Smily face Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠶⠒⠒⠒⠒⠒⠒⠲⠦⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣶⣤⣤⣀⣀⣀⣀⣀⣀⣤⣤⣶⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠶⠤⣤⣤⣄⣀⣀⣀⣠⣤⡤⠤⠖⠚⠋⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⠴⠶⠶⠶⠶⠤⢤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄
⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣀⠀⠀⠀⠘⢦
⠀⠀⢀⡼⠁⠀⠀⢀⠔⠋⠁⡴⠋⠉⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⡴⠊⠀⠉⢢⡀⠀⠈⢧
⠀⠀⣾⠁⠀⠀⢠⠃⠀⠀⡎⠀⠀⠀⠀⡨⢆⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⡜⠀⠀⠀⠀⠠⢷⠀⠀⠈⣇
⠀⣸⠇⠀⠀⠀⢪⠀⠀⢸⠀⠀⠀⠀⠸⡀⢸⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⡇⠀⠀⠀⠀⠇⢸⠀⠀⠀⢹
⠀⡿⠀⠀⠀⠀⠘⡄⠀⠀⢇⠀⠀⠀⠀⢉⠆⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠐⡄⠀⠀⠀⢀⠏⠀⠀⠀⠈
⢰⡇⠀⠀⠀⠀⠀⠈⠢⢄⣀⠓⣄⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⣈⣢⠤⠔⠁
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠈⣇⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⡄
⠀⢻⡀⠀⠀⠀⠀⠀⢸⢣⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⡠⠇⠀⠀⠀⠀⠀⢸
⠀⠘⣧⠀⠀⠀⠀⠀⠀⣆⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⠂⠀⠀⠀⠀⠀⡞
⠀⠀⠘⣇⠀⠀⠀⠀⠀⠘⣄⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⢠⠃⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠈⠢⡀⠈⠓⠤⣀⡀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠉⠀⡰⠃⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⣀⠴⠊⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠉⠓⠲⠤⠤⠤⠤⠤⠔⠒⠉⠁⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣤⣄⣀⣀⣀⣀⣀⣀⣠⡤⠶⠚⠋⠁
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

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


⣿⣿⢟⣿⡻⣿⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠄⠐⠂⠐⠀⠀⠠⠤⠤⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⢀⠤⠤⡀⠀⢀⠤⠤⠤⣀⠀⠀⠀⠀⠀⢀⠤⠠⣀⠀⠀⡠⠄⠤⡀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠃⠀⠄⠈⠱⠁⠠⡂⠐⠈⡆⠀⠀⠀⠠⠃⠀⠀⠈⢣⡌⠀⠢⢂⠈⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠣⠀⠑⠡⡂⢐⠠⠂⠁⠂⠁⠀⠀⠀⠸⠀⠕⠀⠢⡀⢐⠅⠨⠂⢀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠈⠀⢄⠄⠂⡠⠁⠀⠀⠀⠀⠀⠡⡀⠁⡨⡂⢐⠁⡊⠠⠂⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⣀⠥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⢊⢔⣁⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⠤⢀⡀⢀⣀⡀⢀⡀⠠⠄⠒⠈⠁⠀⠀⠀⠠⠁⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠤⣁⣈⡐⡁⣀⣀⡀⢈⢀⣀⡀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⡀⠀⡠⠀⡀⠄⡠⢀⠠⠂⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⡀⠄⢂⠠⠐⡀⠀⢂⠡⢀⠠⠐⡈⠔⡈⠄⠂⠠⠂⠁⢂⠡⢂⠠⢀⠠⠂⡠⠐⡡⠀⠡⠊⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠈⠁⠐⠁⠐⠉⠀⠈⠀⠈⠀⠈⠀⠈⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠓⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⢀⣠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠲⢦⡀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠊⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠙⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⢠⣾⠋⣻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠉⢿⡄⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⢀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⢀⠀⠀⠀⡀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠑⠒⢒⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡙⠚⠉⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡿⠁⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠈⢻⡿⢿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⠿⢿⡟⠁⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠃⣀⠴⠋⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⢤⡤⠤⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⢤⣀⣀⣀⣀⣀⣀⣀⣀⡤⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣷⣄
⠀⢠⣤⣤⣤⣠⣤⣄⠰⣿⣿⣿⣿⣿⣦⠀⢤⣶⣾⣿⠆
⠀⣿⣿⣿⣿⣿⣿⣿⣧⣹⣿⣿⢿⣿⣿⡟⣿⡟⠁⠋
⠀⣨⣿⣿⣿⡏⠉⠻⣿⣧⣿⠏⢀⣿⡟⣴⠋⢙⣀⣤⣴⣶⣶⣾⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣀
⠀⢻⣿⣿⣿⣿⣦⣀⠹⣿⡿⢀⣼⣿⣾⣷⣾⣿⣿⡿⠿⠟⠛⠛⠛⠋⠉⠛⠛⠛⠛⠿⢿⣿⣿⣿⣷⣦⣄
⠀⠀⣉⣉⣉⣙⣻⣿⣧⢩⣴⣿⠿⠟⠛⠛⢻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣶⣄
⣴⣿⣿⣿⣿⠋⠉⠁⣠⣦⡁⢶⣿⠿⣿⣷⣾⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣷⣦⡀
⠹⣿⣿⣿⣇⣀⣠⣾⣿⣿⣿⡄⠙⣿⣦⡙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣄
⣼⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣧⣠⣿⣿⣿⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⡀
⠹⢿⡿⠿⣿⣿⡿⠋⢸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡄
⠀⠀⠀⣼⣿⡿⠁⠀⢿⣿⣿⣿⣿⣿⡏⠀⢀⣴⣾⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄
⠀⠀⣸⣿⣿⠃⠀⠀⠈⠛⠋⠙⠛⠋⠀⠀⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡀
⠀⢠⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧
⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⣿⣿⣷⠀⠀⠀⠀⠀⢀⣠⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⢸⣿⣿⡀⠀⠀⠀⠀⠛⠿⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⠿⡇⠀⠀⠀⠀⠀⠀⣾⣿⣿
⠀⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡇
⠀⠀⠘⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟
⠀⠀⠀⠹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁
⠀⠀⠀⠀⠙⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣶⣶⣶⣶⣶⣶⣶⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡿⠿⠛⠉

⠀⠀⠀⢠⠁⠀⠀⣴⣶⡄⠀⠀⣨⣦⡀⠀⠁⠀⡀⠄⠐⠒⠃⠀⠀⠘⠓⠁⠀⠀⠈⠉⠀⠀⢀⠀⠀⠉⠁
⠀⠀⠀⠂⠀⠀⠀⠿⠼⠁⠀⠐⣏⣿⠇⠁⡴⠋⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⢸⡧⠀⠂⠀⠐⠚⠦⡀
⠐⠒⠐⠾⢄⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⢀⣀⠀⠀⠀⠈⣢⣄⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠈⢲⠤
⠀⠀⠀⠀⠀⠈⠢⡈⠂⠤⠠⠄⠂⠀⢠⠀⠀⠀⣿⠟⡧⠀⠀⢸⠻⣿⠘⠀⠀⣠⣦⡄⠀⠀⣠⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠔⠀⠈⠉⠉⠙⠀⠀⠀⠈⠛⠁⠀⠀⠈⠛⠁⠀⠀⠀⠻⠥⠃⠀⠀⡰⠁
⠀⠀⢾⡿⣿⣿⠀⠀⢡⠀⠀⠀⠀⠀⣀⢣⠀⠀⠀⢀⠤⠒⠂⠤⡀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠃⠀⢸⣿⡿
⠀⠀⠈⠛⠛⠁⠀⠀⠸⣠⣤⠀⠀⢸⠛⡧⠑⣄⠀⠁⢀⡀⠀⠀⠁⢀⠠⠒⠂⠀⠊⠒⢖⠘⡄⠀⠀⠛⠛
⠀⠀⠀⢀⠀⠀⠀⢀⠃⠻⣭⠇⠀⠀⡩⠓⠉⠀⠀⠀⠀⠀⠁⠲⡖⠁⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⢀
⠒⠐⠒⠁⠀⠀⡠⠋⠀⠐⠠⡀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢠⡀⠀⠀⠀⠀⠀⠀⠀⠳⣄
⣀⣀⡠⠤⠒⠉⠀⠀⠀⠀⠀⠈⠞⠀⠀⢠⡿⢿⠀⠀⢀⣶⣦⠀⠀⠈⡄⠉⠀⠀⠀⢤⡤⠀⠀⢀⡀⠑⠢
⠋⠀⠀⠀⣄⣀⠀⠀⠀⣀⡄⠀⠃⠀⠀⠀⠛⣊⡀⠀⠘⠦⠟⠀⠀⠀⡗⠢⠤⣀⡀⠀⠀⠀⢀⣟⡳
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠘⡤⠂⠉⠀⠀⠀⠈⠐⢄⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⡀⠤⠂⠘⠂⠀⠄
⠑⣄⢆⠀⠀⠢⢀⣀⠠⠂⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣀⠔⠉⠀⠈⠁⠒⢶⠊
⡰⠁⠀⠑⠠⠀⠀⠀⢀⡀⠄⡃⠀⢼⣷⢿⡆⠀⢸⠿⣿⡆⠀⢀⠀⠀⠀⠀⣀⠀⠀⠑⣄⡀⠀⠀⠀⣠⣤
⠁⠀⠀⣶⣷⡄⠀⠀⡾⢿⡆⠃⠀⠈⠙⠋⠀⠀⠈⠙⠋⠀⠀⢸⣤⡀⠀⢸⣛⡷⠀⠀⠸⠿⡆⠀⠀⢟⣻
⠀⠀⠀⠻⠶⠃⠀⠀⠙⠚⠁⠐⡄⠀⠀⠆⡀⠀⢀⠐⠀⠀⢀⠾⣭⠇⠀⠀⠈⠀⠀⠀⢘⠛⠁⠀⠀⠀⠁
⣆⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠨⠢⢀⠀⠀⠉⠀⠀⡀⠔⠅⠀⠀⠀⢀⡀⠀⣀⣀⢀⠆⠰⣶⣤⣬⣼⠟
⠀⠢⡀⠀⠀⠀⠘⠟⠀⠀⠀⣠⠁⠀⢠⣮⡄⠀⠀⣥⡄⠀⠀⣄⠔⠊⠁⠀⠀⠀⠀⠉⠒⢄⠀⢉⠝⠁
⠀⠀⠈⠑⠂⢤⡄⠤⠤⠐⠈⠉⠀⠀⠘⠧⠃⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠳⠃
⠀⠀⠾⠁⠠⠊⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⡀⠀⠀⠄⠀⠀⣼⡿⡆⠀⠀⡟⢿⠆⠀⠀⠀⠀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⡀
⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄
⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠻⣷⡀⠀⠀⡴⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⢰⡏⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⡇⠀⠀⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⢦⡀⠈⣷
⠀⣾⠁⠀⠚⢹⡉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⢹⡆
⠀⣿⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢸⡇
⠀⣿⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢸⡇
⠀⢻⡄⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⣼⠃
⠀⠸⣧⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⢠⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⢀⡤⠴⣶⣤⡀⠀⠀⠀⠀⠀⠀⣠⡤⣶⣦⣄⠀⠀⠀⠀⠀⠀⠹⣿⣧
⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⢠⡏⣰⣿⡟⠛⢻⡄⠀⠀⠀⠀⣼⢃⣾⣿⠋⠙⣧⠀⠀⠀⠀⠀⠀⢻⣿⡆
⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠘⣇⣿⣿⣷⣤⣾⠃⠀⠀⠀⠀⢻⣸⣿⣿⣦⣴⡟⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠀⠀⠀⠀⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⡟⠁⠀⠀⠀⠀⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⠀⠀⠀⠀⠀⠙⢿⣷⣤⣄⣀⡀⠀⢀⣀⣀⣤⣴⣿⠟⠋⠀⠀⠀⠀⠀⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⣠⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉

⠀⡠⠒⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠒⠉⠉⠉⠉⠉⠑⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠢⡀
⠀⡅⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⢀⡤⠒⠲⢄⠀⠀⠀⣀⣀⡀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⡅
⠀⠑⣄⠀⠈⠢⡀⠀⠀⠀⠀⡠⠃⠀⠀⠎⠀⢠⣄⠈⢣⠀⠎⠀⣄⡈⢳⡀⠈⢣⡀⠀⠀⠀⠀⢠⠎⠀⢀⡴⠁
⠀⠀⢀⣱⠀⠀⠀⠀⢠⠀⢠⠃⠀⠀⠀⡀⠸⣿⡿⠀⢸⠀⠀⠻⠿⠃⠀⡇⠀⠀⢣⠀⢀⠔⠀⠀⠀⢠⡋
⡠⠊⠁⣠⠄⢄⠀⠀⠀⢡⡎⢀⡀⠀⠀⠱⢄⣀⣀⡠⠎⠀⠢⢀⣀⡀⠜⠀⣤⡀⠘⣦⠃⠀⠀⢀⠤⢄⡈⠑⠢
⢇⠀⠀⠀⠀⢀⣇⠀⠀⣸⡇⠉⠙⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⠤⢖⠏⠀⠀⠀⣿⡀⠀⢀⣇⠀⠀⠀⠀⢀
⠀⡗⠒⠒⠒⠁⢠⢧⠀⠀⢱⠀⠀⠀⠈⠢⣭⣉⡛⠛⠛⠛⠉⢉⣠⣴⠏⠀⠀⠀⢰⠁⠀⢀⢏⠈⠓⠲⠔⠒⡏
⠀⠈⡖⠒⠒⠚⢁⠜⡱⠁⠈⢇⠀⠀⠀⠀⠙⢿⠛⠉⠉⠉⠉⠙⢻⡏⠀⠀⠀⢠⠏⠀⠱⠙⣄⠑⠂⠤⠐⡎
⠀⠀⠈⠐⠶⠊⠥⠒⠁⠀⠀⠈⠣⡀⠀⠀⠀⠈⠳⣆⡀⠀⢐⡶⠋⠀⠀⠀⡠⠋⠀⠀⠀⠑⠬⢑⣒⠶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⡀⠀⠀⠀⠉⠉⠁⠀⠀⣀⠴⠊
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣽⣶⣶⣶⣶⣶⣾⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠷⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⡀
⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄
⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠀⠀⠀⠀⠠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀
⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢿⣦⠀⠀⠀⣰⠛⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⣾⣿⠆⠀⠀⣿⣶⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢶⣤⡀⠀⢹⡇
⠀⢸⡏⠀⠀⠾⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠟⠀⠀⠀⠘⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⠈⣿
⠀⣼⡇⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⣿⡄
⠀⣿⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⣹⡇
⠀⢻⡇⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⣿⠃
⠀⢸⣇⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⢀⣿
⠀⠀⣿⡀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤⣀⡀⠀⠀⠀⠀⠀⢀⣀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣉⡛⠛⢛⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⡶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠉⠉⠉⠁
⣿⣿⣿⣿⣛⣻⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣛⣛⣛⣿⣿⣛⣛⣛⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠟⠛⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣷⣄
⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄
⠀⠀⠀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧
⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀
⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧
⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⣿
⢿⣿⡆⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⢰⣿
⠸⣿⣧⠀⠀⠀⠀⠀⢻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡟⠀⠀⠀⠀⠀⣼⣿
⠀⢻⣿⣆⠀⠀⠀⠀⠀⢻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠀⠀⠀⠀⠀⣰⣿⡟
⠀⠈⢿⣿⣆⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⣤⣀⣀⣀⣀⣀⣀⣤⣴⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⣰⣿⡿⠁
⠀⠀⠀⢻⣿⣧⡀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⢀⣼⣿⡟
⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣷⣦⣤⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣾⣿⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠒⠚⠛⠛⠛⠛⠓⠒⠶⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⢠⠴⠒⠚⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠖⠲⠶⢤⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⣴⣿⣿⣷⡄⢷⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⣿⣿⣿⣿⣿⣸⠀⠀⠀⠀⠀⠀⠋⠉⠉⠉⠉⠉⠓⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠘⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠙⢿⣿⠟⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣤⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⣿⣿⡟⠒⠲⠤⢤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡤⠤⠶⣾⣿⡗⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠘⣿⣿⣷⣶⣤⣤⣀⣀⣉⣉⣉⣉⣉⣉⣡⣤⣤⣶⣶⣿⣿⡿⠁⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠶⠤⢤⣤⣤⣤⣤⡤⠤⠶⠒⠛⠉

⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣆⠀⠀⠀⠀⣀
⠀⣴⣶⣶⣦⣶⣦⠹⣿⣿⣿⣿⣦⣀⣾⡿⣿⠂
⠀⢻⣿⣿⡿⠿⣿⣷⣿⣿⠛⣿⡿⣠⠿⡀⠀⢀⣀⣀⣠⣤⣤⣄⣀⣀⣀
⠀⣿⣿⣿⣷⣄⠈⢿⣿⡇⣠⣿⣵⣯⣴⣶⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣶⣦⣄⡀
⠀⠈⢛⣛⣛⣿⣷⡜⣫⣴⣿⠿⠿⠻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢿⣿⣷⣦⡀
⣴⣾⣿⣿⠟⠋⠉⣠⣍⠱⣶⡿⣷⣶⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣷⣄
⢹⣿⣿⣿⣄⣤⣾⣿⣿⣇⠈⢿⣦⡛⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡀
⣾⣿⣿⣿⣿⣿⡿⢹⣿⣿⣶⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣆
⠈⠛⠋⣽⣿⡟⠁⣿⣿⣿⣿⣿⡿⠋⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧
⠀⠀⣼⣿⡏⠀⠀⠻⠿⠿⠿⠟⠁⢀⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣇
⠀⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠙⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⣿⡀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⢿⣿⡇⠀⠀⠀⠠⠾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡆⠀⠀⠀⠀⠀⣼⣿
⠀⠸⣿⣿⡀⠀⠀⠀⠀⠀⠙⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠏⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⠀⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏
⠀⠀⠀⢻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⣀⡀⠀⠀⠀⠀⢀⣀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟
⠀⠀⠀⠀⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠋
⠀⠀⠀⠀⠀⠘⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⡿⠿⠛⠉

