢈⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠂
⠀⠀⠀⢤⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣦⡤
⢀⣤⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⢿⣁⣀
⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⣿⣿⣿
⠈⢻⣿⠡⣶⠀⠀⠀⠀⣀⣤⣀⣠⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⢠⡯⢻⠟
⠀⠀⠹⣄⠹⣧⣴⣿⣿⣿⡟⢿⣿⣦⡉⡓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣰⣿⣿⣿⣿⣿⠶⣶⣶⠞⠃⢨
⠀⠀⠀⠛⠀⠈⠻⢧⠀⠈⠙⢿⣍⠻⣿⣿⠂⠙⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢊⣾⣿⠟⠉⡼⠋⠉⢠⠜⠁⣄⠀⠘
⠀⠀⠀⣀⠀⠀⠄⠙⠃⠀⠀⠀⠙⢄⠈⠻⣿⣏⡀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢀⣿⡿⠁⠀⠈⠀⠀⠀⠀⠀⠀⢀⣰⣶
⠀⠀⢠⡿⠿⣦⣤⡄⠀⠐⠀⠀⠀⠈⢃⠀⠙⣿⣿⣡⡐⣆⠀⠀⠀⠀⠀⠀⢠⠂⢠⣾⣿⠁⠀⠀⠀⠀⠀⠃⠀⠀⡰⠿⢿⣿⡆
⠀⠀⠈⣴⡆⠈⠙⠿⣄⠀⠀⣦⠀⠀⠀⢳⡀⠹⣿⣿⡷⠈⢆⠀⠀⠀⠀⢀⠎⣠⣮⣿⡏⢠⠆⠀⠀⠀⡼⠆⢀⡔⠁⢠⣿⣿⠃
⠀⠀⠀⠀⠉⠆⠀⠀⠉⢢⣤⣾⣷⠀⠀⠈⣳⣄⢹⣿⡇⢀⠘⡄⠀⠀⠀⠸⠀⣿⣿⣿⣳⣿⠀⠀⣀⢰⣧⣤⡞⠀⢠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠠⡀⠀⠨⠻⣿⣿⣆⢲⡀⠻⣿⣆⢻⣿⣿⡇⢁⠀⠀⠀⠃⣰⣿⣿⣿⣿⣿⣤⣴⣯⣿⣿⣿⠄⣠⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠙⢇⠀⠘⣿⣿⣿⡌⢷⣶⣿⣿⣿⣿⣿⣆⢠⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠄⠘⣿⣦⣿⣿⣿⣿⡘⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⡄⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣹⠇⠀⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⡿⢁⣿⣿⣿⣿⣿⠿⠿⠃⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢿⣿⡿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⣿⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠤⠤⠤⠤⠤⣤⣄⣀⣀⣀⣀⣀⣀⣠⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠶⠦⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣻⣿⣿⣿⣿⡿⠿⠛⠛⠉⠉⠉⠉⠉⠉⠉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⢿⣽⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⢠⣾⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣦
⠀⠀⠀⣰⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⡀
⠀⠀⣰⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⡀
⠀⢰⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷
⢀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣇
⢸⢏⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢋⢿
⡟⠘⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠈
⣇⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢀⡀
⡟⢳⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⢰⠛
⣧⠸⡆⡇⠀⠀⣀⣠⣤⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣤⣀⡀⠀⠀⡇⡾⢀
⢸⠀⢇⢱⣰⠋⠁⢹⣿⣿⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣾⣿⣿⠁⠉⢳⣰⢁⠇⢸
⠈⡆⠘⡀⣿⠀⠀⠸⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⠀⠀⢸⡇⡘⠀⡎
⠀⠸⡀⢣⣿⠀⠀⠀⢽⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡅⠀⠀⢘⣧⠃⡸
⠀⠀⠹⠁⢻⠀⠀⠀⠈⢿⣿⣿⣿⣷⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢰⣿⣿⣿⣿⡏⠀⠀⠀⢸⠋⠸⠁
⠀⠀⢰⣧⣼⢇⠐⡀⡀⠘⣿⣿⣿⣿⣧⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⣾⣿⣿⣿⡟⠀⡀⡐⢀⢿⣤⣷
⠀⠀⠘⣿⡄⠘⡄⢡⢠⠈⣿⣿⣞⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⣿⣿⣟⣾⣿⡇⢀⢡⠃⡜⠀⣼⡟
⠀⠀⠀⠹⣿⡤⡻⣦⡯⣧⣘⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣟⣠⡾⣣⡼⡣⣸⡿⠁
⠀⠀⠀⠀⠹⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⡿⠁
⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣖⣖⢢⡠⣤⡄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣴⣦⡷⠿⠿⠿⠿⠿⠟⠶⠿⠿⠿⢿⣿⣿⣕⢢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣲⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠷⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⣙⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣃⡑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣣⣯⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣽⣜⠄
⠀⠀⠀⠀⠀⠀⠀⠠⣱⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⠄
⠀⠀⠀⠀⠀⠀⢀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡀
⠀⠀⠀⠀⠀⠀⡸⢋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡛⢃
⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄
⠀⠀⠀⠀⠀⣸⣿⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⣿⡇
⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏
⠀⠀⠀⠀⠀⠘⣿⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⠁
⠀⠀⠀⠀⠀⠀⢁⣺⣿⣤⣄⠀⠀⣴⢶⣖⠶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠶⢶⡶⣦⠀⠀⣠⣤⣿⣕⡐
⠀⠀⠀⠀⠀⠀⢠⠯⣊⠿⣿⣽⠟⣿⣸⣿⠆⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠰⣿⣇⣿⡻⣯⣿⠿⣑⠝⡄
⠀⠀⠀⠀⠀⠀⠈⡎⣡⣾⣯⢐⣩⣿⣿⣿⠂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⣿⣿⣿⣍⡊⣿⣷⣌⢱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣏⢿⣿⠿⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠿⣿⡿⣸⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢃⢻⣿⣿⢾⣿⢘⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⡃⣿⡳⣿⣿⡟⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠻⡿⠸⣿⢸⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⡇⡿⠏⢿⠟⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢓⣲⠿⣿⢸⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⡇⣿⠿⣆⡚⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢛⡥⠞⣿⢸⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣿⡇⣿⠳⣬⡛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢏⣠⣾⣿⢸⣿⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⣿⡇⣿⣷⣄⡹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠋⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⢠⣿⣿⣿⠛⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠙⠻⣿⣿⣧⡀
⠀⠀⣰⡿⣽⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡽⣷⡀
⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧
⠀⣼⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡄
⢀⣿⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣧
⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿
⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣼⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿
⠀⠸⣯⣹⡆⠀⠀⠀⣠⣶⡶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⣶⣦⡀⠀⠀⠀⣾⣩⡿
⠀⠀⣿⣿⢃⡴⠟⣸⣿⣽⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣽⣿⡘⠷⣄⢻⣿⡇
⠀⠀⢛⡅⣼⣿⡇⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⡤⣝⠃
⠀⢠⣿⡇⣿⣿⡇⣿⢾⣿⣿⢇⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⡇⣿⣷⡀
⢠⣿⣿⡇⣿⣿⡇⣷⣼⣿⣿⢸⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣷⡿⣴⢬⣿⣿⣾⡿⣿⣿⡇⣿⣿⣷
⢸⣿⣿⡇⣿⡿⡇⣿⣿⣿⣿⣸⣧⣹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣿⣡⣿⣸⣿⣿⣿⡇⡿⣿⡇⣿⣿⣿
⢸⣿⣿⣇⢿⢷⣿⢸⣿⣿⣿⡇⣿⣿⣿⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢻⣿⣿⡇⣿⣿⣿⣿⢸⢷⢿⡇⣿⣿⣿
⠈⣿⣿⣿⢸⣿⣿⡏⣿⣿⣿⣿⢻⣿⣿⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣿⣿⢻⣿⣿⣿⡏⣿⣿⣿⢸⣿⣿⡏
⠀⢹⣿⣿⡆⣿⣿⣿⣹⣿⣿⣿⡼⣏⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⡿⣾⣿⣿⣿⣹⣿⣿⡇⣾⣿⣿⠁
⠀⠈⢿⣿⣿⠸⣿⣿⣧⢿⣿⣿⣿⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⣿⣳⣿⣿⣿⢧⣿⣿⡿⢸⣿⣿⠏
⠀⠀⠀⠻⢿⣇⢻⣿⣿⣎⢿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣿⣿⢏⣾⣿⣿⢃⣿⠿⠃
⠀⠀⠀⠀⠀⠉⠈⢿⣿⣿⣯⡻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⣫⣿⣿⣿⠏⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠀⠀⠂⠀⠀⠀⠂⠀⠀⢀⠀⠀⠄⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢁⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠆⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⡐⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣠⠞⠀⠈⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⡀⠛⡀⠰⠃⡠⠀⠀⠀⢀⠈⠀⠀⠠⠀⠀⡠⠂⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠈⠢⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⡬⠀⡀⠁
⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢄⠈⠠⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⢠⠖⠉⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⢀⠄⠈⠁⠁⠀⠠⠀⠄⠈
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁
⠀⠀⢀⠊
⠀⠐⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣷⣒⣯⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⣉⠤⠴⠒⠒⠒⠲⠦⢌⡙⠢⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠴⢒⡪⠥⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢫⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡌⢦
⠀⠀⠀⠀⠀⠀⡰⢁⠔⠁⢀⣀⡀⠀⠙⣦⣤⣤⡤⠶⠒⠒⠲⢤⣤⣤⠤⣤⣄⡀⠀⠀⠀⡸⢡⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡌⢧
⠀⠀⠀⠀⠀⢰⠃⠈⠀⡰⢋⠐⡈⠆⠀⢹⡟⢁⠀⠀⠀⠀⠀⠈⢻⣿⣷⣦⠀⢷⠀⠀⢀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡀
⠀⠀⠀⠀⢠⣾⡁⠀⠀⢡⠘⢃⣀⠆⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠉⠀⠀⢸⠀⠀⢸⠁⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡷
⠀⠀⠀⠀⣾⠀⠳⡀⢄⠀⠉⠉⠁⠀⡰⣇⠐⠀⢐⠈⠀⠀⠀⠀⠀⠀⣀⡤⠔⠋⠀⠀⠀⣅⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢾⣇⡜