⡏⠉⠉⠉⠉⠉⠉⠉⢉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢿⣿⡯⢿⣿⡽⣿⡏⣿⣏⣿⣟⣽⢏⣿⣍⣿⣿⣋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡉⠉⠉⠉
⡇⠀⠀⠀⠀⠀⠀⠀⢨⡄⠀⠀⠀⠀⠂⠓⠀⠀⠀⠠⢿⣿⣧⠿⣶⣯⡿⣇⣯⡟⣮⣯⣾⣞⣹⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⡇⠀⠀⠀⠀⠀⠀⠀⢈⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢻⣿⣿⣽⣿⣽⣿⣾⣿⣷⡿⣾⣽⣟⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡
⡇⠀⠀⠀⠀⠀⠀⠀⢈⡛⠛⠛⠓⢶⡀⠀⠀⠀⠀⠀⠀⢉⠽⠛⢿⢿⣾⣯⣿⣷⣶⢿⠟⠻⢌⠀⠀⠀⢰⣿⣶⠀⠀⠀⠀⠀⠀⠀⠤⡀⠠⠃
⡇⠀⠀⠀⠀⠀⠀⠀⣿⠟⠛⠛⠋⠩⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⡟⠙⠉⠀⠀⠀⠀⠠⠀⠀⠘⠛⠛
⡇⠀⠀⠀⠀⠀⠀⠀⠹⣶⠶⢶⣶⣶⠇⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠈⠈⠑⣦⡤⠀⡄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢾⡀⠀⡀⠀⠘⠡⠔⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣤⠌⠩⣤⣶⡶⠟
⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣀⡐⠀⠀⠢
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⡠⠌⠀⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠿⠖⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⣒⢶⣀⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢧⣛⡼⠥
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠈
⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠦⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣇⠘⠋⢀⡟⠂
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡟⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢤
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉
⡇
⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⣠⣀⣄⣄⢀⡀⠀⠀⣲⡀⠀⠀⠀⠲⡤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠈⠉⠀⠀⢠⣄⠀⠙⠂⢀⠈⠀⠁⣉⠋⣷⡆⠀⠀⣬⠖⠠⣇⠀⠈⡲⠄⡉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼⣄⠀⠀⣀⠀⠀⠄⣆⢬⡼⠓⠀⢠⣰⡧⣀⣀⣻⣇⡀⠀⠀⠀⢀⠉⢀⠙⣄⠈⠉⡒⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡻⠀⣧⡄⡈⣥⢾⣜⡓⢉⣁⡀⠀⡀⠈⠁⠀⠀⠀⠈⢛⣁⠐⠤⠤⢀⡉⠁⠳⢽⡄⠀⡇⠀⠀⣷⣼
⠀⠀⠀⠀⠀⠀⠀⢰⡈⢳⣶⣿⣦⣿⠿⢋⠁⡠⢈⣨⠍⣁⠐⠦⠀⠀⠀⠀⠀⠈⢥⡆⢀⠀⠨⡇⠢⣀⠀⣿⠢⣅⠀⠀⠹⣿⠀⢀⡄
⠀⠀⠀⢀⠀⠀⠀⠎⠀⣠⣿⡏⢱⢋⣴⠥⠐⠀⠀⠀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢀⡆⣷⢀⠈⠀⢹⠆⢺⣷⡀⢣⢹⣦⠞⢹⡆
⠀⠀⠀⢸⡄⠀⡄⠀⣸⠿⣸⠷⣿⠁⣀⢂⡂⣔⣬⣰⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⢿⠓⠾⢬⣤⡈⢧⡑⣼⢠⣿⣦⣿⠁
⠀⠀⠈⡀⢧⣠⠓⣤⣿⢟⡟⣸⡿⠬⠋⠣⠑⠈⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣳⠌⢳⣄⠸⡋⠙⢫⣷⣼⠁⢸⣿⠁⢰
⠀⢢⠀⢧⠸⣧⠑⣾⢧⡾⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠙⣿⡗⢾⣿⣊⣋⠄
⠀⠈⣧⢨⠃⠸⣿⣣⡾⢛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠶⣄⣿⣧⠸⣿⠈⣯⠆
⠀⠀⠘⣷⣀⠀⢻⣿⡡⣺⣻⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⣌⢻⣿⠀⣿⣇⡳⠂
⢦⡀⢰⡛⣿⣦⣾⣯⣠⣿⢫⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣍⠹⣿⠳⣿⣧⣟⠁
⠈⢷⡌⡾⠰⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣱⣿⣧⣿⣿⠃
⠀⠈⢷⡸⡇⢸⣿⣿⠁⣀⡀⠀⣤⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⢹⣿⣿⣿⠇
⠀⠀⠘⣿⠷⣸⣿⣿⠘⡿⠛⡸⡯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣤⠀⠈⠣⣼⣿⣿⣿⣆
⠠⣼⡇⣹⣯⢸⣿⣿⡏⠀⠐⣮⣿⢅⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⢷⣫⣴⣶⣼⣿⣿⡇⢸
⠀⢨⣟⡵⢻⣿⣿⣿⣇⠀⢐⡫⢷⢝⡂⠀⢄⣧⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⢭⣷⡋⠡⣼⣿⣿⡇⢸
⠀⠀⢻⣫⠌⢻⣿⣿⣿⡆⠀⢩⠽⣝⣃⣨⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣗⡂⢀⣿⣿⣿⡃⣾⠀⢸⠁
⠀⠀⠈⠧⣞⢄⢹⣿⣿⣿⣄⠈⠬⣯⢲⣵⡿⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠬⢽⣿⠒⣾⣿⣿⣿⣶⠃⠀⠅
⠀⠀⠀⠀⠻⢎⢔⣿⣿⣿⣿⣦⠨⣧⣾⣿⢓⣂⣤⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⢲⣶⣯⣄⠀⡄⠀⢀⣦⣄⢺⣿⣃⣼⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠈⢏⣿⣿⣿⣿⣿⣷⣾⣿⠻⠛⢻⣟⣿⣿⣤⣤⠀⠀⠀⢀⠀⠀⠐⡩⣻⣽⠇⡇⣇⡼⣻⠏⡽⢷⣾⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠿⠿⣿⣿⣷⣬⣧⣼⣽⣽⣿⣿⣀⠀⣈⣄⣄⣀⣈⡴⠖⠓⣚⡛⠛⣿⣾⣾⣿⣿⣿⣿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠷⣤⣀⡀⢹⣿⣟⠁⠀⠀⠀⡀⢀⠌⠋⠙⠻⣧⡊⠁⢀⣅⠚⢻⣛⣠⣿⣿⣿⣿⣿⠋⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣽⠿⢿⣯⣭⣭⠾⢿⣤⣀⢀⠠⠊⢀⣱⡤⢶⣿⠖⡛⠛⠋⠛⠛⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⣿⣿⣧⣼⣾⣾⠾⠷⣦⠾⡉⠐⢣⡏⠀⠀⠀⣈⡥⠖⠚⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣁⣀⣙⣇⣀⣜⣁⣀⣈⣠⣎⣈⣀⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣏⠭⣟⡛⣛⣛⡛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⢀⡀⠀⢀⠄⠀⠰⢤⠀⠔⠃⠀⠀⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⢀⡀⠀⠤⣬⠝⢫⣴⠊⢉⢰⠀⠴⠒⠚⠍⣤⠄⠀⠝⠀⠀⠠⠄⠀⠀⢤⣦
⠀⠀⠀⠀⠀⠀⢀⡾⠃⡤⠄⠀⠀⠐⠂⠠⠉⠨⠀⠀⠀⠀⢬⠴⠀⠄⠘⠈⠏⢨⡁⠀⠐⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⢀⣴⠶⠷⠐⠀⡖⠒⣆⠴⠀⠉⠊⠚⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢜⢢⡄⠀⠀⠀⠀⠀⣿⠷⡄
⠀⠀⠀⠰⠏⠀⡤⢤⡀⠀⣁⡴⢉⡤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⢀⠀⠘⠐⣀⣀⠀⠄⢀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⡿⠀⠀⣐⠀⠀⠂⠨⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠩⡄⢍⣷⡁⢾⠉⠀⠃
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠸⠃⣰⠋⠹⢏⣤⣒⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠅⣸⠀⢀⣌⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢋⠅⢠⣀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⡁⡟⢴⡄⠛⠅
⠀⠀⠀⢀⣀⠀⡀⢠⡞⢶⣇⣴⣵⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⢸⠻⡎⢷⠂
⠀⠀⠀⠀⡀⠀⣠⡏⣵⣙⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠣⣾⠀⠀⣸
⠀⠀⠀⠀⠳⣴⣿⣶⣝⣿⣿⣿⠿⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠁⠀⢀⠀⠀⠐⠀⣠⡊⠈⠓⠚⠃
⠀⠀⠀⠀⣠⣿⣿⣾⡿⢿⠟⠁⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⢺⡄⠰⢆⠀⢠⡜⠃
⠀⠀⢀⡄⣙⡿⠛⣩⣛⠿⠆⠀⠲⡀⠑⡀⠀⢀⡀⢠⠀⡀⠀⠀⠀⠠⡀⠉⠡⣁⠈⠁⢞⡁⠠
⠀⠀⠐⡻⠋⠐⡹⣵⠿⠇⠀⠀⠀⣅⣤⢈⣀⠄⠉⢀⡀⣀⡀⣀⡘⠀⠀⢳⡀⠈⠽⠯⡁⠁⢦⠰⡿⠈
⠀⠀⠈⣄⢨⠙⣠⣿⣠⡆⠀⠀⠀⠸⠓⠸⠋⣢⢀⡁⡀⠉⠁⠀⠈⠉⠒⠈⢤⠠⠀⠈⢳⡤⠈⠇⠄
⠀⢀⣀⡀⠠⣼⠋⢉⣉⡀⠀⠀⠀⠀⠀⣰⣞⡻⠯⠉⠀⠒⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⡄⠀⠁
⠀⠈⠄⣠⠹⡏⡇⢸⢶⡧⠀⢀⠀⢰⡷⡿⢿⡅⠢⠀⠀⠀⠀⠀⣤⠀⠠⢠⡂⡀⠀⠀⠀⠀⢀⢠⡶⢀
⠀⠀⢠⠃⠀⣱⣿⣶⣻⣿⣄⡏⣄⢾⣿⠇⠈⡠⢀⠀⠀⠀⠀⡀⠀⠁⡰⠁⠈⠀⠂⠀⠀⠀⠠⠎⠀⠀⠀⣠
⠀⠀⠰⠆⠀⠒⠒⢒⣾⣩⡏⠀⠿⠓⠋⢀⠈⠀⠈⠁⠀⢀⠈⣀⠀⡗⠁⡈⠁⡀⢀⣨⣀⣶⡅⠡⠆⣤⠊⣉⠅
⠀⠀⠀⠓⠀⡀⢀⣿⣰⢿⠫⡆⡀⣑⡴⠈⢠⡄⢤⡥⠀⢬⣤⡴⢸⣧⡀⠀⢒⢻⣄⣠⡹⣽⠾⣱⢦⣼⣇⡀
⠀⠀⡃⠘⠃⣤⢤⡈⠋⠸⡟⠗⠃⢘⢣⣌⣿⣉⢳⣶⣖⣆⡽⡃⠾⠀⣝⠶⣯⣤⣼⠚⠏⢹⡳⣴⣿⣿⡘⠳
⠀⠀⢃⣐⢤⡍⠀⠀⠀⠐⡇⡦⠐⠺⠺⠙⠟⠹⠛⠉⢉⠁⠀⠉⠉⠋⠛⠷⢭⣦⡿⠀⠀⠀⠀⠎⢼⠋⣃
⠀⠄⠀⠿⠛⢿⠀⠀⠀⢀⣹⣄⠀⠀⠈⢀⠈⠤⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠀⠀⢀⣌⠈⣰⠓⢽⠂
⠀⡂⠀⢠⠐⡎⢃⠀⣰⣾⡛⠋⠃⠀⠀⠀⠁⠀⠤⠀⠠⢀⠀⠀⠁⠀⠀⠀⠛⠿⣴⣆⡄⠟⠛⣇⣹⠉⠫⠁
⠀⠀⠀⠤⠄⠼⠈⣦⠋⠨⡅⠀⡄⠀⠀⠀⣰⣳⢘⡞⢓⣞⢻⡦⠄⠀⠀⡀⠘⡄⠸⣿⡗⣼⠋⢀⣛⠠
⠀⡆⠀⠀⠻⠶⠓⠚⢂⣠⢦⠀⠤⡐⠉⣡⠺⠷⢭⠞⠛⠟⠫⡔⠻⢊⣿⣲⣞⣹⣅⣾⡱⢦⢮⣟⠉
⠀⡄⠀⠀⢀⠠⡌⠉⣂⣋⢈⠀⡘⠛⠀⠩⠋⢙⠷⠉⠀⠀⠠⠷⠷⠟⠶⠿⡯⡏⠉⢶⠆⠀⠈
⠀⠇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⠒⠒⠦⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠒⠒⠤⢄⡀
⠀⠀⠀⠀⠀⠀⣠⠔⢉⡤⠒⢶⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢀⡗⠒⠦⡈⠒⢄
⠀⠀⠀⠀⢀⠞⠁⣴⢋⠔⡩⣻⡆⠀⠀⠣⣀⣀⠀⠀⠀⣀⣠⠜⡀⢈⣰⣟⢌⠢⡘⢦⠀⠑⡄
⠀⠀⠀⡠⠁⣤⠚⡧⡎⡼⢨⢯⢟⡷⣦⣄⣠⠬⠷⠀⠚⠤⢄⣠⣴⢾⡻⡝⡅⢣⣹⢼⡓⣦⠈⢆
⠀⠀⡰⢁⡴⢋⡾⣱⢫⢗⡿⣼⣨⣊⡶⠋⠀⠀⠀⠀⠀⠀⠀⠙⢶⣐⣅⣷⢿⡺⡝⣎⢳⡜⢲⡈⢆
⠀⠠⢁⠞⣠⠟⡴⢣⡯⠞⠚⢧⡇⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣸⠼⠉⠓⠽⣌⢢⡙⣄⠱⡌⠄
⣐⡡⠮⠴⠷⠚⠉⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠙⠚⠳⠽⢮⣢

⠀⠀⠀⠈⠉⠀⠐⢄⠀⠀⠀⠀⠀⠠⠀⠈⠉⠁⠐⢄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢀⠀⠀⠀⠀⠀⡠⠂⠈⠉⠁⠀⠄⠀⠀⠀⠀⠀⡠⠀⠀⠉⠁
⡀⠀⣴⡄⠀⢴⡦⠀⠂⠀⠀⠀⠀⠀⠔⠀⠀⠠⠂⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⣤⠀⠀⠀⢤⠀⠀⠀⠀⠀⠐⠀⢤⠀⠀⠀⢠⠀⢀
⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠘
⠀⠄⠁⠄⠀⠄⢊⠐⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠊⠀⠁⠀⠀⠀⠈⠀⠐⠄⠀⠀⢂⠀⠀⠀⠀⠀⠈⠀⠈⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⡈⠀⠀⠀⠁⡠
⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁
⠀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢄
⡀⠀⣤⡄⠀⣠⣄⠈⠄⠀⠀⠀⠀⠀⣤⡄⠀⢠⣄⠈⢂⠀⠀⠀⠐⠀⣤⡄⠀⢠⣤⠀⠂⠀⠀⠀⠐⠀⣠⡄⠀⢠⣤⠀⠀⠀⠀⠀⠀⠁⣠⣄⠀⢠⣤
⠇⠀⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠸
⠀⠀⠐⠒⠒⠒⠂⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠐⠀⠀⠢⠤⠔⠀⠠⠂⠀⠀⠀⠀⢄⠑⠤⠀⠤⠊⠀⠀⠀⠀⠀⠈⢄⠑⠤⠀⠤⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠶⠿⠛⠛⠛⠛⠛⠛⠛⠛⠿⠶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦
⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⡠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⣸⣿⡄⠀⠀⢸⣄⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢿⡀
⠀⠀⣼⠃⠀⠀⣠⣶⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠃⠀⠀⠘⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡟⠛⠄⠀⠸⣇
⠀⠀⣿⠀⠀⠈⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿
⠀⢸⣿⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⡆
⠀⠸⣿⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⣿⠃
⠀⠀⣿⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⢤⣤⣄⣀⣤⡤⠤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⣤⣤⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⢶⣦⣤⣤⣤⣤⣤⣤⣴⡶⠾⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠰⠀⠄⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⡀
⠀⠀⠀⠈⠃⠂⠀⡀⠀⢀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⡢⠀⠀⢂⣤⠔⠛⠛⠁
⠀⠀⠀⠀⢒⣌⡳⣾⣄⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠀⠀⠀⡄
⠀⠀⠀⠀⠈⢉⣿⣿⣷⣮⣶⠁⠂⠀⠀⠈⠀⠀⠀⠀⠀⠐⠊⠀⠑⠀⣀⠄⠀⠀⠀⠀⠀⠈⡠⣦⡀⠶⡤⠄
⠀⠀⠀⠀⠀⠰⢻⠛⢳⡦⣿⢀⡀⢈⢤⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠘⠉⠀⠀⠀⠀⠀⠐⠚⠁⣄⡁⠀⢀
⠀⠀⠀⠀⠀⠀⢈⣹⣭⣽⣆⠄⠀⠀⠎⠠⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠂⠀⠀⠀⠀⠀⣠⣤⠀⠰⠷⠅⠊⠐
⠀⠀⠀⠀⠐⠀⠀⠙⢿⣧⣟⡊⠀⢲⡔⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣀⣀⣀⠀⢀⣀⠀⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠩⣶⠥⠀⢉⣯⠐⡀⠀⠀⠀⠀⠐⢠⢁⡔⠀⠀⠀⠀⠐⠀⠀⠈⠀⡼⢂⠐⠀⠀⠀⠂⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡀⠈⠽⠃⠐⠀⠀⡆⠀⠀⠈⠀⠉⢀⠀⠀⠀⠀⠀⢀⡀⠌⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠈⠑⣤⣤⡤⠤⠤⠂⠁⠀⠄⡘⣀⡃⢼⠆⠈⠑⢏⠁⠂⠠⡬⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠠⡄⠀⠀⠀⠀⠓⠒⠀⢀⡠⠀⠋⢰⣋⣠⣉⡁⠘⢄⠠⣀⠀⠀⢀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⠀⠀⢀⠔⠊⠁⠀⠀⠀⠁⡠⢉⡃⢴⡄⠈⢃⠀⠑⠢⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⣛⡚⢛⢹⡇⠀⠀⠡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠲⡿⠥⣈⠛⠏⠩⠀⢠⠎⠀⠀⣤⡀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠚⠷⢶⠒⠘⠆⠘⠀⠈⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⡤⠤⠤⠔⢛⣂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠆⠀⢱⠛⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⠀⠀⠀⠀⠘⢠⡟⠲⣄⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⡤⠀⠀⢹⡀⠀⠻⠇⢠⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡤⠀⠀⠸⡆⠀⠐⡀⠀⠂⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡇⠀⠀⠀⡇⠀⠀⢸⣥⠀⠀⣿⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠄⠀⠠⠤⠀⠠⠄⠶⠂⠾⢀⠇⠀⠀⠸⡇⠀⠀⠈⡷⠀⠀⢻⠀⠠⠄⠺⠇⠠⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⡀⢀⣰⡆⠀⠀⡠⠟⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡡⠁⠀⠀⢠⠀⢆⠀⠀⠀⠀⣀⡄⠈⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠐⠀⡁⠂⠔⠁⠁⡂⠀⠂⠉⠁
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⢢⠀⠀⠀⠀⠀⠀⠊⠀⠀⠆⠀⠀⠀⠄⠘⠀⠈⠡⠀⠋⠀⡀⠀⠀⠄⠄
⠀⠄⠀⠀⠀⣠⠀⠀⠀⣀⠈⠁⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠚⠀⠀⢀⡀⠀⠀⠄⠀⠀⠀⠀⢀⡀⠀⠀⣤
⠀⢀⠀⠀⠀⠐⠁⠀⠈⣿⠀⢠⡄⠀⠈⠁⠁⠒⠈⠉⠃⠄⡈⠡⠀⠠⠤⠀⠊⠑⠦⠀⠀⠀⢠⣄⠀⢸⡏⠀⠀⠑
⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⣀⡀⠶⢶⠀⠀⠀⠀⠈⠀⠐⠀⠁⠀⠁⠀⠀⢰⠶⠆⣀⡀⠹
⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠇
⠀⣾

⠀⠀⢠⠀⠀⠀⠀⠀⠀⣤⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢰⠀⠀⠀⡀⠀⠀⣿⠀⠀⠀⠀⠆⠘⠃⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢀⣇⠀⠀⣿⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠂⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠈⠁⠈⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⣀⣠⣦⡀⠀⢀⠀⠀⠀⠈⠉⠀⡀⠀⠀⠀⠄⡀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠈⠙⢉⡟⠁⠀⠀⠀⠀⢤⠀⠀⠀⣷⠀⠀⠀⠀⠁⠀⠀⠀⠂
⠀⢰⣤⣠⠀⠀⠀⠄⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⢀⣿⡄⠀⢰⣿⡇⠀⠀⢠⠀⠀⠀⣀⣂
⠀⠀⠁⠀⠀⠀⠀⠀⠐⠿⠂⠀⠀⠀⢰⠛⡚⣅⠀⠀⠀⠀⢸⣿⡯⠀⠀⡞⠃⠀⠀⣿⣧⠀⠀⠈⠉
⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠸⣿⣿⣧⣤⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠻⠉
⠀⠀⠀⠀⢀⠀⠀⠀⠁⢶⣀⠀⠀⠀⠀⠹⡿⡛⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠄⠈⢆⡀⠀⠀⠐⢍⣣⡀⠀⠻⠿⠿⢷⣿⣽⠄⠀⠘⠀⠶⠀⠀⠀⠄⡠⠀⠀⠢⣄⣠⡆⠉
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠉⠁⠀⠀⣀
⠀⠀⠀⠐⠀⠀⠀⠀⠖⠛⠇⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠁⠀⢈⣴⠛⣹⣤⠀⠀⠀⣠⠖⢀⠠⠀⠀⠀⠀⠀⠀⠀⢠⡩⠘⠁
⠀⠀⢠⠀⠀⠀⠀⠀⢼⣦⡄⠀⠀⠀⠀⠈⢹⡿⣿⡇⠀⠀⢀⣒⣀⡀⠏⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠛⠀⠀⢰⠶⠶⠆⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠠⠄⠀⠀⠀⠀⠀⠶⠦⠄⠀⠀⠀⣅
⠀⠀⠀⠀⠰⣛⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠛⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆

⠀⠀⠀⠀⠀⢀⡀⡀⢀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷
⠀⠀⠀⠄⣀⣼⣿⣷⠞⠛⠲⢿⣷⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡞⠉⠋⠀⠀⢀⡴⠦⡶⠆
⠀⡀⣰⠋⠀⣠⡄⠐⢲⣷⣦⠀⠀⢳⣆⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⢸⣟⢰⠇⠈⠓⡀
⢀⣷⠃⠀⣄⣿⣝⣷⣶⡁⣿⣽⠀⠀⢻⣀⠀⢰⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢀⠋⢹⣿⣤⣛⣾⡃
⢸⡇⠀⠀⠹⣿⣛⠏⠈⠀⣄⠃⡰⡶⠋⠉⢱⠇⠀⠀⠀⠀⠀⠀⢠⠙⢦⣀⠀⠀⠀⣀⣈⣿⡷⣽⠛⡇
⠀⢷⠆⠙⣦⠈⠙⠛⠄⠠⡤⣶⠏⢸⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠙⣦⠀⠀⠀⠈⠿⠆
⠀⠈⠀⠛⠁⣀⣀⠐⢄⣨⠇⠉⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢸⣿⡀⠀⠀⠀⠀⢀⠀⠀⣀⣴⡄
⠀⠀⠀⠠⡈⠛⠠⡄⠉⠀⢠⠀⠀⠈⢹⣿⣆⠀⠀⠀⠀⠀⠀⠀⡀⡇⠀⣿⠉⠀⠀⢀⠀⣴⡃⠀⢿⡽⡀⠹⠂
⠀⠀⠀⠀⣹⣦⡴⣿⣄⠀⢁⠀⠀⢠⣾⡽⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣿⠛⠁⠀⠴⣦⠛⢧⡀⠀⠀⠀⠂
⠀⠀⠀⠈⠉⠁⠐⠋⡉⠁⠀⠀⠀⠀⢸⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢋⣠⠀⠀⠀⠂⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣦⣠⣀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣼⣿⣀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢤⡶⠦⣤⣄⣛⣁⣩⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣴⣧⣙⣿⠀⠀⠀⠰⠋⠀⠀⡀
⠀⠀⠀⠀⣹⡾⡇⠀⠋⢹⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠏⣼⣿⣿⣿⡇⠀⠀⠀⠿⠶⣢⣿⣄⠀⡀
⠀⠀⠀⠀⢨⠟⡠⣷⢖⣼⡷⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢰⣿⣿⡝⠋⠹⣆⢀⣤⣤⡼⠋⠀⠀⠉⠁
⠀⠀⠀⣰⠃⣾⢃⠻⣿⣿⡟⢷⣤⠀⠀⢀⢀⢄⠀⠀⠀⠀⠀⠀⠈⢫⠟⠓⠢⠀⠘⠛⠻⠟
⡀⢀⠠⠋⢝⡻⠈⢇⡈⢻⣷⣤⣿⠀⠀⠀⢿⡙⡇⠀⠀⣠⣤⠀⡟⣿⣠⡀⠀⠀⠀⠘⠁⠄
⠈⠉⠀⠀⠈⠀⢀⡺⠃⢀⢻⣿⣌⢧⠀⠀⢀⢻⡇⠀⠀⢛⠖⣠⡇⢿⡟⠛⣀
⠀⠀⠀⠀⠀⠀⣮⠀⢠⣶⣿⣿⣿⢀⠀⢀⡼⢫⠃⠀⠀⠘⣄⣇⠁⣼⣡⢸⠏⠀⠀⠀⠰⣶⡀
⠀⠀⠀⠀⠀⠀⠻⣷⠷⢿⣿⣿⣿⢆⣀⣤⡿⠋⠀⠀⠀⠀⠈⢺⡤⢿⠗⢉⣦⣤⣄⣠⣶⠟⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣿⣿⣭⣥⣤⣤⣤⣤⣤⣤⣤⣬⣤⣬⣥⣶⣿⣿⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠁⠀⠀⠄⠒⠀⠀⠈⠃⠐
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢀⠀⠀⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠈⠀⢀⢀⣀⠈⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠄⠀⢸⠞⠉⢆⠀⠀⠀⢀⠉⠀⢀⠘⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⡀⢀⠈⠙⠖⡋⠘⠂⠂⠀⠚⢂⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠄⠉⠐⡀⠚⡅⠛⠐⠧⡤⠀⢶⠀⠆⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠸⠖⠌⠀⠸⠧⡇⠀⡀⠠⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢀⠷⡀⡁⠞⠀⠀⠀⠀⢀⠀⠆⠀⠐⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠐⡄⠀⡐⠂⠄⠈⠙⢱⠾⠶⣁⠀⠀⠒⣈⠦⡲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⠀⠀⠘⠛⠲⣄⢸⡆⢠⡄⣵⢀⡔⠋⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⠀⠀⠈⠀⠀⠀⠀⠄⢸⠀⠀⠀⠀⠈⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠸⠀⠠⠀⠀⠀⠀⢀⠊⠘⡁⡀⠀⠀⢀⣸⠀⠂⠀⠀⠀⠀⠀⣀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀⠸⠷⠈⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣠⠞⠀⠀⠀⢱⠈⠑⠔⠀⡆⢥⡀⠀⠀⠀⠻⣄⠀⠀⡾⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠙⢄⠁⠀⠀⠀⠄⠀⠀⠀⠀⠁⢀⢧⠀⠀⠀⠀⠈⠀⠀⠙⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⠟⠴⡆⣿⢳⡄⠧⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢸⢀⣬⠀⠀⠀⢿⠠⠃⢰⠀⢀⠀⠀⠀⠐⠶⠄⠀⠠⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⣁⠛⢢⡀⠀⠸⣧⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣍⡄⠀⠳⠀⠀⡿⣇⢰⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣧⡟⢰⡗⠀⣰⠇⣇⣿⠀⢀⣀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⠁⠀⠀⠈⠀⢀⣤⡠⠞⡩⠀⡞⠀⡐⠛⣠⣿⠟⠀⠸⣁⠉⣠⡀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠂⠂⠀⠴⠦⡈⠀⠄⠀⠊⢀⣼⠁⠐⣇⠀⢼⡸⣟⡄⠁⠀⠀⢨⣄⠠⠀⠀⢤⡀
⠀⡀⠀⠀⠀⠀⠀⠘⣃⡀⠀⢄⡑⠆⠀⠑⠲⡆⠰⠶⠋⠉⠃⢰⡿⠄⠀⠓⠿⠄⠒⠀⡴⠕⠘⠧⠀⣀⠀⠀⠀⢀⡀
⠀⠅⠀⠀⠀⡠⠄⠀⠈⠀⠘⠉⣔⠊⡇⠀⠀⠱⠀⢢⡀⠁⠸⠸⠫⢶⡀⢢⣴⠲⠶⢏⡁⠀⠈⠦⠘⠋⡈⢰⠐⠊
⠀⠂⠀⠀⠀⠀⠤⠀⠀⠠⠀⠀⠈⡠⠇⣘⠂⢀⡲⡦⢄⢠⡴⢐⠁⢺⠀⣠⠀⠀⠐⢀⠱⠀⠁⠀⠆⠀⠐⢣⣄⠀⡁
⠀⠀⠀⠀⠀⠀⠘⡂⠀⠘⠑⠄⠘⣠⠠⣀⡼⠏⠀⠀⠀⡈⢤⢀⣀⠈⠻⠑⡀⢠⠀⢀⠠⠃⠂⠉⠤⡷⠄⠀⠀⠈⠉
⠀⠃⠀⠀⠀⠈⠒⠓⠖⣠⡄⠐⠀⡠⠏⠈⠀⠚⠀⠀⠀⠈⠠⠠⠈⡼⠀⢈⠲⢈⡕⠠⠆⠠⡄⠹⠏⠀⠉⠁⠠⠐⠐⠒
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠃⠀⠘⠂⠀⠀⠀⠀⠀⠚⠒⠈⠁⠀⠁⠀⠉
⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢼⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠠⠁⣀⣠⣂⠀⡤⠃⠀⠀⠀⠤⠀⠀⠀⠤⠀⠀⠀⢀⠈⢸⡆⠀⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡰⠃⠄⠀⠁⠀⠁⠏⠀⠀⡤⠂⣠⠾⠅⠀⠀⠊⠭⠋⠀⣈⠉⠛⢤⡀⣧⡀⠀⠘⣿⢃
⠀⠀⠀⠀⠀⠀⠀⢠⢦⡟⠀⢁⠞⠁⠀⣢⠎⠀⣂⣴⡤⠊⠁⠀⠈⠈⠁⠀⠀⠀⣸⣿⣿⡧⠀⠙⢿⡄⠑⢀⣿⡈⣞
⠀⠀⠀⠀⠀⠀⡰⠃⡿⠀⢸⠃⣠⡶⢋⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣷⡄⠘⠀⠉⣷⣾⣿⣧⡿⡄
⠀⠀⠀⠀⠀⣰⠁⢰⡇⠀⣿⣟⠁⣰⣿⠡⠄⠀⠀⠀⠀⠀⠀⠒⠠⠤⣭⡽⠦⠤⡿⣿⣿⣿⣧⠀⠀⠀⣌⣿⣿⣿⡇⠘⡄⠀⡀
⠀⠀⠀⠀⢠⣿⠀⢸⣧⣰⡿⠈⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠀⠀⠀⠀⠀⠀⠀⠘⢿⠿⢦⡀⠀⠀⣿⣿⣿⡇⠀⢸⣠⠃
⠀⠀⠀⠀⠘⣿⠀⠀⣿⣿⣿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣾⣿⣿⣿⡇⢀⡾⠁
⠀⠀⠀⠀⠀⢻⡄⠀⣿⣿⣿⡏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣷⣼⠁⠀⢸⡆
⠀⠀⠀⠀⠀⠘⣧⠀⣿⣿⣿⡇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣇⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠘⣦⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣿⣿⣿⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢠⣿⣿⣿⣿⣴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢇⣾⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⡀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡄⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⢠⠃⠀⡊⣉⣷⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣧⣧⠀⢀⠀⠀⠀⠀⠀⢈⣽⡇⠀⣿⠀⠀⣄⡟⣠⣶⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠟⠛⠻⠿⡿⠶⡷⠶⠶⣤⣬⣾⣿⣸⣿⣶⡶⠿⡿⣿⠟⠋⠉⢙⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠿⣧⣤⣤⣴⣷⣤⣧⣦⣀⠠⠬⣿⣿⠛⡲⣗⡂⢠⢠⣿⠀⠀⠒⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣨⣿⣾⣿⠁⠀⠀⠴⠿⠿⢭⣭⡭⠀⠼⠿⠷⠦⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠼⠶⠒⠾⠖⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⢔⢶⣪⣧⣵⣥⣭⣏⣜⡰⠢⣄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣐⣤⣲⡽⠞⠛⠉⣽⣿⣿⣿⡟⣿⣿⡉⠙⠳⢭⣗⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⡋⠁⠀⠀⠀⢸⣟⣿⣿⣿⣿⣿⡿⡇⠀⠀⠀⠈⠙⢿⣶⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠨⡑⠦⣄⣀⠈⢿⣿⣿⣿⣿⣟⣹⠃⠀⢀⣀⡤⢖⡫⠒⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠴⢂⢌⣉⡛⠛⠿⠿⠿⠿⠗⠒⢋⡩⡵⢮⠋⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠜⠙⠑⢰⠐⠺⡙⠌⠂⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠤⠤⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠶⠶⠲⠒⠶⠤⣤⣀
⠀⠀⠀⠀⠀⠀⡠⠔⠋⠉⠀⠀⢀⣀⣀⣀⣀⠀⠉⠛⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠁⠀⠀⣀⠀⠀⣀⡀⠀⠀⠀⠈⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠶⢷⣶⣶⣶⣶⡯⠶⢤⡀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢷⣶⣶⣶⣶⡶⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠠⠼⣿⣿⣿⡿⠁⠀⠀⠁⠀⠀⠈⡄⠀⠀⠀⠆⠀⠀⠈⠀⠀⠌⣿⣿⣿⣿⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⡀⠀⠀⢀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠠⠦⠤⠐⠒⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡄⠀⠀⠀⠄⢀⣀⠄⠀⠀⠀⠀⡴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⢀⣀⣀⣀⠀⠤⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠀⠈⠙⠢