⠀⠀⠀⠀⠘⠷⠶⠟⠲⠶⠤⠶⠶⠋⠁⠹⡄⢆⠈⡄⠀⠀⠀⢀⣨⠋⠀⠀⠀⠀⠀⠀⠀⢡⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⡿⠀⡼⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠷⢬⣤⠤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡼⣇⡠⣄⠀⠀⠀⠀⣠⡾⠋⠉⢁⣀⣰⢃⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡏⠀⠘⡄⠀⠀⠀⠻⣶⡄⡴⠉⠀⡅⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢸⠀⠀⠹⡀⠀⢀⣴⢏⡼⠁⠀⡘⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⢉⣠⡤⠶⠶⠒⠲⢤⡉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠣⡀⠀⡧⢠⡾⠃⠸⣄⡠⠊⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢋⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠞⠋⠀⠘⠷⣦⠀⣨⡷⠒⠋
⠀⠀⠀⠀⠀⠀⠀⢠⡋⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢋⣴⠏
⠀⠀⠀⠀⠀⠀⣰⠋⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣵⡿⠃
⠀⠀⠀⠀⠀⢠⠃⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⢀⡏⠠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠧⣤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣀
⠀⠀⠀⠀⢸⠁⠃⠊⠉⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢰⠏⠀⠀⠀⠀⣀⣠⣤⣤⣴⠶⢤⣴⠋⢈⠉⠙⢻⠷⣄⡀
⠀⠀⠀⠀⢸⠀⠀⠀⢠⡄⡇⠀⠀⠀⠀⢀⣀⡀⠀⣠⠞⠁⢠⠏⠀⠀⢀⡴⠞⠋⡽⠉⠡⠙⣷⡀⣯⠀⡗⠗⠀⠀⡇⠈⠙⠳⢶⣄⡀
⠀⠀⠀⠀⢸⡀⢷⠀⢪⠁⡇⠀⠀⡠⠚⠉⠀⠙⠋⠁⠀⡴⠃⠀⠀⠀⠘⣧⠀⠀⡇⠁⠀⠀⢸⡇⠘⠦⣄⣀⣠⠼⠛⠉⠙⠓⠺⢯⡙⢦⡀
⠀⠀⠀⠀⢸⣧⣈⡵⢶⣾⡄⠀⡞⠀⠂⠀⠠⠀⡀⣠⠎⠀⠀⠀⠀⣴⠾⠋⠀⠀⡇⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣌⢷
⠀⠀⠀⠀⠸⡇⣿⠀⢸⣿⣇⣀⣘⣄⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠻⠶⠶⠶⠶⢷⡀⠀⢸⣇⣀⣴⡟⠛⠛⠛⠛⠛⠛⣷⣤⣤⣤⣴⠾⣾⣿⠿⠂
⠀⠀⠀⠀⠀⣿⠹⣦⡾⠈⠛⠉⠙⠛⠓⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⢯⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟
⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⢇⣉⠉⠓⠒⠒⠚⠛⢋⣩⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⡿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷
⠀⠀⠀⠀⠀⢀⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣇
⠀⠀⠀⠀⠀⣸⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢿⡄
⠀⠀⠀⠀⠀⠏⠄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠎⠇
⠀⠀⠀⠀⢸⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⢸⠟⠄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⢿
⠀⠀⠀⠀⠈⡄⢠⢱⠀⠀⢀⣠⣤⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣤⣀⠀⠀⢠⢁⠀⡄
⠀⠀⠀⠀⠀⠇⠨⠈⣠⡏⠁⢹⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠃⠉⣧⡘⠸⠀⠇
⠀⠀⠀⠀⠀⠘⡀⠇⢹⠁⠀⠸⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⠀⠀⢸⠁⠇⡘
⠀⠀⠀⠀⠀⠀⠡⡌⠿⡀⠀⠀⢿⣿⣿⣿⣿⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣿⣿⣿⣿⠃⠀⠀⠸⡞⣠⠁
⠀⠀⠀⠀⠀⠀⠀⣁⠘⡇⢀⠀⠀⣿⣿⣿⣿⣆⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣾⣿⣿⣿⠇⠀⢀⠀⡞⢀⡅
⠀⠀⠀⠀⠀⠀⠀⣿⡞⠫⠀⠆⠀⢘⣿⣿⣿⣿⣌⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⣼⣿⣿⣿⣟⠀⠀⠆⠨⠙⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⣧⣈⢦⡈⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⠏⣰⢎⣰⡇⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠁⠈⠉

⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣿⣿⠿⠻⣿⠛⡿⢿⡿⢿⡿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠀⠒⠒⠀⠀⠀⠀⠒⠒⠀⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂⠉⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠐⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⣀⠠⠐⠒⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂⠤⡀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⡀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢄⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⢠⠂⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠐⡄
⠀⠀⠀⠀⠀⢀⠃⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠐⡀
⠀⠀⠀⠀⠀⡈⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⢀
⠀⠀⠀⠀⢠⠁⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⡄
⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢀
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⢠⠀⡆⠠⠐⠉⠀⠱⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠎⠀⠉⠂⠄⢰⠀⡈
⠀⠀⠀⠀⠈⡄⢸⠑⡀⠀⠀⠀⠐⡄⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢠⠂⠀⠀⠀⢀⠊⡇⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠈⢄⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⡠⠁⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠈⡀⠄⠀⠈⢆⠀⠀⠀⠈⢂⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⡐⠁⠀⠀⠀⡰⠁⠀⠠⠀⠁
⠀⠀⠀⠀⠀⠀⠇⠈⠄⠀⠈⢢⠀⠀⠀⠀⠣⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⡜⠀⠀⠀⠀⡔⠁⠀⠠⠁⠸
⠀⠀⠀⠀⠀⠀⠘⡄⠈⢆⠀⠀⠡⡀⠀⠀⠀⠱⡈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⠎⠀⠀⠀⢀⠌⠀⠀⠠⠁⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⢆⠀⠀⠱⡀⠀⠀⠀⠐⡌⢢⠀⠀⠀⠀⠀⠀⠀⠀⡔⢠⠂⠀⠀⠀⢀⠊⠀⠀⡰⠁⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠢⠀⠀⠘⠄⠀⠀⠀⠘⢄⠡⡀⠀⠀⠀⠀⢀⠌⠠⠁⠀⠀⠀⠠⠂⠀⢀⠔⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠑⡀⠀⠈⢆⠀⠀⠀⠈⢂⢡⠀⠀⠀⠀⡌⡐⠁⠀⠀⠀⡰⠁⠀⢀⠊⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⢈⢆⠀⠀⢢⠀⠀⠀⢀⠏⠀⠀⠀⠀⠹⡀⠀⠀⠀⡔⠀⠀⣰⠁⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠒⠤⠵⠐⠊⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠮⠤⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⠾⢿⠛⠟⡟⡿⠟⢿⠿⢷⢶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⢻⡛⣏⡁⡵⠉⣈⣰⣧⣄⣤⣶⣦⣄⣤⣦⣈⡈⢘⡅⣩⡟⣻⢳⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠻⠛⢀⢸⣷⣬⣿⣿⣿⣻⡿⠿⠿⠯⠿⠯⠿⠿⠿⣿⣻⣿⣿⣧⣴⣷⢠⠘⠙⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣰⡿⡟⠑⣤⣬⡾⣛⠯⠓⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠫⣟⡻⣮⣦⡖⠙⡿⣶⡀
⠀⠀⠀⠀⠀⢠⣾⡛⣡⣄⣼⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣄⣤⡙⣻⣦
⠀⠀⠀⠀⣰⡟⠒⢴⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⠔⠚⣧⡀
⠀⠀⠀⢰⣟⠃⣸⣿⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣽⣿⠀⢛⣧
⠀⠀⢠⣟⠠⣲⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡂⢘⣧
⠀⠀⣼⡟⢳⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠟⣿⡄
⠀⠀⣹⣿⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⣿⡁
⠀⠀⡿⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⡇
⠀⢰⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰
⠀⢸⣁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⣹
⢀⡼⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⣄
⡎⠀⢰⠏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⢷⠀⢈
⠘⢲⣿⣴⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣾⣷⠚
⠀⢸⠟⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⠿
⠀⠀⣦⣼⣷⠀⠀⠀⠀⠀⠀⢀⣀⣄⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣀⣀⠀⠀⠀⠀⠀⠀⢰⣿⣤⡆
⠀⠀⢿⣿⣿⡄⠀⣠⣶⣶⣾⣿⡭⠍⣽⡿⢋⣳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡋⠻⣿⡭⠬⣽⣿⣶⣶⣦⡀⠀⣼⣿⣿⠃
⠀⠀⢸⣿⣿⣿⣿⠿⣿⣿⣿⣛⣒⣿⣿⡇⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⣿⣿⣗⣊⣻⣿⣿⡿⢿⣷⣿⣿⣿
⠀⠀⠀⣿⠿⣇⡇⢰⠻⢻⣿⣞⢛⣿⣿⡇⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⣿⣟⢛⣾⣿⠻⢳⠀⣇⡿⢿⡇
⠀⠀⠀⢡⠀⢻⡅⢸⠀⢸⣿⣌⣰⢿⣿⡇⢸⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⠀⣿⣿⢗⣈⣼⣿⠀⢸⠀⣿⠁⢠⠁
⠀⠀⠀⠈⣆⣈⣷⣸⣤⣼⣯⣭⡁⣼⣿⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣸⣿⡄⢩⣽⣿⣤⣼⣰⣏⣀⠆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⣒⣢⣼⣿⡀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⣸⣿⣤⣒⣺⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣛⡯⢿⣿⡅⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⣿⣿⠯⣟⣻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⡇⡏⢹⠉⢹⣿⣶⠖⣺⣿⡅⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⠀⣽⣿⡒⢶⣾⣿⠋⢹⠉⡇⡇
⠀⠀⠀⠀⠀⢧⣧⣸⠀⠘⣿⣶⠟⠛⣿⡇⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠀⣿⣟⠛⢳⣾⡏⠀⢠⣰⣥⠇
⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣶⣞⣿⣿⠊⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⢺⣿⣗⣶⣿⣿⣿⣿⡿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⠿⠿⠿⠿⢿⡿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⢟⣋⠉⠀⠀⠀⠀⠀⠀⡀⠀⠠⣍⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣴⣾⣿⣿⣿⣏⠀⣈⣭⣤⡟⢧⣤⣤⣀⣀⡀⡀⠈⠁⢽⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⠿⠋⠈⠀⠀⠀⠀⠀⢠⡌⠹⣟⣿⣷⣤⣤⣾⣄⡃⢉⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⡄⠸⠟⢿⣿⣿⣿⣷⣿⣼⣿⡿⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠁⠀⣈⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣼⣋⣴⣿⣿⣿⣷⣟⣃⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⣰⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠜⢓⣱⢿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠃⠀⠀⣀⠀⠀⠋⠀⠀⠘⠂⠀⠀⠀⠀⠈⠀⠀⠤⢤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢆⡀⢺⣿⠄⠀⣼⠏⠈⠀⠀⠐⠇⠀⠀⠀⠐⠀⠀⠀⠄⠀⠀⣠⣴⣿⡟⠉⢻⣿⣿⣿⣿⢿⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⡆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢠⣾⣿⣿⣿⣿⣶⣼⣿⣿⣿⣟⣿⣿⣧⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠰⣤⠾⣿⡿⠀⠁⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⣾⣿⣿⣿⣃⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢶⣬⡆⣿⣀⣤⣶⣾⣿⣷⣦⠀⢤⣶⣶⣾⣾⣿⣧⣤⣄⣠⡄⡻⣿⣿⣿⣿⣿⣣⣿⢳⣿⠟⣠⣾⣿⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣿⣿⣿⣿⣿⣿⣿⠟⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣸⣿⣿⣿⣿⣿⣧⣿⢇⣼⣿⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣾⣿⣿⣿⣿⣯⣶⣄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣏⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢾⣿⡏⢿⣿⡿⠟⣿⣿⣿⣿⡟⢧⣿⣿⣿⣿⣿⣿⣿⣿⠏⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⣤⣤⠀⣤⣿⣿⣿⣿⣷⣴⢃⠀⣉⣉⣙⣛⡉⢁⢂⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣽⣿⣿⣿⣽⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⣿⠇⠘⠛⠃⢿⠿⠃⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡤⠀⠀⠒⠀⠐⠾⣷⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⠀⣠⠀⡀⣿⣾⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⠟⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣁⣈⣀⣹⢙⡟⣿⣽⣯⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⠿⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⠛⢹⠁⠀⠐⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠸⠆⠀⢠⣤⣤⣤⡄⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠻⠿⠛⢏⠀⠠⠀⠀⠐⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠛⠀⠀⠢⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣤⣾⣿⡷⢷⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣋⠠⠀⠀⠈⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣷⣪⣽⣶⣖⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡄⣿⣽⡝⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣻⣿⣿⣴⣿⣵⡞⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⢿⣿⣿⣿⣿⣿⣿⣯⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⣿⣿⣿⠛⠋⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣛⣿⣍⣢⡀⣶⠀⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣷⣦⣭⣨⣾⣷⣦⡀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣼⣷⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠋
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡠⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⢶⡇⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠻⢷⣤⣀⣀⡀⠈⠛⢠
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢩⣱⡄⠠⠃
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡗⠉⢷⢀⡄⣿⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡀⢀⠏⡄⠻⠿⠿⣋⠼⣉⢻⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣾⡯⠈⡛⠊⠁⣠⠌⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠤⢄⣀⣀⣀⣂⣉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⣄
⣀⣀⡀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠁⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇
⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡩⠐⠊⣉⣉⣁⣒⢌⠢⡅⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠈⣠⠖⠉⣥⡄⢠⣦⠙⢧⡘⡀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⢀⠜⠁⠀⠀⠁⠀⠀⠀⠨⢠⣷⠁⠀⢱
⠀⠀⠀⠀⢀⡤⣰⠇⠀⠀⢀⣀⠀⠀⢀⣤⣄⠀⠴⠀⢀⠃⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡸⣆
⠀⠀⠀⠠⠈⠒⠛⠀⠀⠀⡼⠟⠃⠀⡼⠛⠋⢀⡇⠀⠀⠀⢰⣷⣆⠀⠀⠄⢀⣀⠀⠀⠀⠀⠇⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠁⠀⢐⠇⠀⠀⢀⡇⠀⠀⢨⠅⣠⡜⠋⣉⣍⡉⢀⢀⠔⠀⠀⠀⠀⢰⠆⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⣿⣿⣿⣦⠃⠀⠠⢂⠤⠚⠁⠀⠀⠁
⠀⠀⠈⠻⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠹⣿⣿⡇⠀⠀⡐⢁⣴⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢶
⢀⣤⡆⠀⠉⠀⠀⠀⠀⠀⠠⡴⠓⠢⠀⠀⠀⠀⠀⠙⣄⢀⠀⠈⠛⡃⡆⠀⠁⣾⣿⣿⣿⣇⣤⣄⠀⠀⠠⢶⠖⠀⠸
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠈⠑⣳⠄⠀⠰⢶⡘⢧⣛⢿⡿⠟⠘⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⢙⣰⡀⣤⡦⢽⠂⠉⣘⣦⣤⠄⠻⡂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⡀⠀⠄⡂⠀⠉⠋⣀⣳⠍⠐⠘⢏⠁⣀⢱⡨⢷⠒⠷⠉⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠒⠘⡍⢀⡀⠤⠄⢿⢶⡁⠁⣀⣼⡦⠐⠀⠹⡅⣴⣶⣧⠤⠔⠒⠉⠉
⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⡠⠤⠒⠂⠹⣀⣀⠠⠄⠘⣖⢸⣉⣥⣠⠿⠄⠐⠂⢻⠉⠛⢁⡀⠤⠔⠒
⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⢀⠠⠄⠒⠊⢹⣀⠀⠠⣾⣿⠟⠉⠀⡀⠀⠠⠄⠒⠚⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠖⠊⠉⢇⢀⣠⠭⠕⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠈⠙⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄
⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣀
⠀⠀⠀⠀⠀⠈⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠘⠋
⠀⠀⠀⠀⠀⠙⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠿⠿⠛⠛⠛⠻⠿⢿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⢸⣿⠀⢀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠀⢀⣄⠀⣿⡇⢀⣀⠀⣶⡆⢸⣿⠀⣿⡇⢀⣄⠀⢸⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⠀⣿⡇⢸⣿⠀⣿⡇⢸⣿⠀⣿⡇⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⠀⣿⡇⢸⣿⠀⣿⡇⢸⣿⠀⣿⡇⢸⣿⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠀⠘⠛⠀⣿⡇⠘⠛⠀⢿⠇⢸⣿⠀⣿⡇⠘⠛⠀⢸⣿⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⢸⣿⠀⠉⠁⠀⠀⠀⢸⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠘⠻⠛⠉⠉




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⠭⣟⡛⣛⣛⡛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢴⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⣸⣿⢿⣿⣿⣷⠀⠀⠀⢀⣤⣼⠖⠒⠒⢶⣦⣄⠀⠀⠀⠀⣿⠟⠋⢻⡆⠀⠀⠀⢠⣿⠿⠛⠛⢿⣆⠀⠀⠀⠀⣘⣡⣚⣆⡀
⠀⠀⠀⠀⠀⠀⠹⡛⠟⠛⠛⡿⠀⠀⠀⠀⠉⠓⢀⣠⡀⠘⠉⠁⠀⠀⠀⠀⡃⠀⠀⠈⠇⠀⠀⠀⢸⣿⡓⠀⠐⢺⣿⠀⠀⠀⠀⡟⠁⠈⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⢀⣰⣄⣀⣴⣦⠀⠀⠀⠈⢿⣧⡀⠀⣾⠏⠀⠀⠀⠀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠦⠤⢤⣄⠀⠀⠀⢀⠀⠀⡈⠠⠄⠑⠀⢀⠀⠀⠀⠸⠥⠽⡗⢿⠾⠀⠀⠀⠀⠀⡈⠀⠀⢁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠈⠀⠀⠀⠨⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⢻⠘⣆⠀⠀⠀⠀⠈⢓⢄⡠⠎⠁⠂⠀⠐⠂⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠅⠅⠀⠜⠀⠀⢰⠀⠀⠀⠀⠀⠀⢠⠂⠸⠀⠀⠀⠀⠀⠀⠈⠀⠀⠛⠱⠉
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⣠⣴⣶⣤⠀⠀⠀⠀⠀⠀⣼⠿⣿⣿⣦⠀⠀⠀⠀⠀⢀⣴⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠟⢿⡀⠀⠀⠀⠀⣾⠏⠀⠙⣧⠀⠀⠀⠀⠀⡟⡋⠙⢻⡇⠀⠀⠀⠀⠀⠿⠀⠀⠈⣛⠀⠀⠀⠀⠀⣿⠻⠛⠉⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠀⠀⣠⡀⠀⠀⠀⠈⢄⣀⣄⣠⠋⠀⠀⠀⠀⠀⠙⠀⠀⢀⠃⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⢰⣿⡷⠀⠀⠀⠀⠈⠛⠟⠋⠀⠀⠀⠀⠀⠀⢀⡈⠀⠈⣀⠀⠀⠀⠀⠀⢀⠠⠂⠐⡀⣀
⠀⠀⠀⠀⠀⠀⣀⣤⣦⣠⣀⣴⣄⠀⠀⠀⢠⠐⡂⠀⢈⠛⢣⡤⠀⠀⠠⣆⠁⠀⠀⣶⠀⠀⠀⠀⠀⢉⡁⠚⠒⣍⠁⠀⠀⠀⠀⠛⠈⠀⠀⠈⠙
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⢠⠍⠃⠐⠊⠱⡀⠀⠀⠀⠀⡌⠋⠈⠈⠋
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠸⠿⠀⠀⠀⠿⠇⠀⠀⠀⠘⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⡇⠀⠀⠀⠄⢦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⠀⠀⠀⠀⢀⣾⣿⡿⢿⣷⡀⠀⠀⠀⠀⡠⠾⠟⠭⡦⡀⠀⠀⠀⠀⢠⣾⣿⣿⣦⠀⠀⠀⠀⠀⢀⣤⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠟⠤⠤⠤⠽⠄⠀⠀⠀⢸⠟⠿⠀⠴⠻⡇⠀⠀⠀⠀⣧⠶⠓⠣⢷⠆⠀⠀⠀⠀⣿⣿⣟⣿⣿⡇⠀⠀⠀⢀⣿⣿⠋⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡐⠀⠀⠀⠀⢸⣷⡀⠀⠀⣼⡇⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⢹⣍⣡⣉⣽⠁⠀⠀⠀⢸⣿⡋⠀⠈⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠈⡀⠀⠀⠀⠀⢸⣿⡟⠀⠘⣿⡇⠀⠀⠀⠀⠀⠚⢠⠐⠳⠀⠀⠀⠀⠀⠀⢻⣿⡿⠏⠀⠀⠀⠀⠈⠿⣷⠀⠰⡿⠟
⠀⠀⠀⠀⠀⢀⠀⠈⠀⠘⠀⠁⠀⠀⠀⠀⠘⠋⠀⢀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣦⡀⠐⠀⠐⠃⣠⡆⠀⠀⠀⠀⠂⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡄⢰⣿⣿⣶⡔⣢⣾⣿⣿⠀⠰⠀⠀⠐⢳⡾⠒⠀⠐
⠀⠀⠀⠀⠀⠐⠐⠀⠈⠀⠀⠀⠂⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠁⠙⣿⣿⣿⠇⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠒⣒⣒⠒⠢⢤⣀
⠀⠀⠀⠀⠀⠀⢀⡀⠤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡥⠖⠉⠉⠀⠀⠈⠉⠓⢮⡳⡄
⠀⠀⠀⠀⠀⡰⢋⠔⠉⠀⠀⠙⣦⣀⣀⡤⠤⠤⠤⣄⣀⣀⣀⡀⠀⠀⠀⣰⢡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡘⡄
⠀⠀⠀⠀⢰⠁⠀⢠⢊⡁⠑⠀⢸⡟⠉⠀⠀⠀⠀⠈⣿⣷⣦⠉⡇⠀⠀⡇⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢱
⠀⠀⠀⢠⡾⡅⠀⠘⢜⣡⠄⠀⣸⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⡷⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢸⠃
⠀⠀⠀⢸⣇⣑⣔⣄⡀⣀⣀⡴⢻⡀⠀⠄⠀⠀⠀⠀⢤⠄⠒⠉⠀⠀⠀⠷⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡖⢻⢷⠇
⠀⠀⠀⠀⠉⠉⠀⠈⠉⠉⠁⠀⠀⠑⢵⣌⣂⣀⣠⠖⠃⠀⠀⠀⠀⠀⠀⠸⢹⠀⡀⠀⠀⠀⠀⣠⠶⠒⠛⠁⡜⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⡏⠙⡆⠀⠀⠸⢷⡄⡴⠋⢹⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢃⠀⠸⡀⠀⣠⢞⡼⠁⢠⠃⣸
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⣩⡴⠖⠛⠋⠁⠒⢤⡙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠳⡈⢢⣠⠇⣼⡋⠈⠢⣔⣁⠴⠁
⠀⠀⠀⠀⠀⠀⢠⠊⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠱⡀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢈⣽⢃⡼⠋
⠀⠀⠀⠀⠀⣠⠋⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣱⠟
⠀⠀⠀⠀⢠⠃⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⡇⠀⣸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢣⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤⣤⣀
⠀⠀⠀⢸⠀⠎⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⡔⢁⡾⠀⠀⢀⣠⡴⡶⠿⢿⡛⢻⠇⣠⣀⠈⢋⠳⢤⣀⡀
⠀⠀⠀⢸⠀⡆⠠⡇⡀⠀⠀⣠⠔⠒⠦⠔⠉⢀⠜⠀⠀⠀⣏⠁⢸⠁⠈⠀⢹⠘⢇⠉⠁⢀⡼⠦⠤⠬⣽⠲⣄
⠀⠀⠀⠸⣇⣐⡤⣵⡅⠀⡞⠀⠀⠀⠄⠀⡰⠋⠀⠀⢀⣴⠟⠀⢸⠀⠀⠀⡸⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠑⢌⢧
⠀⠀⠀⠀⣿⣯⠀⣿⣏⣀⣹⡀⠀⣀⠴⠋⠀⠀⠀⠀⠘⠓⠒⠒⠾⣆⠀⢸⣥⣤⡾⠛⠛⠛⠛⠛⢷⣤⣤⡤⠾⣾⣿⠗
⠀⠀⠀⠀⣿⠻⠶⠃⠉⠁⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠋
⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣿⠦⠤⣄⣀⣀⣤⠤⢶⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠤⠤⠖⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⣠⣤⣤⣶⣶⣶⣖⣶⣶⣦⣀⣤⣄⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣟⣻⡿⠿⣿⣿⣿⣶⣶⣤⣀⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢀⣠⣾⡿⢋⣹⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣿⡛⢻⣿⣿⣿⣶⣤⡙⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠿⢀⣫⣾⣿⣿⠿⠟⠛⠛⠋⠉⠉⠉⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⠃⠹⠻⣿⣷⣾⣿⣧
⠀⠀⠀⠀⠀⠀⣄⢠⣾⣿⣿⣿⡾⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⣿⣶⣌⠈⣽⣿⣿⠙⢧⡀
⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣧⣨⣷
⠀⠀⠀⠀⠀⢾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⢀⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣇
⠀⠀⢀⣀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦⣇
⢀⣶⣾⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣻⣤⣤
⢺⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿
⠈⠻⣿⠉⢾⡆⠀⠀⠀⢀⣠⣤⣀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⣼⡏⢛⠛
⠀⠀⠹⣆⠘⢿⣤⣶⣿⣿⣿⣿⣿⣿⣦⡍⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣠⣿⣿⣿⣿⣿⣷⣶⣶⡦⠛⠁⣈
⠀⠀⠀⠛⠃⠀⠙⠿⣁⠀⠉⠙⣧⡝⠿⣿⣿⣶⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢣⣾⣿⠟⠉⣴⠟⠉⠃⡼⠛⣀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⣔⠿⢄⠀⠀⠈⠻⣆⠈⢻⣿⣿⠃⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢰⣿⡿⠁⠀⠀⠁⠀⠀⠘⠁⠀⠙⠀⣠⣦
⠀⠀⠀⣼⣶⣦⣄⢁⠀⠀⠢⠀⠀⠀⠘⠆⠀⠙⣿⣿⡷⡀⠳⡀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣠⣿⡿⠁⠀⠀⠀⠀⠀⠆⠀⠀⠀⣠⣿⣿⣿
⠀⠀⠀⣏⡄⠉⠻⢿⣤⠀⠀⠀⡄⠀⠀⠀⢢⡀⠘⣿⣷⣿⡄⢳⡄⠀⠀⠀⠀⠀⢠⠃⣠⢿⣿⡗⢀⠀⠀⠀⠀⢸⡄⠀⢀⠔⠁⢠⣿⣿
⠀⠀⠀⠙⠛⠄⠀⠀⠙⢧⡀⠀⣽⣄⠀⠀⠀⢿⡀⠘⣿⣿⡀⠀⢰⠀⠀⠀⠀⢠⡏⢰⣿⣿⣿⣠⣾⠀⠀⠀⢠⣿⠀⢠⠎⠀⢀⣿⣿⡏
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠸⣿⣿⣿⡀⢀⠀⣼⣿⣦⢹⣿⣦⣴⡄⠇⠀⠀⠀⡌⠀⢸⣿⣿⣧⣿⣇⠀⢠⡶⣾⣿⣿⡏⠀⢀⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠐⣤⠀⠈⣹⣿⣿⣷⡈⣧⡀⣻⣿⣷⣹⣿⣿⡃⠰⠀⠀⠀⠃⣸⣿⣿⣿⣿⣿⣿⣷⣿⢿⣿⣿⣿⣏⣠⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⠈⣿⣿⣿⣷⠸⣿⣿⣿⣿⣿⣿⣿⣷⠸⡇⠀⢠⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠘⢠⣸⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⢠⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⡼⠃⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⠃⣼⣿⣿⣿⣿⡿⠿⠛⠁⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⠚⠛⠛⠓⠒⠒⠒⠒⠒⠒⠶⠦⠤⠤⠤⠴⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠲⠶⠤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠶⠿⢿⣿⣿⣿⡯⡧⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠒⠓⠳⠦⢟⡭⡴⠞⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣐⣦⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠴⠲⠲⠶⠦⣨⣗⣶⠾⠞⠟⠛⠓⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣯⡇
⠀⠀⠀⢀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⡶⣴⠼⣭⣿⡚⣯⣦⣶⡶⠶⠶⠦⢤⠀⠀⠀⠀⠀⠀⡀⠀⠘⠂⠠⠍
⠀⠚⠿⣺⣮⣇⣸⡇⣰⡿⠁⣠⡴⠗⠀⠁⡀⠀⠴⠔⡄⠀⡘⡷⢌⢁⣄⣆⣤⣀⡀⠢⠁⠀⡀⠀⠂⠀⠀⠀⢀⠉⠐⠄
⠀⠀⠀⢡⢺⣧⠿⢷⣟⣇⣰⣿⡀⢀⣤⡾⠏⢀⢠⣠⣶⠛⠈⢿⣞⠏⠉⣈⡄⠅⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠐⠂
⠀⠀⠀⠰⠋⢠⣼⠿⢸⢛⣏⣽⣤⣺⣿⣿⡀⣼⣿⣛⡀⠃⣿⣆⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⡼⠗⠉⣀⣮⡯⣿⢹⡟⢻⡏⢙⢮⣿⣻⣛⡂⢀⠀⡀⣤⣤⣀⠀⠰⠂⠠⠀⠀⠀⠈⠀⠀⠈⠰⣌⠐⣦⠐⣤⣤⣀⡀
⠀⠀⠀⠈⠀⢠⣾⡿⠟⠁⠋⠀⢽⣿⢷⣽⣿⡿⠶⢦⡰⣼⣇⡛⠷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠿⡐⠻⢾⣿⠟⠉⠉
⠀⠀⠀⠀⢠⠛⠁⠀⠀⠀⠀⢤⣾⢻⡞⢿⠹⣦⠲⢶⣿⣟⢿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠀⣀⣤⣤⣀⠈⠓⠦⠈
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣺⣿⠻⡀⠓⢈⣙⣲⣷⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠙⡄⡉⠉⠉⠉⠛⢦
⠀⠀⠀⠀⢀⣀⢀⠀⠀⢠⣿⢈⡀⠀⠀⠀⠶⣞⣻⢿⣿⣏⡛⠀⠀⡄⠀⠀⠀⠀⣶⣇⠀⠀⠹⡐⣇⠁⠀⠠⣄
⠀⢀⡀⠀⠀⠛⣿⣷⣦⣼⠁⡅⣷⣖⡤⡀⠉⣟⣷⠯⡝⠆⠀⢠⠀⠁⠀⠀⠀⠀⡼⠝⣷⣀⣶⣦⣀⣀⢀⣄⣐⣧⣴⣦⣤⡀
⠀⠀⠙⠿⣾⣶⣤⣄⠛⢾⣷⣯⣉⣿⣿⣁⡄⣾⣿⠅⠀⢠⠀⠐⠂⢀⠀⠀⠀⢰⠀⠉⠇⠈⠉⣱⣾⣿⣿⣿⣿⣿⣿⣿⣟⡛⡀
⠀⠐⠶⡒⠻⣯⣟⠢⢁⡼⢿⡻⠁⢚⣻⠟⣫⢼⡟⠀⠀⠈⡄⠢⠌⠈⠁⠀⠀⡌⠀⡌⠀⠀⣸⣿⣯⣿⠟⡵⠹⠋⣔⡿⣿⣿⠂
⢀⣴⢳⠿⢒⣽⡯⠀⢀⡾⣓⠆⠀⠁⡴⢋⡗⣃⠀⠀⠀⠀⢡⠀⡄⠐⠀⠠⢠⠃⢠⠀⢀⣼⡿⠻⠁⠋⠈⠁⠀⠀⠀⠈⠿⣿⡄
⠐⠝⠸⡆⢉⢼⣽⠀⠀⠼⣩⣧⠀⠀⠀⠊⢿⣿⡇⠀⠂⠀⠸⡄⠇⠀⡆⠀⡼⢠⠃⢠⡿⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⢀⢰⡀⢯⠀⠚⣿⡄⠀⠀⠫⢿⡄⠀⠀⠀⠀⠹⢧⠀⠈⠄⠀⢇⢀⠀⡇⢃⠇⡎⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠠⣶⠃⡀⠃⠀⠙⠷⡄⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠁⠀⠀⡀⢸⡌⡄⡇⣸⣸⡀⠠⠑
⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣄⣧⣡⣷⣿⡟⣠⡧
⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣶⣔⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣆⣠⣦⣤⣤⣤⣀
⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠿⠗⠢⠚⠛⠻⠿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⣶⣿⣿⣿⣦⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢻⠀⠀⠀⠀⣶⣄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣰⣧⣤⣤⣤⣤⣤⣄⣀⣠⠀⠀⠀⠀⢀⣬⠀⠀⠀⠀⡷⢌
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⠜⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠰⠃⠈⠁⠀⠀⠀⣠⡇
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠑⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠘⣿⣿⣿⣿⣿⣿⠿⠟⠛⠁⢹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⢿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠈⢻⣿⠏⠁⠀⠀⠲⠤⢸⠆
⠀⠀⠀⠀⠀⠀⠀⣠⠞⡇⠀⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⠠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠇⠀⢀⣿⣿⣿⣿⣿⣧⡱⠄⠀⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀
⠀⠀⠀⠀⠀⠀⠘⠃⠀⢀⠔⠋⠀⠽⢿⣿⣿⣿⣿⡶⠲⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⠿⠟⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠠⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⡀⠀⠀⠀⣴⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠿⠿⠶⢦⡴⠋
⠀⠀⠀⠀⠀⣠⣤⣴⣶⣶⣶⣶⣶⣾⣿⣷⡀
⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⣰⣦⡀
⣀⠴⠒⠉⠉⠉⢁⣀⣉⣉⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣶⣦⣄⡉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠈⠉⠙⠻⣿⣿⣷⣶⣤⣈⠉⠛⠛⠿⠿⠿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠓⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠀⠀⠀⣉⣩⣭⡭⠁⣐⣤⡀
⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⠟⠋⢉⣀⣤⣿⣿⣕⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⢀⣴⣴⠿⠛⠋⡉⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⢰⣿⣿⣿⠟⠑⢁⣴⠿⠿⠻⣿⣿⣿⣿⣷⡈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣄⣀⣤⣶⣿⠟⡡⠐⠈⠘⠳⣄⡀⠀⠀⠈⣿⣟⠄
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠊⡴⠋⠀⠀⠀⠀⠀⠙⢿⣿⣿⣇⠀⢳⡀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠋⠊⠀⠀⠀⠀⠀⠘⢿⣦⠀⠀⠸⣿⣎⠄
⠀⠀⠀⠀⠀⠀⠀⢀⠂⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⠀⢷⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠻⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠘⢿⡄
⠀⣴⣿⣿⣿⣿⣿⣿⣮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⠈⡆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠘⣷⠃
⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⢑⠀⠀⠀⠀⠀⠀⠀⢀⣠⠂⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠿⠂⠀⠀⣙⠔
⠀⢿⡿⣿⡟⢩⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣿⣿⣿⣏⣿⡇⠀⠀⠀⢲⣶⣾⣿⡧⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢸
⠀⠀⣤⣤⣤⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⣸⠇⠀⠀⢀⣜⣀⣀⣀⣠⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡞⡀
⠀⣀⣉⣉⣉⠉⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡛⠛⠛⣗⠋⠀⠀⠀⠈⠉⠉⠉⠙⡏⠀⢸⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢛⣿⠛⠛⠙⠄
⠀⣿⣿⣿⣿⡄⢿⣿⣤⡤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢸⣿⠁⣿⣿⣿⣧⠀⠀⠀⠐⠄⣀⠀⡀⠻⠄⡄⠁⠒⢤⡉⠐⠄⠠⢀⣀⣀⡐⠀⢸⣯⠀⠀⠀⢘
⠀⠈⢉⣿⣿⣿⣶⠏⠻⣿⣷⢭⡻⣷⣶⣞⣉⡉⠙⠻⣿⣤⣿⣿⣿⡟⠀⠀⠀⢀⠔⠁⡀⣀⣀⡴⣿⣶⣤⡈⢪⡲⡀⠀⢉⡉⠻⣿⣷⡄⠀⢄⠠⡄⠂
⠀⣴⣿⡟⠛⠉⣰⣦⣄⠀⠙⢿⣝⢎⢿⣿⡛⠛⢶⡀⠈⢻⣷⡽⣆⠀⠀⠀⠀⠂⠀⠀⠿⠿⠟⠁⢀⡙⢿⣿⣆⠑⡽⡄⠈⢿⣷⣌⢻⣿⡄⠀⢣⢹⣆
⣼⠟⣿⣷⣶⣾⣿⣿⠙⢷⡄⠀⠹⣯⣏⢿⣷⠀⠀⢻⡀⠈⣿⣿⣻⣰⡀⠀⠨⢰⡇⠀⠀⠀⠀⠀⢸⣷⡄⢻⣿⣧⠸⢹⡄⢸⣿⣿⡌⣿⣷⠀⠈⡈⡇
⡟⣰⣿⣿⣿⣿⣿⣿⡀⠈⢿⡄⠀⢹⣾⡜⣿⡂⠀⢸⡇⠀⣿⣿⣿⣿⡇⠀⢰⠛⠀⠀⠀⠀⠀⠀⠀⠛⢿⠀⣿⣿⡆⡆⡇⠘⣿⣿⡇⣿⣿⠀⠀⡇⠁
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣷⡀⢈⣿⡇⣿⡃⠀⢸⡇⠀⣿⣿⣿⣿⠃⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠉⠛⠃⡀⡇⠸⣿⣿⢁⣿⠇⠀⢀⠃⡠
⠸⡝⣿⣿⣿⣿⣿⣿⣿⣿⣾⢿⣿⣿⣿⣷⣿⠁⠀⢸⠁⣸⣿⣿⣿⠋⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⡑⠁⣼⣿⡿⣼⡟⠀⠀⡔⠐
⠀⠙⣾⣿⣿⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⣿⢏⡠⢠⠇⣰⣿⣿⣻⠃⠀⠀⠀⠀⠀⠐⢄⢠⠀⠀⠀⠀⠢⠖⠁⠀⢀⠜⠀⢐⣫⠟⣽⠏⠀⢀⠜⠔
⠀⠀⠈⠻⢼⣿⣿⣿⣿⣾⣿⣿⣿⣿⠿⠛⣉⠴⣣⣾⣿⣟⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣀⠈⠁⠀⠀⠀⢀⠠⠴⡾⠛⠵⠚⠁⠀⢐⠡⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠐⠚⠋⠉⠉⠙⠓⠦⣄
⠀⠀⠀⠀⠀⠀⣀⡤⠒⠋⡁⠤⠒⠀⠈⠉⠁⠐⠒⠤⣀⠙⠦⡀
⠀⠀⠀⣠⠔⠋⢁⠤⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⢦
⠀⢠⠞⠁⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠑
⢠⠋⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⡟⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠠⣀
⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠆⠀⠀⠑⣄⢀⡀
⣇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⡄⠀⠀⠘⣄⢹
⢸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣷⠀⠀⠀⢹⣼
⠀⠃⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠋⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣸⣈⠂⡰⠁
⠀⠀⠀⠀⠀⠄⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡿⠈⠈⠁
⠀⠀⠀⡆⠀⠈⢢⡀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂
⠀⠀⠀⢱⠀⠀⠀⠙⢦⡀⠀⠙⠲⢄⡀
⠀⠀⢰⠈⢧⠀⠀⠀⠀⠙⠶⣄⡀⠀⠈⠐⡆
⠀⠀⠀⠓⢄⣓⣦⣀⠀⠀⠀⠈⠙⠳⠄⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠈⠁⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⡠⠄⠒⠢⢄⡀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠙⢦⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⢱⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠤⠤⠚⠁⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠤⣀⡀⠀⠀⠀⠀⡠⠔⠊
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣤⣴⣶⠶⠶⢶⣤⣤⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣂⠽⡿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⣟⠡⢆⣤⡀
⠀⠀⠀⠀⠀⢀⠄⠉⣠⣺⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠐⠳⣄
⠀⠀⠀⠀⡠⠋⠀⣴⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠘⢧⡀
⠀⠀⠀⠰⠁⠀⢰⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠈⢷
⠀⠀⢀⡆⠀⠀⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠘⣧
⠀⠀⠈⡇⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⡄
⠀⠀⠀⠃⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣾⠂
⠀⠀⠀⠘⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⣸⡇
⠀⠀⠀⠀⢁⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡿
⠀⠀⠀⠀⠀⠠⣤⣬⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢯⣿⠁
⠀⠀⠀⠀⠀⠔⠛⠛⠛⠓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠃⠀⢸⡆
⠀⠀⠀⠀⠀⢠⣴⣦⣀⣴⣧⡤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣤⠤⡼⣷⠓⢶⠚
⠀⠀⠀⠀⠀⣙⠀⠀⠉⠙⢆⡀⠄⠈⠑⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠉⠀⠀⠀⠀⢀⠀⠉⢾
⠀⠀⠀⣰⢎⣁⡀⠑⢆⠀⠀⠱⡀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⣦
⠀⠀⠈⠀⠈⠘⡽⡆⠀⢢⠀⠀⠘⡄⠀⠀⠀⠉⡄⠀⠀⠀⡴⠁⠀⠀⣰⣬⡖⢻⡶⠀⠀⠰⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠰⢻⠀⠀⣀⠀⠀⠸⠀⠀⠀⠀⠆⠀⠀⡜⠀⠀⠀⣾⠃⠀⠊⠀⣸⠂⠀⡀⠀⠀⠘⡇
⠀⢰⠀⠀⠀⠀⠀⣼⡇⠀⢹⠀⠀⠀⡇⠀⠀⠀⠴⠀⢠⠁⠀⠀⡼⠈⠀⠀⠀⠀⡿⠀⢀⠃⠀⠈⡷⠃
⠀⠀⣄⠀⠀⠀⢠⡹⠟⠒⠋⠀⠀⠀⡇⠀⠀⠀⡀⠀⠸⠀⠀⠀⢁⠄⢠⠄⢂⡜⠁⢠⠎⠀⢠⢺⡱
⠀⠀⠐⢆⡀⢀⣼⠃⠸⠀⠀⠀⠀⠀⠏⠈⠀⠀⠇⠀⠀⢆⠀⠀⠘⠺⠖⠛⠉⢀⡴⠋⠀⠀⢣⠏⠁
⠀⠀⠀⠀⠀⠈⠨⡄⠁⠀⠀⠀⠀⡸⠀⠀⠀⠘⠀⠀⠀⠈⢢⡀⠀⠀⠀⣀⡤⠊⠁⢀⢐⣡⣪⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⢤⠚⠁⠈⢠⠄⠀⠀⠀⠀⠀⠀⠙⠳⠶⣾⣥⣤⣤⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⠣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣥⣤⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⣙⣶⣦⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠸⠖⠈⡁
⠀⠀⠀⠀⠀⠀⠀⡃⢿⠛⠶⡌
⠀⠀⠀⠀⠀⠀⠀⡳⠬⣤⠴⠃
⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⡀⢡
⣠⣄⣴⡭⠔⠁
⠉⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠉⠙⠀⠀⣀⠀⢀⣹⣆⠀⠀⠀⣀⣠⣤⣤⣤⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠉⠛⢿⣷⣶⣶⣟⠁⠀⠈⠻⣿⣿⡿⠿⠿⠛⠛⠛⠻⣿⣆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣡⣤⡶⠶⠶⠶⠶⣦⣿⣿⣿⣿⣉⠁⠀⠀⣀⣀⣀⣠⣤⣤⣀⠀⠀⠈⠻⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠁⠀⠀⠀⠀⣀⣨⣿⣿⣿⣿⡉⠀⠀⠀⠙⠉⠉⠉⠉⠉⠛⠳⣶⡂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣇⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⢆⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⠿⣿⣿⠛⣻⢿⣿⡿⠀⠀⣀⣤⠉⢻
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢀⣤⣾⣿⣿⣿⣿⣦⡄⠀⠈⠉⠉⠀⢾⣄⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣴⣿⣿⣿⣿⣿⣿⣟⠉⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⡀⠀⠀⢹⣿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⣿⣿⣿⣿⡿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠙⢿⣄⠀⠀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⡿⣿⡏⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠹⡆⠀⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⠀⣿⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⠀⣼⡏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠘⣿⠀⢸⣿⣿⠟⠋⠙⠛⠛⠛⠛⠛⠻⣿⣿⣿⡟⠀⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠁⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⢠⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣄⣦⠑⠀⡀⠀⠈⠛⠛⠁⠀⠀⣸⡿⠃⠀⢸⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣷⣌⠛⢿⣶⣶⣶⣶⣾⡿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣍⡉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠋⠉⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣀⣀⣀⣀⣤⣶⠿⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⡀
⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷
⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧
⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄
⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢹⣇⠀⣤⣾⣿⣯⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣤⠀⣸⡏
⠀⠀⠀⠀⠈⣿⣾⣽⣿⣿⣿⣿⣻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣯⣷⣿⠁
⠀⠀⠀⠀⠀⢻⣿⣿⣞⣿⣿⣿⣿⡽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⣿⣿⣿⣿⣳⣿⣿⡏
⠀⠀⠀⠀⠀⠘⣯⣿⣿⣿⢿⣿⣿⣿⣟⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣻⣿⣿⣿⣿⣽⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢿⣯⣿⣿⣿⣿⣿⣿⣿⣾⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣿⣿⣿⣟⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣻⣄⠀⠀⠀⠀⠀⠀⣰⣿⣾⣿⣿⣿⣿⣿⣿⢿⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣞⣿⣿⣿⣿⣽⡆⠀⠀⠀⠀⣰⣯⣿⣿⣿⣿⣷⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⡯⢻⣿⣿⢿⣿⣿⣿⠏⠀⠀⠀⠀⠹⣿⣿⣿⣿⣽⣿⡟⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠋⠁
⢀⢀⣀⡀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⡀⠀⠀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣄⣀⣤⠀⣀⠀⠄⠀⠀⠀⠀⠈⣀⣤⣀⣀⣀⠉⠉⠉⠃⠀⣀⠀⠀⠀⠀⠔⠀⠀⢠⢄⡀⠀⠀⡀⠠⠈⠀⠁⠀⠀⠀⠈⠀⠈⡗⢀⠀⡀
⠀⠀⠀⡼⠧⠠⠀⢑⠀⠀⣰⠋⠀⠾⠿⣿⡞⣷⠀⠀⠀⡜⠛⠛⠲⡀⠀⠀⠀⢠⠏⠒⠚⡆⠀⠀⠁⠀⡀⠀⠀⠛⠁⠀⠀⠀⡌⡁⠀⠘⢆
⠀⠀⠀⠱⠀⠀⠀⠘⠀⠀⠁⠠⠀⠁⠀⠁⠀⠤⠀⠀⠸⠀⠀⠀⠀⡇⠀⠀⠀⠘⠀⠀⠀⠗⠀⠀⠀⠀⣷⠊⠂⠉⡻⠍⠭⠍⢵⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠂⠀⠰⠀⠁⣄⠀⠂⡀⠀⠀⠀⡈⠁⠀⠀⠀⠀⠀⠀⠠⠈⠠⠀⠀⠈⠁⠀⠈⠂⠈⠀⠐⠒⠒⠒⠒⠢⠉
⠀⠂⢀⡀⠸⠷⠿⠀⠀⠀⠧⡠⠘⠀⠀⢱⢀⡀⠖⠀⠀⠀⢤⠤⠆⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⣀⡀⠀⠀⣀⠀⢀⣀⠀⠀⠀⠠
⠀⠀⡆⠁⠀⠀⠀⠀⢐⠲⠺⡢⡄⠀⠀⠀⠩⡄⣀⠈⠐⠀⠀⠀⠀⠀⠜⠗⢰⡄⠀⠐⠀⠀⡼⢛⡉⢤⠀⠑⠉⠋⢩⠵⢯⣁⣦
⠀⠀⠐⡀⠂⠀⠀⠀⡆⠤⠤⠤⡇⠀⠀⠀⢇⠀⠀⠀⣀⠀⠀⠀⠀⡌⠀⠀⠀⢨⠀⠀⠀⠠⡇⠀⠀⠸⡆⠀⠀⠀⠳⠀⠀⠀⠹
⠀⠀⠀⠁⠀⠀⠀⠀⠰⠐⠢⠐⠀⠀⠀⠀⠊⠀⠠⠀⠃⠀⠀⠀⠀⠁⠀⠒⠀⠈⠀⠀⠀⠀⢇⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢀
⠈⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠨⠀⠈⠀⠀⠀⠀⠀⠀⡆⠄⢰⠀⠀⠀⠀⠀⣴⠁⠀⢿⡀⠀⠀⠀⠀⠄⠀⠀⠄
⠦⡤⠶⢶⠾⠆⠒⢂⠈⠀⠀⢡⠀⡠⠀⠀⠀⠀⠉⠀⠀⠠⠤⢤⣀⠀⠀⠉⠀⢠⡆⠀⠐⢄⠀⠀⠀⠀⠀⠄⡤⠀⠀⠀⠉⠁⠀⣤
⠀⠇⠀⢠⠤⠄⠤⡴⠀⠀⠀⠀⠀⠈⠀⠀⠒⠤⠀⠀⢀⠈⠈⠀⢸⠀⠀⠀⠀⡌⠉⠉⠀⠸⠢⡂⠔⠂⠈⠀⠃⠠⢀⠀⠀⠀⡒⠀⠀⠀⢀
⠀⠀⠀⠈⠀⠒⢀⠁⠀⠀⠀⠒⠀⠀⠀⠒⠀⠀⠈⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠠⠀⠃⠀⠈⠂⠐⡀⠀⠀⠈⡎⢈⠀⠀⠁⢠⣦⠀⠊
⠀⠀⠀⢀⠁⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠁⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠰
⠤⡤⡀⠀⠀⠐⠀⠀⠐⠠⢀⠀⠀⠀⠀⠀⣀⠄⠀⠤⠈⠀⠀⠀⠁⢀⠄⣀⠀⠀⠁⢀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⡀⠀⢀
⠘⠈⠴⠀⠀⠀⠠⡀⠧⡀⠀⠀⠀⠀⠀⢊⠈⠀⠀⠀⠄⠀⠀⠀⢠⣤⠀⠸⡉⠀⠀⠀⠀⣰⠏⠈⢻⡄⠀⠀⠀⠀⢍⠀⠀⠷⡀⠊⠀⠑⡿
⡀⠀⡚⠀⠀⠀⠐⡇⠀⠀⠈⢇⠀⠀⠀⢈⡁⠀⠀⢀⠄⠀⠀⠀⢸⠟⠂⠚⢻⠀⠀⠀⠀⡽⠭⠤⠝⠏⠀⠁⠉⠁⡏⠀⡀⠀⡇⠀⠀⠀⢇
⠈⠀⠀⠀⠀⠀⠀⠱⡄⠁⣔⠂⠀⠀⠀⠀⠑⠀⠁⠚⠀⠀⠀⠀⢀⠢⠈⠠⠪⠀⠀⠀⠀⢧⠀⠤⠀⢤⠀⠀⠀⠀⠈⠀⠚⠀⠁
⠀⠀⡀⠀⠀⠀⠀⠀⠿⠾⠟⠂⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⣁⢀⠀⡏⠀⠀⡀⠀⠮⠄⠀⠀⠰⠀⠀⠀⠀⠠⠄⡀⠤⠀⠀⠀⢀⡀
⡀⠀⠀⠀⠠⠒⠂⢄⠀⠀⠀⠀⡔⢆⡄⢠⡀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⢸⠇⠋⢶⡀⣀⡀⠀⢀⡠⠂⢄⣀⣀⣀⣀⡠⢟⠉⡁⠁
⠁⠀⠀⠐⡄⠀⠀⠀⡄⠀⠐⣾⡁⠀⠀⠈⢀⠀⠀⠀⠀⢀⠀⠀⠀⡕⠐⠂⠀⠐⢌⠀⠀⠀⠇⢸⠀⠀⢰⣶⠀⢘⣄⠂⠀⠺⣗⡅⠀⠉⠉
⠀⠀⠀⠀⢣⠠⠄⢸⠇⠀⠀⠀⠁⠠⠦⠀⠀⠀⠀⠀⠀⠈⠐⠓⠐⠁⠀⠀⠀⠀⠀⡄⠆⡴⠀⠀⠀⠀⡻⠉⠁⠁⡛⠀⠀⠀⠈⠳⡀⠃⠸
⠀⠀⠀⢠⠀⠓⠐⠟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⡙⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢇⡄⠀⢰⡧⠁⠉⠉⢉⡁
⠀⠀⢠⡀⠀⣈⠂⢠⠇⠀⠄⠀⠀⠀⠀⠀⢀⠔⠂⣀⠀⠀⠀⠀⠀⠀⡖⠀⠐⠂⠀⠀⠛⠄⠀⠔⢲⣤⠀⠠⠀⠄⠀⠀⡀
⠀⠈⠄⠘⡀⠲⠟⠢⡐⠀⠀⠐⠃⠀⠀⠀⠆⠀⠀⠛⢿⡄⠀⠀⠀⣆⠀⠀⠀⢀⠀⠀⠀⢀⡁⠈⠀⠐⡆⠀⠀⠀⠀⠸⠆⠀⠀⣒⠀⠂
⠀⡀⠀⡔⠁⠀⠀⠀⠣⠠⠤⠘⠑⠀⠀⠀⢃⠀⢀⠀⡸⠁⠀⠀⠀⢀⠀⠤⠀⢼⠀⠀⠀⠁⠂⠀⡀⠀⠃⠀⠀⠀⠸⠁⠀⠀⠙⠂⠒⠀⠛
⠀⠂⠀⠀⠀⠀⠀⠒⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠁⠀⠀⠀⠀⢀⡀⠀⣈⠀⠂⠀⠀⠀⢦⠈⢠⡌

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⢠⣿⣿⡿⠛⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠙⠻⣿⣿⣧⡀
⠀⠀⣰⡿⣽⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡽⣷⡀
⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧
⠀⣼⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡄
⢀⣿⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣇
⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿
⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣼⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿
⠀⠸⣯⣹⡆⠀⠀⠀⣠⣶⡶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⣶⣦⡀⠀⠀⠀⣾⣩⡿
⠀⠀⣿⣿⢃⡴⠟⣸⣿⣽⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣽⣿⡘⠷⣄⢻⣿⡇
⠀⠀⢛⡅⣼⣿⡇⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⡄⣝⠃
⠀⢠⣿⡇⣿⣿⡇⣿⢶⣿⣿⢇⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⡇⣿⣷⡀
⢠⣿⣿⡇⣿⣿⡇⣷⣼⣿⣿⢸⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⢶⢸⣿⣿⣾⡟⣿⣿⡇⣿⣿⣷
⢸⣿⣿⡇⣿⡿⡇⣿⣿⣿⣿⣸⣧⣹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣡⣾⣸⣿⣿⣿⡇⡿⣿⡇⣿⣿⣿
⢸⣿⣿⡇⢿⢷⢿⢸⣿⣿⣿⡇⣿⣿⣿⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢹⣿⣿⡇⣿⣿⣿⣿⢸⢷⣿⢇⣿⣿⣿
⠈⣿⣿⣿⢸⣿⣿⡏⣿⣿⣿⣿⢻⣿⣿⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⣿⣿⢻⣿⣿⣿⡏⣿⣿⣿⢸⣿⣿⡏
⠀⢹⣿⣿⡆⣿⣿⣿⣹⣿⣿⣿⡼⣏⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⡿⣼⣿⣿⣿⣱⣿⣿⡇⣾⣿⣿⠁
⠀⠈⢿⣿⣷⠸⣿⣿⣧⢿⣿⣿⣷⣻⣿⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣽⣿⣳⣿⣿⣿⢧⣿⣿⡿⢰⣿⣿⠏
⠀⠀⠀⠻⢿⣇⢻⣿⣿⣎⢿⣿⣿⣷⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣿⣿⣿⢏⣾⣿⣿⢃⣿⠿⠃
⠀⠀⠀⠀⠀⠉⠈⢿⣿⣿⣯⡻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡿⣫⣿⣿⣿⠏⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⢷⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣯⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⣰⡿⣿⣿⠟⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⢿⣿⡿⣷⡀
⠀⠀⠀⣼⡿⣽⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡽⣿⡄
⠀⠀⣸⣿⣹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣹⣿⡀
⠀⢠⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧
⠀⣼⡟⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⣿⡄
⠀⣿⢷⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⢿⡇
⢸⣿⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣷
⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿
⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿
⠘⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠟
⠀⠈⣿⣬⣳⡄⠀⠀⠀⠀⣠⣶⡶⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠶⣶⣦⡄⠀⠀⠀⠀⣴⣋⣼⠏
⠀⠀⢸⣿⣿⠇⣠⡶⠇⣼⣟⣻⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣛⣿⡆⠷⣦⡀⢻⣿⣿
⠀⠀⠸⡿⡁⣰⣿⣶⢰⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣷⢰⣶⣷⡀⡙⣿
⠀⠀⢀⣾⠇⣿⣿⡏⢸⡟⣻⣿⣿⣿⢻⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⢻⣿⣿⣿⡋⣿⠈⣿⣿⡇⢻⣆
⠀⢠⣿⣿⠀⣿⣿⡇⢸⡟⢿⣿⣿⡇⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡆⣿⣿⣿⠟⣿⠀⣿⣿⡇⢸⣿⣧
⢀⣿⣿⣿⠀⣿⣿⣧⢸⣷⣾⣿⣿⡇⡿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠻⡇⣿⣿⣿⣶⣿⢠⣿⣿⡇⢸⣿⣿⣧
⢸⣿⣿⣿⠀⣿⡿⣿⢸⣿⣽⣿⣿⡇⣿⣆⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⣿⢃⣾⡇⣿⣿⣿⣿⣿⢸⡿⣿⡇⢸⣿⣿⣿
⢸⣿⣿⣿⡇⣧⣧⣾⡎⣿⣯⣽⣿⣷⢹⣿⣾⣿⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢸⣿⣿⣿⢱⣿⣿⣯⣿⡏⣾⣧⣧⡇⣾⣿⣿⣿
⠀⣿⣿⣿⡇⢻⣼⣼⣧⢻⣿⣿⣿⣿⡜⣿⣿⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⣿⡿⣸⣿⣿⣿⣿⢡⣿⣽⣼⠃⣿⣿⣿⡏
⠀⢹⣿⣿⣿⠸⣿⣿⣿⡌⣿⣿⣿⣿⡇⣿⡟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⣿⡇⣿⣿⣿⣿⡏⣼⣿⣿⡿⢸⣿⣿⣿⠁
⠀⠘⣿⣿⣿⡇⢻⣿⣿⣷⢹⣿⣿⣿⣿⡸⣶⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⡾⣸⣿⣿⣿⣿⢱⣿⣿⣿⠃⣿⣿⣿⡟
⠀⠀⠹⣿⣿⣿⡘⣿⣿⣿⣇⢻⣿⣿⣿⣧⢻⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢣⣿⣿⣿⣿⢇⣿⣿⣿⡟⣸⣿⣿⡿⠁
⠀⠀⠀⠈⠻⣿⣧⢹⣿⣿⣿⣎⢿⣿⣿⣿⣷⣽⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣵⣿⣿⣿⣿⢏⣾⣿⣿⣿⢡⣿⡿⠋
⠀⠀⠀⠀⠀⠈⠙⠆⢻⣿⣿⣿⣎⠻⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡿⢋⣾⣿⣿⣿⠃⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣷⣌⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⢋⣴⣿⣿⣿⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⠒⠒⠂⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⢁⠀⠄⠒⣀⣠⣴⣶⣶⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⡡⠂⠉⣁⣴⣾⠿⠛⠛⠛⠋⠉⠉⠳⢬⡻⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠀⣠⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢯⣦⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣡⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⠧⠘⠺⢦⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠻⣦⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠣⠀⠁⠀⠹⣷⣤⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⡀⠀⠐⠠⢄⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⢠⡀⠀⠀⠁⠀⠀⠀⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣹⣯⣽⣾⠁⠀⠀⢠⠀⠡⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⣷⣤⠀⠀⠀⠀⠀⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠉⢻⡄⠀⠀⠘⣧⠀⢢⡀⠀⠀⠀⠀⠀⠀⢳⡀⠈⢿⡀⠀⠀⢲⣾⣿⣿⣿⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⠀⢠⣧⠀⠀⠀⠙⣷⠀⢱⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⡅⠀⠀⢸⣿⣿⡏⣹⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢿⡄⢸⣿⣆⠀⠀⠀⢸⡆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⣼⢿⡿⠃⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠜⢿⡘⣿⣿⣆⠀⠀⠀⠓⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⠼⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣅⣾⣿⣿⣿⣿⣦⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⠖⠁
⠀⠃⠀⠀⠀⠀⠀⠀⢀⡼⣻⡋⢋⣿⠿⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠁⠀⠈⠸⠈⠟⠀⠙⢷⣤⠀⠀⠀⠀⠀⠀⠀⣸⡄
⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠒⠶⠿⠟⠛⠁
⠀⡅
⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⡶⠺⠿⠛⠟⠓⡲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠫⠃⠁⠀⠀⣀⣠⣤⣤⣈⡲⡈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡡⠂⠀⠀⣠⠶⠋⠉⠀⠀⠀⠈⠙⢶⡄⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⠊⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠡⠃⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠣⠃⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠻⢶⡴⠿⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠱⢺⠋⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⠁⡞⠀⢠⣎⠉⠙⢦⠈⢷⡀⠀⠀⣀⣤⠤⠶⠶⢼⠇⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢼⠀⣇⠀⢸⠀⠱⡀⠀⢣⠈⣧⠴⠋⠁⢀⣠⠤⠔⣮⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⢸⠀⠘⡄⠀⢱⠀⢀⠖⠁⢀⡤⠚⠁⠀⠀⡔⠀⠀⠁⢢⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠈⡆⠈⢆⠀⠱⡀⠈⡴⠃⢀⡴⠁⠀⣀⠔⠂⠉⠀⣀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠸⡄⠈⢆⠀⠈⢺⠁⢠⠋⠀⢠⠊⠀⡠⢔⡩⠠⠄⢑⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣙⢦⠈⠣⡀⢂⢀⠇⠀⢰⠃⠀⠌⡐⠁⠀⢀⣤⢂⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⣬⣽⣾⡀⠀⢸⠀⠀⡀⠑⠤⡔⣇⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⣤⣤⠬⠽⠖⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠒⠂⠉⠉⠉⠉⠉⠉⠐⠒⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡉⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢉⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⢑⠝⠒⠂⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠫⡊⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠙⢄
⠀⠀⠀⠀⠀⠀⡜⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⢢
⠀⠀⠀⠀⠀⡜⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⢣
⠀⠀⠀⠀⢰⣁⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⣈⡆
⠀⠀⠀⠀⣸⠀⢸⣀⣀⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⣀⣀⡇⠀⣇
⠀⠀⠀⢰⡇⠀⠀⢸⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⡇⠀⠀⢸⡄
⠀⠀⠀⡎⡇⠀⠀⠈⡀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢀⠁⠀⠀⢰⢱
⠀⠀⠀⡇⡇⠀⠀⠀⡇⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢸⠀⠀⠀⢸⢸
⠀⠀⠀⡇⡇⠀⣀⡀⢰⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⡆⢀⣀⠀⢸⠘
⠀⠀⠀⡆⢡⠸⡀⡸⠈⡄⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⠁⢇⢀⠇⡌⢰
⠀⠀⠀⢣⠘⡄⢀⠤⣄⢃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡘⣠⠤⡀⢀⠃⡜
⠀⠀⠀⠘⡄⢣⠸⠄⠜⠘⡀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⢀⠃⠣⠠⠇⡜⢠⠃
⠀⠀⠀⠀⠱⡈⡆⠀⠀⠀⢇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡘⠀⠀⠀⢰⢁⠎
⠀⠀⠀⠀⠀⠑⢜⡄⠀⠀⠘⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⢠⠃⠀⠀⢠⡣⠊
⠀⠀⠀⠀⠀⠀⠀⠙⣄⣀⣀⠕⠒⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠪⣀⣀⣠⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠿⠟⠛⠛⠉⠉⠉⠉⠉⠉⠛⠛⠿⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⢀⣀⣾⣷⣾⣷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣶⣿⣄⣀
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣻⣿⣿⣷
⠀⠀⠀⠀⠀⣾⣿⣿⣿⣽⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣽⣿⣿⣿⡀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣼⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣽⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣽⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣾⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠈⠛⠿⢾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⡤⢄⠀⡠⠚⠓⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⠀⠀⠘⠁⠀⡼⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⢦⠀⠀⠀⡜⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠑⠦⠞⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠟⠋⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⣴⣶⣆⠀⠀⠀⢀⢀⣸⣿⠁⡄⠀⣉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⢀⠙⠛⢿⣿⣶⣿⣿⣿⣿⣿⣧⣄⣼⣯⣿⣦⣤⣤⡀⠀⠀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣻⣿⡇⠀⠒⠻⣿⣿⣿⣿⣿⣿⣿⡏⠛⢻⠟⠛⠿⠿⢿⣿⣄⣾⣿⣿⣿⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣯⣤⡀⠀⠸⠟⠁⣿⣿⣿⣿⣿⣿⠀⠀⣾⣷⢄⣴⣄⣹⢻⣿⣿⣿⠤⠀⠤
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣄⣸⠟⠋⠉⣉⣹⣆⣠⣤⣤⣄⠻⠛⠛⠿⠿⡇⠸⣦⡶⢦⣙⣩⣴⣬⣿⣁⣿⣶⡶⠂
⠀⠀⠀⠀⠀⠀⢺⣿⠟⠛⢛⣿⡷⠾⠗⣀⠛⠋⣻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⢻⣿⡟⠻⢿⣿⡟⢋⣀⣀
⠀⠀⠀⠀⠀⠀⠘⣧⣴⣾⡿⠿⡏⢤⣼⣯⣷⡞⠁⠀⠉⠁⠀⣀⠀⠀⡀⠀⢀⣦⣄⣀⣠⣬⡋⠱⠀⠠⣨⣿⡿⠿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠹⣍⢿⡷⣡⣷⣶⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣿⣿⣀⠀⠀⡈⠇
⠀⠀⠀⠀⠀⠀⠀⡀⣤⣿⣽⣿⠿⠋⠙⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠁⠀⢻⣿⣀⣤⣤⣄⣸⣿⡀⠈⠀⠈⠁
⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣷⡆⠀⠀⠀⣿⣿⠀⠀⠀⢀⣀⣀⡀⠀⠈⢤⠀⠐⠂⢸⢿⠟⠿⣿⡿⣿⣏⠁
⠀⠀⠀⠀⠀⠀⠉⠀⢀⡙⣿⡿⠁⢀⣤⣴⣿⣿⡦⠀⢰⣿⠿⠛⠻⣤⣄⠀⣀⣀⣀⡀⢸⠠⠀⠠⡄⡿⠻⣦⣤⣴⠇
⠀⠀⠀⠀⠀⠀⠰⠂⠈⠀⠈⠃⠀⣿⣿⣿⡟⠁⢀⣛⣺⢃⠀⠀⡀⢸⣿⡿⠿⣿⣿⣿⣿⣦⣖⣦⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠁⠁⢀⠀⠀⠙⢿⣿⣿⡅⠉⢀⣬⣭⣌⣠⣤⣁⣠⣿⡆⠀⢸⢿⣿⣿⡟⠛⠛⣇⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠃⠀⠶⠤⠤⠼⢿⣿⠿⣻⣿⣷⣄⡀⠸⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣤⣶⠖⠒⠒⠀⣤⠄⠛⠛⢛⣿⣇⣀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⣿⡄⢠⣾⣿⣿⣿⣿⣿⣿⣿⣦⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆⠀⠘⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠚⠛⠛⠛⠛⠓⠲⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⣀⣠⣤⣤⣤⣄⣀⠀⠀⠀⢩⣙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠁⢀⣠⣶⣿⣿⣿⠿⠟⠛⠛⠻⠿⢦⡀⠀⠈⠳⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⢀⣴⣿⡿⢋⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠈⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⢠⣾⣿⠟⢡⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠈⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⣴⣿⠟⠁⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⢠⣾⡿⠁⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣷⣶⣿⣿⡇⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⢠⣿⡿
⠀⠀⠀⠀⠀⢠⣴⣿⣿⠟⠋⢁⣤⣽⠿⠿⠿⠿⣶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢸⣿⡇
⠀⠀⠀⢀⣴⣿⡿⠋⠁⣠⡾⠟⠉⠀⠀⢠⡀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⢸⣿⡇
⠀⠀⢀⣾⣿⠋⠀⢀⣾⠏⠀⢠⣀⠀⠀⢸⡇⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠿⠧⣄⠀⠀⠀⣿⣿⠇
⠀⠀⣸⣿⠁⠀⢀⣾⠁⠀⠀⠀⠈⢧⣠⣿⣄⣀⡼⠃⠀⢹⠀⠀⠀⠀⠀⣠⣶⡿⠋⠁⠀⠀⠀⠀⢹⣧⠀⢀⣿⣿⡀
⠀⠀⣿⣿⠀⠀⣸⡇⠀⠀⠀⠀⢀⡼⠋⠀⠈⣏⠀⠀⠀⢸⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⠐⣿⣿⣶⣿⣧
⠀⠀⢹⣿⡀⠀⢿⠀⠀⢀⣤⣤⣟⠀⠀⢀⣀⡟⠀⠀⢀⡟⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⡀
⠀⠀⠘⣿⣷⣤⣸⡆⠀⠀⠀⠀⠈⢳⡾⠋⠉⠙⠆⢀⡾⠁⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣷⠀⠀⠀⠀⠀⢠⡴⢦⡀
⠀⠀⠀⠘⢿⣿⣿⣿⡄⠀⠀⠀⠀⠚⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠀⠀⠀⠀⠀⢸⣷⢸⠇
⠀⠀⠀⠀⠀⠙⢿⣿⣿⣦⣤⣀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀⠀⠀⠀⢸⣏⢼
⠀⠀⠀⠀⠀⠀⠀⢙⣿⡿⣿⣿⣿⡶⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠁⠀⠀⠀⠀⠀⣾⠟⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣤⣴⣾⣿⣿⣷⣦⣀⣀⣠⣴⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⢸⣿⡄⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡏⢀⣠⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣷⡿⠿⠿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣶⠶⠶⢦⣄⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠾⠿⠛⠛⠷⢶⣤⣴⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⢿⡄⠀⠀⠙⠳⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠶⠶⢾⡿⠛⠶⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⢸⠁⠀⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⡀⠀⠀⠀⣠⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢶⣶⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣁⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⢒⣒⡩⠭⠥⠤⠤⠤⠤⣍⣑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⡩⠔⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢌⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⡵⠋⠀⠀⣀⡤⠤⠒⠒⠒⠒⠒⠢⠤⣄⡀⠀⠈⢣⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢋⠞⠀⢀⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡈⡎⡏⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡞⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡇⡇⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠴⣅⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣾⣝⣺⡧⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⡇⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⣁⡞⠀⢀⣤⣦⣤⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢰⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣰⠃⢰⣿⠁⢰⣿⣿⣿⣿⣿⡄⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡞⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⡿⠀⣼⣿⣿⣿⣿⣿⣷⠀⢸⡀⠀⠀⠀⢀⣀⠤⠤⢄⣀⣀⣴⣟⠫⣕⡢⢤⣠⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢹⣿⠀⢸⣿⣿⣿⣿⣿⣿⡆⠀⡇⠀⢠⠞⠁⢀⡤⣲⠿⠃⠀⠀⠈⠙⠢⢍⣳⡟
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠸⣿⡀⠘⣿⣿⣿⣿⣿⣿⡇⠀⡇⣰⠃⠀⡰⡫⠊⠀⠀⣀⠤⣤⣤⣀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⢻⣷⡀⠹⣿⣿⣿⣿⡿⠁⡸⢱⠃⠀⡼⡹⠁⠀⢠⡮⢷⣫⢷⣳⢯⣣⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡑⠙⠦⣈⣉⢉⣉⡤⠚⠁⢸⠀⢠⢣⠃⠀⢠⢿⣺⡽⣞⡯⡖⣎⣿⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠛⠉⠁⠀⠀⠀⢸⡀⢸⢸⠀⠀⢘⡏⣗⣣⠽⢚⣹⠵⡏⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡸⡸⡄⠀⢰⢳⡹⡜⣞⣯⢧⡿⠀⠀⡜⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡁⠀⠀⠳⢶⣻⣽⡼⠋⠀⢀⢞⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦⡀⠀⠉⠒⠤⣀⣀⣀⣀⠀⢠⣖⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣆⣒⡒⢒⣋⣉⠥⠜⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⢀⣤⠼⠟⠛⠛⠛⠙⠛⠒⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠀⣠⡴⠛⠉⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠈⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⡰⠊⠀⠀⣠⡾⣉⡠⠔⠊⠉⠀⠀⠀⠀⠈⠉⠙⠒⠦⢄⡀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⢠⠎⠀⠀⣠⣾⣿⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣤⣤⣘⣷⡀
⠀⠀⠀⠀⡴⠁⠀⢀⡞⡉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠿⠿⢟⠻⡄
⠀⠀⢀⡜⠀⠀⣰⡟⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢹⡀
⠀⠀⡜⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠀⠀⠀⢧
⠀⠸⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣃⣸⠄
⠀⠇⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠡⠸⡆
⠠⢄⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡇
⢘⠛⢫⣹⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⢼⣄⠀⠀⠀⣧
⡄⠠⢐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠉⠳⣆⠀⢻
⠇⠀⢰⡿⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⢀⡴⠶⡄⠀⠀⠈⡆⢹⣆⢸
⠀⠀⠀⣯⠀⠀⣠⠐⠯⠑⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢰⡿⠁⢐⡾⠀⠀⠀⢴⢈⣿⠘
⢨⠀⠀⣿⠀⣰⣿⢮⡠⡀⠘⠷⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣼⡟⠀⠀⡍⠀⠀⠀⠰⢘⣿
⠀⠆⠀⠹⣇⢹⣿⡢⡁⢁⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠘⣿⡄⢀⣰⢃⠀⠀⠀⡎⣸⢿⣺
⠀⠀⢄⣀⣿⡄⢻⢷⣅⢀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠃⠀⢼⣿⣯⣿⠃⠀⠀⠀⡴⢰⢃⣿⡟
⠀⠀⠈⢿⡟⠻⣄⠠⣟⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠃⠀⠈⠛⠛⠁⠀⠀⠀⡸⡡⣣⣾⠟
⠀⠀⠀⠈⢳⡀⠹⣦⠈⠑⢀⠀⠀⠀⠀⠀⠰⠀⠀⢡⠀⠀⠀⠀⠐⣌⠀⠀⠀⠀⠀⣀⣾⠝⠚⠋⠁
⠀⠀⠀⠀⠀⠑⡄⠙⣷⡄⠠⣅⠀⠀⠀⢠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠄⠐⠚⠉
⠀⠀⠀⠀⠀⠀⠈⠠⡰⣿⣦⠹⣧⠀⠀⠘⣇⣤⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠎⢙⣷⡘⣿⣶⣷⡿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠶⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⢀⣀⣤⣤⣀⡨⡙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⢀⣠⠞⠋⠁⠀⠀⠀⠙⢶⡀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠫⠂⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠣⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⢦⣄⠾⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠴⡞⠁⠀⡀⠉⠳⡀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⠀⠁⠀⠎⡀⠑⢄⠹⡄⠀⣀⡤⠶⠒⠒⠾⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢿⠀⡄⠘⡀⠐⡀⠈⣆⠹⠋⢁⡠⠔⠂⢉⠇⠀⡀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⠀⢣⠀⢣⠀⢀⡠⠋⢀⠔⠁⢀⠠⠔⠃⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢣⠈⢆⠀⠑⡼⠁⡔⠁⢠⠂⠁⡠⡐⠀⠐⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣣⡀⠣⣀⡇⠸⠀⢠⠁⢀⠂⠊⠀⢀⡄⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠦⠽⢧⠀⠘⠀⠸⠈⠀⣒⡥⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠛⠋⠉⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⣿⣿⣿⣷⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⢛⣭⣵⣶⡶⠖⠊⠉⠻⢿⣿⣿⣿⣿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢫⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠙⣿⡏⣶⣿⣷⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⣿⢣⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡜⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡸⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢻⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⡿⢛⣩⣭⣭⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣼⣿⣿⣿⡿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡇⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡔⣼⣿⣿⣿⡏⣶⣾⣝⢻⣿⣿⣷⡀⠀⠀⠀⢀⣴⣾⣿⣿⢇⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⣇⢿⣿⣿⣷⡹⣿⣿⣷⠀⢀⣴⣿⣿⣿⢋⣵⣿⣿⣿⢿⣻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣧⢻⣿⣿⣿⣿⣎⢻⣿⣿⡇⣿⣿⡿⣠⣿⣿⣿⠟⣵⣿⣿⣿⢟⣵⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣎⢿⣿⣿⣿⣿⣷⣭⣛⣣⣽⡟⣰⣿⣿⣿⢏⣾⣿⣿⡟⣡⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣝⠿⣿⣿⣿⣿⣿⣿⣿⢱⣿⣿⣿⢏⣾⣿⣿⠟⣼⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠍⠉⠉⠉⠉⠀⢸⣿⣿⡏⣾⣿⣿⡏⣼⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⢱⣿⣿⣿⢸⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⠾⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣦⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠻⠿⠀⠀⠀⠀⠀⠀⠀⠿⠏⠛⠛⠋








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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⢶⠟⡿⠛⢻⠛⠛⢿⠻⡶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠛⣏⢳⣤⣧⣤⣼⣷⣶⢾⡷⣶⣾⣧⣤⣼⣤⡞⣹⠹⢳⣦⡀
⠀⠀⠀⠀⠀⠀⣠⣾⢏⣀⣠⣶⣿⣿⠿⠛⠛⠋⠉⠉⠉⠉⠉⠉⠙⠛⠛⠿⣿⣿⣴⣄⣀⡽⣷⣄
⠀⠀⠀⠀⢠⣞⢟⣈⣰⣿⠿⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢿⣿⣆⣁⠻⣷⡀
⠀⠀⠀⣠⡟⠂⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⠔⢻⡄
⠀⠀⢠⡿⠁⣽⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣯⠘⢿⡄
⠀⢀⣿⣤⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣥⣿
⠀⠘⣿⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⣿⠃
⠀⢸⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇
⠀⢈⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡁
⠀⣤⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡇
⡔⠉⣽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⠙
⠳⣴⣧⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⣦
⠀⢹⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠇
⠀⢸⣶⣿⠀⠀⠀⠀⢀⣠⠤⢤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡤⠤⣄⡀⠀⠀⠀⠀⣿⣶⡇
⠀⠈⣿⣿⣇⣤⣾⣿⣿⠷⣢⣼⡏⢱⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡎⢹⣧⣔⢿⣿⣿⣷⣤⣼⣿⣿⠁
⠀⠀⢻⣿⡟⠏⣿⣿⣿⡶⢾⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠷⣮⣿⣿⢯⢹⢻⣿⡟
⠀⠀⠘⡀⢻⡀⡇⢸⣿⣇⣼⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⢯⣺⣿⡇⢸⢀⡟⢀⠃
⠀⠀⠀⢡⣼⣧⣷⣼⣯⠭⠠⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⠄⠭⣿⣧⣼⣼⣧⡎
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣽⣶⣿⡇⢼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢸⣿⣶⣭⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠘⠿⠿⡿⢿⣿⣾⣭⣿⡗⢸⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢺⣿⣭⣷⣿⡿⢿⢿⢻⠁
⠀⠀⠀⠀⣧⣇⡃⠀⣿⡭⠾⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠷⣭⣿⠀⢈⣸⡼
⠀⠀⠀⠀⠈⠙⠿⣷⣿⣿⣶⣿⣿⣚⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣓⣿⣿⣾⣿⣿⣿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠟⣋⣭⣴⣶⣶⡶⠶⠈⠉⠻⢿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⢋⣴⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠉⢻⣿⣿⡟⣡⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⣰⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣇⢻⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢃⣿⡿⣰⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⢻⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢸⣿⣧⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡌⢿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠸⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⢿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢸⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠘⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⣿⠿⢛⣛⣛⣛⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢈⣵⣾⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣾⣿⣿⣿⣿⡿⠫⢽⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡇⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣾⣿⣿⣿⣿⣿⢸⣿⣶⣬⡛⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⡿⢃⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣌⢻⣿⣿⣿⣇⠀⠀⢀⣴⣿⣿⣿⣿⡿⢋⣴⣿⣿⣿⣿⡿⠿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⣿⣿⣿⣿⣿⣿⣆⢻⣿⣿⣿⣿⡌⣿⣿⣿⣿⠀⣠⣾⣿⣿⣿⡿⢋⣼⣿⣿⣿⣿⠟⣩⣶⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⢹⣿⣿⣿⣿⣿⣿⣦⡙⢿⣿⣿⡇⣿⣿⣿⠏⣼⣿⣿⣿⣿⠟⣰⣿⣿⣿⣿⠟⣡⣾⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠹⣿⣿⣿⣿⣿⣿⣿⣶⣭⣙⣥⣵⣿⢃⣾⣿⣿⣿⣿⠋⣼⣿⣿⣿⡿⢋⣴⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣼⣿⣿⣿⣿⠃⣾⣿⣿⣿⡿⢡⣾⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣍⣛⠻⠿⠿⠿⠿⠟⠋⠀⣿⣿⣿⣿⠏⣼⣿⣿⣿⡟⢠⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢸⣿⣿⣿⣿⢡⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⡇⣾⣿⣿⣿⡇⣼⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣬⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉


⣿⡟⣋⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣠⣤⣤⣤⣤⡀⢼⣾⣟⣠⣤⣤⣤⣤⣤⣾⣤⣤⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢿⣿⣿⣿⣿⣿⣿⡇⢸⢿⠁⢸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣷⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠘⣿⣿⣿⣆⠀⣠⣴⠀⠀⠀⠀⣴⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⢋⣡⣴⣾⠟⢠⣆⣰⣿⣿⣿⣿⣾⡉⢉⣿⢃⠄⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⣘⡛⠋⢁⣠⠘⣿⣟⢿⣿⣿⣿⠛⠓⠎⢉⠿⠏⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠁⣀⣉⠙⠀⣬⣩⣾⣿⣿⡏⠀⠀⠀⣠⣶⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⣾⣿⣿⡷⣰⣿⣿⣿⣿⡿⠁⠀⠀⠰⠿⠿⠛⠛⢩⣽⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣇⠀⠀⠀⠀⠀⢠⣶⣤⣂⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢹⣿⣿⡀⠀⠀⠀⠀⢻⣦⣭⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣿⣿⣧⠀⠀⠀⠀⠀⣿⣝⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣤⣼⣿⣿⣿⣷⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣽⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⠘⠛⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⣡⣶⣄⠀⠀⠀⠀⠀⠀⠋⣹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠛⠉⠉⠉⡥⠘⠿⠿⠋⠀⠀⠀⠀⠀⢀⣾⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢯⣤⣄⣀⣀⡀⠀⠀⠀⢀⣴⣶⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠉⠉⠁⠀⠀⠀⢸⠿⢧⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣦⣤⣄⣀⣀⣀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⠀⠀⠀⠀⠴⠂⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣀⠐⠻⢿⣿⣿⣿⣿⠟⠁⣀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠛⠀⠀⠀⢀⡘⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠙⢿⣿⣿⣷⣿⣿⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⠋⠛⠛⠛⣿⣿⣿⣿⡟⠛⠃⠀⢻⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⢀⣠⡴⡆⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⣾⣿⣿⢿⠀⠀⣼⣇⠀⠻⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠈⠁⠀⡇⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⣿⢻⣿⣦⣰⣾⣿⢿⢠⠀⢿⣿⣿⣿⡟
⠀⠀⠀⠀⣀⡄⠀⣾⠇⠀⠀⢠⢏⣆⠀⠀⠀⠀⠀⣀⡤⠼⠦⠈⠹⣿⡟⢁⣾⣇⡄⢸⣿⣿⡏
⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⣸⡺⢉⣉⣑⠀⠀⠈⠁⡤⣤⣤⠀⠀⠙⠀⣼⣿⡟⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⡎⠐⠋⠃⠀⠀⠈⠀⠉⠁⠀⠀⠀⠀⢿⣿⡄⠀⢀⣾⡇
⠀⠀⣠⠴⠚⠀⠀⠀⣶⠦⠀⠈⢯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣿⣿⡿⠁
⠀⢨⠁⠀⣠⠀⠀⠀⢹⠓⠀⠀⠀⠙⠂⠀⠂⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠔⠋
⢀⡾⠘⠃⠁⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⣴⠶⢶⠤⠀⠀⠀⠀⠀⠀⠀⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢡⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠛⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⢿⡿⢿⣿⣿⣿⣿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠐⠒⠂⠈⠉⠉⠉⠉⠉⠉⠀⠒⠒⠤⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⢀⣀⠠⠄⠒⠂⠉⠉⠉⠉⠉⠉⠉⠁⠒⠂⠤⢀⣀⠀⠀⠀⠀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⣀⠤⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠢⢄⡀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⡰⠃⠀⠀⢀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠜⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠘⠄
⠀⠀⠀⠎⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠈⠆
⠀⠀⡜⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠘⡄
⠀⡘⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠘⡀
⠀⠁⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠁
⠰⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢰
⡄⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢁⠀⠃⠀⣀⠴⠊⠁⠫⡙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡩⠃⠉⠲⢄⡀⠀⠇⢠
⠈⠄⢸⡴⡁⠀⠀⠀⠀⠱⡄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⡴⠁⠀⠀⠀⠀⡱⣼⠀⡌
⠀⠇⠀⡇⠘⡄⠀⠀⠀⠀⠘⡄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⡜⠀⠀⠀⠀⠀⡜⠀⡇⠀⡅
⠀⠸⠀⡇⠀⠘⢆⠀⠀⠀⠀⠈⢆⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⠎⠀⠀⠀⠀⢀⠞⠀⠀⡇⢰
⠀⠀⡇⠱⠀⠀⠈⢢⠀⠀⠀⠀⠀⢣⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠃⠀⠀⠀⠀⢠⠊⠀⠀⠰⠁⡆
⠀⠀⢠⠀⠱⡀⠀⠀⠣⡀⠀⠀⠀⠀⠣⡈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⡠⠀⠀⠀⠀⠀⡠⠃⠀⠀⡰⠁⢠
⠀⠀⠈⢆⠀⠱⡀⠀⠀⠱⡀⠀⠀⠀⠀⠱⡀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⡰⠁⠀⠀⠀⠀⡰⠁⠀⠀⡰⠁⠀⡎
⠀⠀⠀⠘⡄⠀⠱⡀⠀⠀⠙⡄⠀⠀⠀⠀⠘⡄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⡜⠀⠀⠀⠀⠀⡜⠁⠀⠀⡰⠁⠀⡜
⠀⠀⠀⠀⠈⢄⠀⠘⡄⠀⠀⠈⢆⠀⠀⠀⠀⠈⢆⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⠎⠀⠀⠀⠀⢀⠎⠀⠀⠀⡜⠀⠀⡜
⠀⠀⠀⠀⠀⠈⢆⠀⠈⢆⠀⠀⠈⢆⠀⠀⠀⠀⠈⢢⠈⢆⠀⠀⠀⠀⠀⢀⠎⢠⠊⠀⠀⠀⠀⢀⠎⠀⠀⢀⠎⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠣⡀⠀⠀⢣⡀⠀⠀⠀⠀⠣⠈⠀⠀⠀⠀⠀⠈⠠⠃⠀⠀⠀⠀⢠⠃⠀⠀⡠⠃⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⢱⣄⠀⠀⠱⡀⠀⠀⠀⢀⡹⠀⠀⠀⠀⠀⠸⣁⠀⠀⠀⠀⡰⠁⠀⢀⣴⠁⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠑⠢⢀⢑⡄⠠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠀⣔⢁⠠⠒⠉⠈⠉⠁
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