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣾⣷⣾⣿⣿⣶⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠿⠛⠛⠛⠛⠛⠿⠿⣿⣿⣷⣦⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⢉⣀⠀⠀⠀⠀⢠⣤⣄⠀⠈⠙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠁⠀⠛⣭⣅⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠙⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡏⠀⠀⠀⠀⣿⣿⡇⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠘⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠁⢀⣀⠀⠀⣿⣿⠇⠀⠀⠸⣿⡇⠀⠀⢀⣭⣳⠀⢸⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢺⢩⣀⠀⠈⠉⠀⠀⠀⠀⠉⠀⣀⣴⣿⠟⠙⠀⢸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡄⠀⠀⢻⣷⣶⣤⣤⣤⣤⣴⣶⣿⠟⣿⡟⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⡀⠀⠀⠙⣿⣩⡏⢹⡏⢹⣇⣨⣿⠟⠀⠀⠀⣰⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣄⠀⠀⠈⠙⠛⠿⠿⠿⠛⡿⠇⠀⠀⢀⣴⣿⣿⠏⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⣆⣠⣶⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⡿⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⡿⠛⠛⠛⠛⢹⠏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⠀⠀⠀⠀⠈⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠊⠳⠄⠀⠀⠀⠀⠲⠉⠊⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⢀⢀⠙⠀⡫⠀⡀⠀⡀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⣉⡡⠀⠈⠒⠀⠁⠐⠠⠂⠀⠀⢀⠈⠈⠈⠊⠁⠠⡉⣩⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠁⠒⠒⠚⠈⠉⣀⡀⠀⣀⣀⠀⠈⠉⠀⠇⠒⠐⠁
⠀⠀⠀⠀⠀⢠⠀⠠⠄⠄⠄⠆⠠⠠⠀⢤⠀⠀⠰⠀⠀⠀⠀⠀⢠⠂⢀⠀⠀⠀⠀⠠⠒⠈⠈⠁⠐⠄⠄
⠀⠀⠀⠀⠀⠏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠌⠐⠀⠀⠒⠀⠀⠈⠁⠀⠀⠈⠈⡁⡀⠀⢀⢈⠈⠁⠀⠈⠈
⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢧⡁⢀⠽⠠⠀⠀⢔⠒⠒⠒⡊⢠⢧⢰⢿⡈⡒⠒⠒⢒⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠄⠀⠤⠤⠀⠈⠶⡬⡉⡣⢲⡤⢏⡞⠀⢇⠳⢼⡲⡜⡁⡤⠎⠀⠀⠠⠄⠀⠤
⠀⠀⠀⠄⠠⠃⠂⠀⠀⢄⡀⢀⠠⠀⠀⠀⠣⠐⣀⠀⠀⠑⠒⠈⣡⢔⣀⡀⢀⢠⢭⠴⠀⠀⠀⠀⠰⠮⡭⢀⡀⡀⣐⢠⡈⠐⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢍⠉⠁⠁
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠠⣄⣀⣠⠄⣴⠀⠀⢀⣀⠀⠀⠀⢀⣿⠀⠀⠀⠀⣼⡀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⢉⢼⠩⡧⡘⡡⠀⢀⣸⡈⢦⠀⠀⢸⣻⡇⠀⠀⢸⢟⡇⠀⠀⡰⠃⣮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⢸⠀⡇⡛⠁⠀⢸⡀⠳⡀⠱⡀⠀⣿⣟⣠⣆⣻⣿⠄⠀⠜⠀⡜⢁⡏
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⠀⡵⠀⠀⠀⢣⠙⢆⠙⠢⡀⢠⡙⠙⠃⠘⠛⢙⡠⢈⡄⠊⡠⠊⡼
⠀⠀⠀⠀⠠⣶⣀⠈⢂⠀⠀⠌⠁⣠⡶⠄⠀⠀⠀⠀⠀⠀⢀⠸⢲⠥⢴⡛⠀⠄⣗⠦⠤⣽⣏⠛⡈⠳⡄⢠⡖⢁⠗⣩⣮⠤⠤⢺⠁
⠀⠀⠀⠰⠲⣌⢉⢷⡶⠂⠲⣶⡾⠉⣰⠾⠀⠀⠀⠀⠀⠀⣤⡴⣹⠇⠸⢧⠣⠶⠈⢟⠒⣚⠣⣄⠘⡀⡽⢻⡀⡪⢀⠬⣓⠒⣺⠁
⠀⠀⢀⣀⡀⡘⠻⡖⠁⠀⠀⠘⠾⠋⢁⢀⣠⠀⠀⠀⠀⠠⡤⠖⢹⠂⠀⣧⠙⠲⠂⠀⠉⠣⢖⣁⡍⢲⡁⢈⡗⢸⣈⣒⠄⠋
⠀⠀⢸⠀⠈⠙⠒⡗⠀⠀⠀⠀⢓⠚⠋⠀⠈⡀⠀⠀⠤⠀⣀⡠⠋⠀⠀⠈⠓⣠⠤⣹⡄⠀⠀⠀⠈⠉⡀⠀⠈⠉
⠀⠀⠳⢆⢤⢇⡐⡏⠀⠀⠀⠀⢟⣂⡤⠤⠰⠃⠀⠀⠙⠉⠈⠀⠀⠀⣠⠞⢉⠍⡓⢀⢦⠀⠶⡆⢒⡩⡉⠳⣄
⠀⠀⠠⠀⢀⣸⠀⠀⠀⠀⠀⠀⠀⢸⡰⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⡜⠁⠐⢅⠒⠤⢏⢨⠀⡑⠁⠥⠒⡈⠃⠈⡑⡄
⠀⠀⠈⢱⡊⣯⠀⠀⠀⠀⠀⠀⠀⢠⣿⢱⠈⠀⠀⠀⠀⠀⠀⠀⠰⡠⢃⠸⡼⠐⠢⣀⠍⠀⠈⣇⡔⠂⢣⠜⢘⢄⡠
⠀⠀⠀⢻⡟⢋⠀⠀⠀⠀⠀⠀⠀⢈⠛⣿⡃⠀⠀⠀⣀⠤⠂⣡⠔⡀⠀⡀⠀⡌⢠⠀⠀⠀⠀⠀⢇⢰⡀⢀⠀⢀⠲⣄⠐⠤⣀⡀
⠀⠀⠀⠈⠓⠬⢧⠀⠀⠀⠀⠀⠀⡾⠴⠋⠁⠀⠺⠩⢤⡶⢛⣡⠞⣡⢾⣁⠜⠑⠋⠀⠀⠀⠀⠀⠈⠊⠑⣄⡷⢄⠳⣬⣙⠶⡤⠌⠵

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠾⠛⠋⠉⠉⠉⠉⠉⠉⠙⠛⠿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠉⠀⠀⠀⠀⠀⡀⠀⢀⢰⡄⠀⠀⠀⠀⠉⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠘⡀⠀⠀⠀⠁⠦⠽⣿⣿⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠇⠀⠀⢠⣤⣀⣀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⢀⣿⢣⣦⡀⠀⠀⠀⠀⡃⠀⠀⣕⠦⣙⣿⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⣠⣎⣿⡄
⠀⠀⠀⠀⠀⣸⡇⣿⠍⠁⠀⠀⠀⠀⠇⠀⢀⣸⠓⠈⠛⠛⢻⣿⣿⣷⠀⠀⠀⠀⠀⠀⠉⢸⣧
⠀⠀⠀⠀⠀⣿⠃⠂⠀⠀⠀⠀⣀⣠⣟⡉⣾⠿⡀⠁⠤⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⢈⡜⠉⣿⣿⡇⠀⠀⢀⠀⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⢸⣿⡟⣿⣿⣿⡄⠄⠼⢶⣿⣿⣿⣿⣫⠛⠻⠆⠀⠀⡀⡀⢸⡟
⠀⠀⠀⠀⠀⠈⣿⡌⣴⣦⡄⠀⠉⡇⣿⣿⡷⠦⠶⠠⢜⣿⣿⣿⣿⣿⣦⣴⠊⣱⣛⢾⣆⣿⠃
⠀⠀⠀⠀⠀⠀⠘⣷⡽⣿⣷⡆⠀⡇⣸⣿⣿⢳⡲⡶⢶⣿⣿⣿⣿⣿⣿⠈⣿⣿⣿⢟⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣮⣿⣯⣤⡇⢿⡿⠁⢸⡇⠀⠀⣿⣿⣿⣿⣿⣿⣶⣿⡿⣳⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣮⣻⠆⠈⠏⠠⢸⣿⡀⠀⣿⣿⣿⣿⣿⡿⣟⣽⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣥⣄⣘⣻⣷⣈⣿⣟⣻⣯⣷⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠖⠒⠛⠋⠉⠉⠉⠉⠙⠛⠒⠲⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡿⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠛⠋
⡇
⡇
⢿
⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡻⠶⢶⣤⣤⣤⣤⣤⣤⣤⣴⠶⠾⢟⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣀⠀⠀⠀⢀⣀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠦⠤⢤⣤⣀⣀⣀⣠⣤⡤⠤⠶⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠟⠛⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣷⣄
⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄
⠀⠀⠀⣴⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦
⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀
⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧
⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠀⠀⠀⠀⠀⣿
⢿⣿⡆⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⢰⣿
⠸⣿⣧⠀⠀⠀⠀⠀⢻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡟⠀⠀⠀⠀⠀⣼⣿
⠀⢻⣿⣆⠀⠀⠀⠀⠀⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠀⠀⠀⠀⠀⣰⣿⡟
⠀⠈⢿⣿⣆⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⣤⣀⣀⡀⢀⣀⣀⣤⣴⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⣰⣿⡿⠁
⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⢀⣴⣿⠟
⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣦⣤⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠁

⠀⠀⠀⢐⣂⠀⠀⠀⡶⡄⠀⠀⠀⠀⠠⠾⠆⠀⠀⠀⠀⠠⣶⠀⢶⠄⠀⠀⠀⣀⣴⣯⣬⣷⣄⡀⠀⠀⠀⠀⠀⡶⠀⠀⢴⡄
⠀⠀⠘⠁⠈⠃⠀⠚⠛⠛⠀⠀⠀⠀⠀⠀⠀⠛⣧⠀⠀⠀⢸⡇⢀⣿⠀⠀⠀⡏⠀⠈⡏⠀⠈⡇⠀⠀⠀⠂⠀⠀⠆⠀⠀⣿
⠀⠀⡶⠘⠃⢶⢰⡆⠛⠀⣶⠀⠀⠀⠀⠀⠀⢀⣤⣿⠄⠀⢻⠁⢸⡏⠀⠀⠀⡇⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟
⠀⠀⠓⠒⠒⠚⠘⠓⠒⠒⠛⠀⠀⠀⠀⠀⠀⠚⠛⠛⠂⠀⠘⠀⠈⠃⠀⠀⠀⠇⠄⠀⠇⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⢀⡀⠀⡀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢰⠁⠒⢹⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⢤⣤⡀⠀⠀⢀⣀⠀⣀
⠀⠀⢀⣿⣷⣼⣧⣿⣿⡄⠀⠀⢀⣾⣦⠀⠙⠃⠀⠀⠈⠓⢒⡋⠄⠘⠛⠀⠀⠀⣀⠀⠰⣌⣿⡾⢿⣿⠀⠀⠘⠚⢠⣿⣄
⠀⠀⠈⠁⠘⣿⣿⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⢘⡇⠐⠀⠀⠀⠀⠈⣿⠀⠀⠨⢾⣿⠀⠙⠀⠀⠄⠀⢿⣿⡿
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⣿⣦⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠰⠿⠶⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠀⡇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠃⢀⣇⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇
⠀⠀⠀⠀⠀⠀⣀⣬⣤⣶⣿⣿⣿⣿⣷⣶⣬⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠈⠏⢠⡇⠘⠇⠀⠘
⠀⠀⠀⠀⣼⣻⣽⣾⣿⣯⣿⣿⣿⣿⣿⣿⣻⣿⣽⣿⡀⠀⠀⠀⠀⢀⣤⣤⣅⣀⡃⠀⠠⠄⢸⡇⠀⠄⠀⠀⣀⣠⣤⣤⡀
⠀⠀⣠⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠿⠟⠓⠀⠀⠀⠈⠙⠛⠻⠿⣿⣷⣷⣶⣼⣧⣴⣶⣾⣿⡿⠿⠟⠋⠉
⠀⠀⠀⠀⠉⠛⠋⠙⠛⠉⠀⠀⠉⠁⠈⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠛⠋⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣤⣴⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠉⠉⠀⠀⠀⠀⠉⠉⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⣴⣶⡀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡄⠀⠀⢀⣠⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠉⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠃⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠈⠙⠓⠦⢤⣤⣤⣤⠴⠖⠋⠁⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤⣀⣀⠀⠀⠀⠀⣀⣀⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉

⠀⢀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠸⠀⢀⡄⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⢮⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠉⢣⡄⠀⠀⠀⣤⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⡀
⠀⢀⠀⠈⠁⠠⠂⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⢀⣀⡴⡼⠁⠀⡠⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢸
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠅⠀⠀⠀⠀⢀⠊⢹⣷⠻⡆⠸⣴⠏⠠⠔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄
⠀⠀⠀⠀⡄⠰⠏⠀⠀⡀⠀⠀⠀⢀⠀⠀⣿⢷⣿⣿⣱⢿⣾⢷⡆⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁
⠀⠀⠆⠀⠀⠀⠂⠀⠀⠁⠀⠀⢀⠈⠀⠀⡹⣾⣿⡿⠁⣾⢃⠌⣰⠀⠀⠀⢠⡜⠁⠀⠀⠀⠀⢀⡀
⠀⢸⣀⡆⠀⡀⠀⠀⠀⢀⠤⡀⠀⠑⠀⠀⠁⢿⣿⡇⢠⠛⡏⣴⠿⠒⠀⣴⠁⠀⠄⢠⠈⠀⠀⠈⠙
⠀⠐⠀⠀⠈⠇⠀⢀⠔⣋⡀⠄⠁⠷⠛⢷⡉⠷⣼⣷⡶⢻⣠⡿⣢⠴⠆⠀⠀⠀⢶⠂⠀⠀⠀⠀⠀⣠⠖
⠀⠀⠀⠀⠖⠈⣩⠖⠈⠀⠀⠀⠀⠀⠀⠚⠳⣦⣴⡬⠛⠛⠿⣵⠄⠀⠀⠛⠓⠚⣁⡴⠆⠰⢤⠤⠄
⠀⠰⡄⢰⠀⡔⠁⠀⠐⣦⡠⡄⠀⠀⠀⠀⠐⠉⣙⡕⠊⠉⠑⣖⠓⣞⡤⡶⠐⣊⠁
⠀⠀⠄⡌⡀⠀⠀⠀⠀⠈⠻⣶⣃⡀⠀⠀⠀⠀⡿⠀⠴⠀⠛⠹⡆⣉⢷⡄⢀⢈⠙⠢⣀⠀⠀⠀⣠⠄⠶⠀⡄⠀⠀⠀⠄
⠀⠰⡎⢀⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⠇⠀⠀⢀⡝⠳⡄⠰⠟⠀⢿⣸⠎⠷⠆⢘⣋⡄⢹⠗⠂⠉⠐⠖⠒⠈⠀⢠⠾⠂
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠰⠀⠉⠒⣰⣷⡶⠟⠊⣠⣔⣻⣧⢈⣁⣙⣧⠳⣄⢦⣄⠠⠀⠉⣸⢇⣀⡀
⠀⢰⠆⡄⠷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣆⣼⠆⣠⣤⡀⢠⠞⢢⣴⢇⣼⠿⠿⡄⣉⡻⣹⡆⠈⠴⣉⣦⡰⠞⠁⠀⠈⢉⠆
⠀⢨⡂⡇⠘⢇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⡧⠴⠇⠀⠳⢶⣢⣶⣶⣿⣷⠄⣀⠿⢿⠙⢦⣛⡶⡘⠗⣤⠸⣄⠀⠰⠆⠈
⠀⢠⠍⠀⠀⠈⠷⢀⠀⠀⠀⠀⠀⠈⢉⠅⡲⣓⢛⠶⠹⠃⠌⢹⡄⣀⠙⠶⡫⠄⠰⢇⠠⡏⢳⠚⣤⠀⠙⢿⡓⠳⣄
⠀⢠⠀⣆⠐⠀⣄⠀⠙⠙⠢⠄⣠⣖⣁⡴⢉⠋⡽⢛⢄⣼⢳⣷⡾⠙⠥⠀⡿⣤⡚⠁⠀⠿⠀⠃⢻⡉⠩⣈⠣⢤⣁
⠀⠈⠀⠉⠠⡀⠈⠀⠀⢀⠀⠉⠉⣠⠞⣴⠋⣼⠳⠟⣘⡣⠙⠁⢀⡐⠂⠤⠭⢙⣡⡴⠂⠀⠀⠙⢮⣹⠶⠺⢿⠂⣉⠓⡀
⠀⠀⢀⠀⠰⠁⠀⠀⠴⣿⠀⠀⠀⠀⠘⠀⠢⠙⠒⠎⠁⠴⠣⠾⣦⡀⠀⠀⠀⠈⠳⠶⢞⡉⣤⡄⡀⠈⢷⡒⠦⠀⢉⡜
⠀⠀⠈⠂⠀⠀⠀⠀⢠⣄⠙⠆⣰⡆⠀⠂⠀⠀⠈⠀⠀⠀⢰⡞⢻⣿⡧⠀⠀⠀⠀⠀⠈⡡⠟⠐⣻⣿⡀⠘⢦⠁⠈⠓
⠀⠈⠀⢀⠄⢰⡆⠀⠰⣿⠀⠘⠉⠇⠀⠀⠀⠀⡄⠀⠀⠀⢠⡿⢇⣈⣿⣀⠀⠀⠀⠀⠀⢀⠀⠀⣿⠏⠿⣄⠈⠼
⠀⠀⠀⠈⢀⣈⠹⠀⡀⠁⣾⠀⠀⠃⠐⠀⠀⠀⠃⠀⠀⠀⢷⣄⣤⠙⣟⠻⡶⣦⣤⣄⣰⡁⠀⢸⣿⣿⠛⡇⢠⠀⠀⠀⡀
⠀⠀⡄⠀⠈⠟⠀⢠⡁⠢⠘⠄⠀⠀⠐⣦⠠⡀⠀⢀⠀⠀⠀⠀⢠⡁⣘⣇⠠⡏⡹⢏⡿⢻⢦⡏⠀⠀⠀⡀
⠀⠀⠁⢀⡈⠀⣀⣾⠑⠊⠀⠀⠀⠀⠈⠈⡠⡏⠀⠘⠀⠀⠀⠀⠀⣉⣹⠟⢻⡷⠇⠈⠱⡟⢬⣿⣶⠟⣿⣀
⠀⠀⠀⠸⠓⠁⠙⢉⠀⠀⠠⢦⠀⢠⡀⠄⠡⣁⠀⠀⠀⠀⠀⠀⠈⠉⠀⣤⣼⢁⢦⡀⠆⢻⡆⣿⠻⣿⣽⣯⣶⡖⠀⠠
⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠈⣇⠄⠻⢠⠀⢈⡇⠀⠐⠀⠀⠀⠀⠀⠀⠤⠜⣡⡜⠀⠈⠀⡌⢛⣦⡁⠈⠉⢻⡎⣠⠀⠇
⠀⠀⠀⠀⢳⡤⠤⣄⡈⠀⠀⠈⠀⡀⣦⠈⢀⣊⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⠁⠻⡄⠀⠀⠸⡇⠙⠻⣦⣡⣤⢹⡗⠀⡀
⠀⠠⠀⠀⠈⠃⠀⠈⠁⠀⠀⠀⠞⠉⢈⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠙⠄⠀⠀⣷⢀⡀⠟⣀⠀⠀⠀⠀⠁
⠀⢰⣤⠐⠒⣋⠟⣚⣡⡾⠲⣟⣵⠞⣍⣓⣶⣤⣼⡵⠦⠠⠀⢠⠀⠠⠄⠠⠤⠆⠤⠤⠔⠉⣉⣠⣾⠷⢦⠟⠷⣦⡄
⠀⢸⡟⠛⠛⠟⠛⠉⠏⠑⠛⠋⠉⠀⡁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠙⠋⠴⠁
⠀⠸⡇⣴⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⣀⣀⡀⢘⡀⢀⠐⠀⡀
⠀⢠⡀⡀⢀⠀⠀⠄⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠋⠁⠁⠀⠈⠉⠉⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣷⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠤⠤⠤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠒⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠉⠓⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢠⠖⠋⠙⠢⡀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠲⣄⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⢠⠃⠀⢀⣀⡀⠹⡄⠀⠀⠀⠀⡼⠁⣀⡀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⣾⠀⢠⣿⣿⣿⡆⡇⠀⠀⠀⢠⣇⣾⣿⣿⣆⠀⢸⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢻⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⢸⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⣆⠈⠿⣿⡿⣻⠃⠀⠀⠀⠀⢻⣿⣿⣿⠏⢀⡞⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⠞⠁⠀⠀⠀⠀⠀⠀⠳⢤⣀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⠤⠤⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠒⠒⠒⠒⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡿⢋⣬⠹⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣋⣴⣿⣿⣿⣿⣿⢟⣿⣯⣿⡿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣗⣿⣽⣿⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣁⣌⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣿⠿⣿⣿⣿⣿⣿⣿⣿⣇⠐⢿⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⣒⣸⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⣿⣿⣿⣟⠋⡽⠋⠉⢻⣿⡿⠿⣿⡿⠛⣿⣿⣿⣿⣿⡟⣭⢹⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇⣓⣽⣿⣿⣿⣿⣇⠀⠀⣼⡿⠁⠀⢈⡇⢀⣼⡷⠿⢿⣿⣿⣶⣾⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⠋⠈⠙⣿⣷⣾⣿⣷⣿⣿⠿⠿⠿⠋⢀⡴⢊⣽⣿⣿⡿⠿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⡿⣠⠴⠚⠙⠻⣿⣿⣿⣿⣿⣷⣶⡶⠋⠉⠉⠁⢿⣿⣿⣆⣣⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣧⣿⣿⣷⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢾⣾⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠿⣷⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠈⠀⡀⠀⠀⠀⣀⡤⠄⢀⣰⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠉⠀⠀⢪⠤⢴⠍⠀⢀⣼⡁⠀⠀⣼⠃⢐⣳⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢤⠀⢠⠂⠂⠀⡋⠀⣈⢻⡿⠖⠛⠛⢳⣦⣾⣿⡇⢳⠀⣠⠆⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⠘⢀⣧⢀⡄⠀⠀⠀⠉⠀⠇⠀⠃⠶⣬⣿⢟⣿⡟⠀⠲⠁⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣯⠈⠄⠀⣿⡆⠎⠀⣰⠀⣾⣦⣾⣿⣿⡿⢆⠀⠀⠀⡠⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣥⢼⡄⠈⣻⠄⠀⠀⠀⠀⣿⣿⣿⢾⣿⢨⡿⣢⠄⠘⠑⣠⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠘⠳⠤⠇⠀⠈⢱⠀⡔⠀⠑⠁⣸⣿⣿⣾⡟⠀⠀⠀⢇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢹⠀⠎⠀⠀⠀⡄⠸⣧⠀⠘⢋⠿⣼⣿⠇⠀⠂⠀⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠑⠀⠀⠀⣄⣧⠀⠉⢄⣤⣯⣤⠸⠃⠀⠐⢡⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡆⠄⢄⠆⠀⠀⠘⠙⢧⠀⠈⠠⣸⡿⠁⣀⠀⡤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢅⠀⠰⠦⠄⢴⣤⣢⣄⣠⢿⠅⣀⠄⠈⠄⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠎⢀⠀⠀⠀⡩⠋⣉⣸⠅⠈⡀⢄⡾⠃⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄⣠⡈⣆⠀⠀⡤⠾⠋⠀⠀⢤⡤⠎⡀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢂⡀⠈⠈⠉⠁⠀⣀⣀⡴⠟⠋⣠⡔⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⢑⢖⠒⣛⢚⣿⠏⠃⣠⡴⣠⠍⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠟⠚⣇⠀⠄⢈⠤⠟⠉⠁⠀⠀⠀⠀⠁⠔⠐⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠴⠊⠁⠀⠀⠀⠀⢀⠴⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠈⢇⣁⣶⠒⠒⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢑⠁⠀⢄⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠣⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠒⠛⠛⠋⠉⠉⠛⠛⠓⠲⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⡠⠴⠒⠒⠒⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠶⠶⠤⡀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠈⠙⣆⠀⠀⠀⠀⠀⠀⠀⣰⠛⠉⠀⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⢠⡏⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⣠⣤⡀⠘⡆⠀⠀⠀⠀⠀⣸⠃⢀⣀⡀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠈⣧
⣸⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢀⣾⣿⣿⣿⡆⢿⠀⠀⠀⠀⠀⡏⣰⣿⣿⣿⣦⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡟⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘
⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠈⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢿⢿⣿⣿⣿⡿⠀⢀⡏
⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠈⠛⠟⢫⠞⠀⠀⠀⠀⠀⠀⠘⢯⠻⠿⠟⠁⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⣀⣀⠀⠀⠀⠀⠀⣀⣠⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣓⣲⣶⣤⣤⣤⣤⣤⣴⣶⣒⣛⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⡋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⠉⠛⠻⢿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠙⢿⣿⣿⣿⣿⣆⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡆⠀⠀⠀⢻⣿⣿⣿⣿⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⣿⣿⣿⣿⡇⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⣿⣿⣿⡇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣈⣿⣿⡟⠀⠀⠀⠀⣾⣿⣿⣿⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⢀⣾⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠉⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠛⠿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⢉⠉⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠸⠶⣤⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⢷⠃⡏⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⣸⣧⠀⢢⠄⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⢦⠀⠁⣤⠀⠀⣤⣠⠄⠀⠰⠬⠀⠀⠄⠀⢙⡿
⠀⠀⠀⠀⠀⠀⠀⠉⢻⠄⡟⠀⠀⠀⡄⠀⠀⠀⠀⠠⡄⢛⠂⠘⠴⢆⠙⠆⡀⠀⠁⠀⠀⠀⠇⠀⠀⠘⡄⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⡀⠀⠀⠀⠀⠘⠀⡒⠙⠂⠀⠀⠀⠄⠠⡙⠛⠀⠀⠀⠀⠀⠀⠐⡀⠀⠰⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡌⠀⠀⠀⠀⠀⠀⠆⠡⠀⠀⡄⠘⠀⠄⡀⠀⠻⣨⠆⠀⠴⠀⠀⠀⠀⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣀⠁⢀⡄⠀⠀⢂⠀⠀⠀⠁⠂⡀⠀⢈⠆⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⣘⡣⠀⠠⣅⠀⠒⠀⠂⢰⡫⠀⠀⢈⡅⠌⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠠⢂⠈⠁⢀⠀⠑⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠀⠀⠀⠀⠈⠀⠈⠀⠄⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⠀⠀⠟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠅⠀⠀⠄⠀⠂⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⣩⠀⠀⡄⠀⡀⠀⠞⠀⠀⠰⠀⠀⠁⠀⠂⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠒⠀⠀⠰⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡇⠀⠀⠀⠀⠀⠆⠀⠀⠀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠠⠠⠀⠀⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⢀⠀⠀⠀⠀⠴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣈⠀⠶⠚⠚⠀⡂⠀⠘
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠲⠆⠀⠀⡘⠁⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⣤⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠁⠋⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠊⢠⠁⠀⠀⠀⠀⠂⠀⠀⠐⠰⠄⠀⠀⠀⡀⠄⠀⠀⠈⠀⠀⢀⡠⠁⠂⠀⠀⠀⢰⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠄⠀⠀⡠⠀⠀⠀⠀⠂⠠⠈⠁⠀⠀⠠⠄⠀⠀⠀⠀⠀⠙⠃⡄
⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⢄⡀⠀⡐⠀⠀⠄⣀⠴⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁
⠀⠀⠀⠀⡠⠀⠤⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⡘⠀⢀⠈⠘⠧⣄⠀⠘⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠐⢀⡽⣀⠀⠀⠀⠀⣠⡴⠂⣀⠄⠁⠀⢩⠄⢀⡀⠁⠄⠀⠈⠰⣄⡈⢷⡄⠀⠀⠀⣰⠠⢀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⢠⣦⠀⠀⠀⣿⠠⡈⢿⣄⡀⠤⠀⠀⠀⠁⠀⠀⠀⠒⣤⠋⠁⠨⣇⠀⠀⠠⠔⠋⠀⠈⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢃⠀⠀⢹⡀⠈⠀⣈⡗⢂⠀⠀⠀⠀⠀⠀⠠⡀⠒⠖⠀⢸⠇⢀⣴⠎⠁⠀⠀⠀⣀
⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⡶⠀⠀⠃⢀⣀⡬⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠑⣀⡔⠋⣁⠐⠀⠀⠀⠀⠀⠀⠁
⠀⡘⠀⠀⠀⠰⠁⠀⠀⠀⠀⡘⠀⠀⠁⢐⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⢚⠣⠀⠴⠫⠄
⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠄⠒⠂⠀⠀⠀⠂⠀⢀⠀⣀⠀⠀⠂⠢⠀⠀⠀⠠⠀⢀⠀⠀⠀⢀⠀⠀⠈⠀⣀
⠀⢨⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠉⠀⠂⡃⠀⠀⠀⠀⠀⢀⡅⠂⡱⠀⠄⠀⠀⠐⠑⠀⠀⢀⡀⠈⠑
⠀⢉⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠈⠀⣀⠀⠀⠀⠀⠀⠀⠲⠁⠈⠀⠠⠉⢀⠀⠀⠸⠀⠀⠀⠁
⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠛

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

⠀⠀⠀⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂
⠀⠀⠀⠀⣠⣽⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣾⡯⡀
⠀⠀⠀⠀⠈⡻⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⠵
⠀⠀⠀⠀⠀⠐⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠈⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡛
⠀⠀⠀⠀⠀⠀⠀⠈⢩⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣠⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣸⣿⡇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⢾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣸⣿⣁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⠋⠟⠋⠉⠻⣿⣿⣿⣿⡿⠻⢿⣿⣿⣿⡿⠟⠉⠻⠏⠳⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣦⣼⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠙⣿⣿⣿⣿⠉⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⣿⣿⣿⣿⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠿⣿⣿⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡀⠠⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣀⣀⣁⣀⣈⣠⣏⠠⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⣠⠖⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⢀⣀⣤⣄⣀⠈⠀⠤⠀⡀⠾⠅⣀⣀⣉⣴⣒⣀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡒⠀⢀⣠⣀⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠒⠋⠉⠙⠉⠉⠁⠀⠀⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠛⠒⠛⠓⠂⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⢀⣀⣀⣀⣀⢀⣀⠀⠀⠀⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢠⠤⠄⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣀⠶⢧⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⣤⡀⠘⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢵⠶⣴⣿⣷⡴⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠋⠛⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠠⠀⠠⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡔⠀⠀⢸⣶⣞⢬⣷⣶⣾⠠⠀⡐⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⢿⣡⠄⡀⢠⣼⣏⣷⣝⣿⣤⠀⡀⢤⣹⢿⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣾⠁⠀⠉⢲⣾⠟⣿⡟⢻⣶⠊⠁⠀⣽⣾⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡙⢻⡇⠀⠀⠘⡇⠄⠈⠀⢄⠏⠀⠀⠀⡿⠋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣉⠂⠃⠀⠀⠀⠘⡂⢈⠀⡊⠀⠀⠀⠀⠃⢊⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠰⢁⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠋⠁⠀⠀⡀⢀⠀⢈⢋⡃⠀⠀⢀⡀⠀⠀⠉⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⡄⠀⠀⠀⠀⠿⡀⡄⢬⡁⣩⢄⡄⣸⠃⠀⠀⠀⠠⡤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢜⡴⠛⠁⠀⠠⣤⡐⠂⠄⠮⢮⣟⣧⠾⢆⡠⠚⣠⣤⠀⠀⠙⠳⣜⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⠁⢀⡘⠃⠚⠉⡄⢶⡀⡀⢴⡶⣿⡷⣶⢄⡀⣱⠖⡌⠙⠀⠋⣀⠁⠉⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠒⠒⢲⠏⠀⠐⢶⣆⠀⠘⣧⠀⢠⠴⠻⠳⢄⠀⢸⡟⠄⢀⣶⠦⠀⠈⢶⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣯⣀⠀⠈⠋⠁⣀⣩⣱⢂⡗⢰⡀⣰⢐⣇⢳⡩⣁⡀⠙⠁⠀⢀⣨⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠋⡩⠛⠻⢂⣶⣀⣷⡏⠘⠋⠚⠷⠟⠎⠛⠈⣷⣆⣘⣆⠚⠛⠫⡈⠣⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠐⠂⠂⠓⠁⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠙⠂⠂⠒⠈⠒


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠆⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢰⠀⠀⣤⠀⢀⠀⠀⢰⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠔⠀⠁⠒⠣⠀⠓⠀⠉⠘⠁⠘⠚⠀⠀⠈⠉⢨⠀⠃⠀⠈⠁⠓⡃

⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⣾⣷⡄⡀
⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⢠⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⢸⣿⠌⡌⣷
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡄⢀⡀⠀⠀⠀⢠⣿⣿⢣⡼⣿⢈⣧⠘⣷
⠀⠀⢠⣄⠀⠀⢀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⡄⠠⠂⠀⠀⢠⢳⣜⣧⠀⠀⣠⣿⣿⠟⣸⡇⣿⢸⣷⢲⠈⠃
⠀⠀⠉⡀⠀⠀⠀⠀⠦⡐⠐⠂⡀⠀⠀⠰⢊⣰⢃⠀⠀⠀⠘⣷⠻⠎⣡⣴⣿⡿⡃⣴⡘⢁⠏⢸⣿⢸⡆⢰⡄
⠀⢀⠁⠁⠀⠀⠈⠘⠀⢣⡠⠀⡞⠢⠄⣀⡀⠀⠀⠀⠁⠀⢿⣿⣿⡷⠿⢟⢻⣾⣷⡙⢡⣿⢠⢲⣏⠸⡇⣧⠁
⠀⠟⢐⠀⠀⠀⠈⠘⠀⠀⠀⠔⠁⡜⠀⠄⠈⠎⠒⠀⠀⠀⠀⢫⣶⣾⡏⣿⠿⡷⠉⣴⣼⣿⢸⢻⣿⢦⣌⢹⡀
⠀⡆⢸⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠙⠖⢤⠴⠣⠀⠀⠀⠀⠀⠘⣣⣙⢃⡌⣴⢰⣿⣻⠆⡟⣾⣻⣿⢸⣿⠘⡇
⠐⠁⣤⠀⢨⠀⢠⠀⢡⡰⡀⡄⠠⠀⢧⠈⠂⠣⠀⠀⠀⠀⠀⠀⠫⠏⣿⢣⣿⢸⡇⡿⡐⢰⣿⢹⣿⢸⣿⠀⣧
⠀⢠⠹⠀⠀⠀⢨⠀⠀⠀⠛⠱⡧⠁⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠸⢹⠸⢡⡄⣿⠈⣿⣼⡏⣿⣿⢀⢹
⠀⡣⠈⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⣻⠇⣿⢰⡏⣿⠇⣿⡋⣾⡌
⠀⠀⢠⠃⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣿⠘⢱⡟⠀⢿⠇⢫⡄
⠀⠀⠀⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡄⡾⠁⠆⠘⠀⠈⡃
⠀⠀⠂⠀⡜⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⡇⠀⡾⠀⠀⡼⡀⡁
⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢠⣡⠀⡇⢽⡇
⠀⠀⠀⠈⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢏⣾⡏⣴⡆⠻
⠀⠀⠀⡀⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⢃⣼⡟⣰⡟⠀⠰
⠀⠀⠘⠀⠀⠀⡀⢀⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⣾⠟⢠⠟⣴⢠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠋⢀⠠⣾⣿⠘⣿⡇
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⣽⣿⠸⣿⣿⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢿⣿⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⠀⠘⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠶⠒⠒⠒⠒⠒⠒⠶⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⣀⡤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣄⡀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢀⠴⠖⠦⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⡇⠀⢠⣾⣿⣷⡸⡆⠀⠀⠀⢠⡇⣴⣾⣶⡄⠀⢸⡀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⡇⠀⣿⣿⣿⣿⣧⡇⠀⠀⠀⢸⣼⣿⣿⣿⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢧⠀⢻⣿⣿⣿⣿⠃⠀⠀⠀⠈⣿⣿⣿⣿⡿⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠈⢧⣀⠉⢋⡵⠃⠀⠀⠀⠀⠀⠘⢎⠛⠋⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⢀⠤⠶⡦⠤⢤⡤⠤⢤⡤⠤⢶⠶⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⣿⣀⣀⣇⣀⣀⣇⣀⣸⣇⣀⣸⣀⣀⣽⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⢿⠉⠉⡟⠛⠛⡟⠛⢻⡟⠛⢻⠉⠉⣻⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠈⠳⠶⠧⠤⠴⠧⠤⠼⠧⠤⠼⠦⠞⠁⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⠤⠤⠤⠤⠤⠤⠶⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠠⠀⣴⣶⣶⣶⡄⠉⠀⠀⠀⠀⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⣰⡀⠻⠿⠿⠟⠃⠸⠂⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠘⢿⠟⠀⠀⠀⠰⠆⠀⠀⠘⠁⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣤⣾⣿⠟⠀⠃⠀⠈⠀⣠⣶⣶⣦⣄⠀⠀⠀⠀⠀⠻⣿⣷⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠉⢀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣷⣄⠀⢰⠄⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠆⠀⠈⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠠⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠺⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠛⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠿⠟⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⡀⠀⠈⠙⠛⢿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⡟⠀⠀⠀⠀⣠⡀⠘⠋⠀⣤⠀⠀⠀⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⠀⠀⠀⠺⣿⠗⠀⠀⢹⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣽⣿⣧⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠾⠿⣿⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣭⣥⣤⣶⠾⠃⠀⠀⠀⠈⠻⠿⠋⠛⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣛⣛⣛⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⢻⡟⡛⢻⡿⣻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠃⠀⠀⢀⡠⠴⡚⠍⠉⠉⠙⠉⠉⠉⠩⠓⠦⢄⡀⠀⠀⠘⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡛⣿⠆⢀⣞⡍⢊⠀⠐⠀⠀⣀⢤⡀⠠⠀⠁⠂⠀⠑⢩⣳⡀⠰⣿⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⣿⣶⠝⡩⠂⠀⠀⠀⠀⢸⣿⣾⠇⠀⠀⠀⠀⠀⠀⠐⢍⠻⣶⣿⢰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⡄⢿⣧⠸⣯⠈⠀⠀⠀⠀⠀⠀⢹⣾⠛⠋⠙⢠⣄⠀⠀⠀⠀⠀⠁⣽⠇⣼⡿⢠
⠀⠀⠀⠀⠀⠀⠀⢤⢻⣾⣿⣦⣘⣧⡀⠀⠀⠀⠀⠀⢸⣿⣀⣀⣠⣤⣈⠀⠀⠀⠀⢀⣼⢃⣴⣿⣿⡟⡤
⠀⠀⠀⠀⠀⠀⠀⡰⣿⣾⣿⣿⣿⣿⣿⣦⣄⢀⡠⣴⣿⣿⣿⡿⠿⠚⠋⠈⠶⣄⣴⣿⣿⣿⣿⣿⣿⣾⢂
⠀⠀⠀⠀⠀⠀⠀⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣇⣽⡾⠿⠶⢶⠀⣀⣴⣾⡀⠈⠻⣿⣿⣿⣿⣿⣿⡥
⠀⠀⠀⠀⠀⠀⠀⠀⣽⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣩⣍⡉⠛⢋⠈⣿⣷⣄⣀⣸⣿⣿⡿⢿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣲⠿⣟⣻⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⢶⡟⠀⠜⢳⣿⣯⡭⢬⣿⣟⣻⠿⣇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⠟⠋⣿⣿⣿⣿⠺⣿⣿⣿⣿⠉⠁⠄⠀⣹⣿⣿⣶⣤⣼⠿⡿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⣿⣿⡻⣿⣆⢹⣿⣿⣿⡀⡀⠀⢰⣿⣿⠿⠅⠤⢱⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣿⣿⣷⣌⠙⠄⢿⣿⣛⡛⣿⡛⣻⣿⣿⣧⡄⢀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣶⣮⣸⣿⣿⣿⠿⢶⣿⡿⠋⣰⣿⣿⡆⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡟⣠⣾⠁⢸⣾⣿⣿⣿⣧⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⡌⠿⣻⣏⣉⣟⠿⢥⠼

⠀⠀⠀⠀⠀⠀⠀⡌⠀⡀⠀⡥⠒⠉⠀⢀⡤⢲⠎⢀⠴⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠙⣟⠀⠀⠙⣆⠠⡇⡇⢀⡔⠁
⠀⠀⠀⠀⡀⠀⣸⠃⢀⠀⢰⠁⢀⣀⣰⣋⣠⣤⡴⠧⠒⠀⠀⢀⡠⠤⠒⣀⠀⠀⠐⠂⢀⡂⠄⠀⡀⠀⠀⣿⠀⠀⠀⠘⣿⣷⢷⣞⡀⠀⢀
⠀⢘⡐⢰⠃⡰⠃⢀⠈⡠⠃⠀⠘⠁⡝⠁⠀⢀⣄⠤⠀⢀⡴⣋⠀⠀⠀⠰⠋⣩⠟⠉⠉⠉⠉⠛⠧⣄⠀⢸⡇⠀⠀⠀⠸⣿⡾⡁⠀⣠⠋
⠀⢸⡇⣿⠞⠁⠶⢉⡼⠀⠀⣈⠀⡼⠁⣄⠐⣠⠃⣀⡶⠫⠤⠅⡦⠤⠖⢊⡉⠀⠀⠀⣰⣷⣶⣶⡊⠈⠳⣌⣇⠓⠠⣄⠈⣿⡇⢧⡴⠁
⢠⡞⣸⡏⠀⣀⡰⠋⠀⠀⣀⡵⠊⠁⣀⣭⣴⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣿⣿⣿⠃⠀⠀⡈⠻⣦⣀⠉⢠⣿⣧⠘⡇
⠏⢰⡿⠀⠀⣽⠁⢀⣴⠟⢉⣴⡶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡄⠈⠉⠐⠀⣹⣷⣿⣿⣿⣆⡿⣄
⠀⢸⡇⠀⢰⣿⡾⠋⠀⣰⣿⢋⣤⡁⠀⠀⠀⠀⠀⠀⠀⠐⠢⢀⣉⣉⣉⣙⣳⣤⣀⣘⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⡈⢹⣿⣿⣿⣿⠇⠙⣆
⠀⢸⡇⠀⣼⣿⠱⠆⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢲⣤⠤⠤⠤⠞⠋⠉⠁⠈⠉⠉⠛⠻⣿⣿⣿⡀⠀⠀⠀⠉⠹⣿⣿⣿⣿⠀⠀⠸
⠀⢸⣿⣰⣿⡏⢀⣶⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠋⠙⢶⣄⠀⠀⢠⣿⣿⣿⣿
⠀⢸⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣿⣿⣿⣿⣿⡆⠀⣸
⠀⢸⣿⣿⣿⣿⡏⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣇⣰⡟
⠀⠈⣿⣿⣿⣿⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿
⡄⠀⣿⣿⣿⣿⣇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡀
⢷⣴⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡇
⠈⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇
⠀⢹⣿⣿⣿⣿⣿⣷⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠄⠀⣿⣿⣿⣿⣿⡇
⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⠍⢸⣿⣿⣿⣿⣿⣷
⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⡿⢣⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⣃⡤⠾⡟⣻⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣄⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⢀⠀⠀⠀⠀⢀⡞⠀⠀⡇⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡼⣿⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⢛⣻⣧⠀⢰⣯⠄⠀⠀⡞⣼⠃⣠⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣧⣤⣦⣤⣀⣀⠀⢀⢒⣻⣷⡒⣶⣻⣧⣤⣤⣿⣿⣾⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣴⣿⣿⠟⠉⢹⣿⡏⣿⣿⡃⠀⠈⠉⠉⡿⡉⠉⡏⢹⠛⠛⠻⠷⠭⣽⣯⣷⣿⠿⣿⠟⠛⠛⡛⢻⡿⠁⠀⠀⠀⣠⣿⣿⠿⠛⠛⠛⠻⠿⠿
⠛⠉⠀⠀⠀⠀⢿⣷⣜⢿⣷⣦⣤⣤⣴⣷⣷⣶⣷⣾⣤⣀⠀⠶⠶⣿⣿⡛⢛⡛⣟⣋⡁⢰⡇⣼⣇⠀⠐⠒⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠉⠀⠀⣿⣷⣾⣿⡏⠀⠈⠉⣉⣽⣿⣿⣝⣋⣛⣏⡁⢀⣼⣷⢿⣿⣤⣤⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣦⣻⣷⣦⣽⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⣀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠓⠶⣿⣿⣟⣿⣿⣿⣿⣿⣦⣤⡀⠀⢀⠠⢀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣷⣿⣿⣯⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⢿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣦⢸⣷⣤⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠙⠻⢿⠿⣿⣿⣿⣿⣿⣿⠿⠷⠿⠛⠀⣴⣿⣿⣿⣿⣿⣿⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠟⢻⣿⣿⣷⣿⣦⣀⠀⠀⣸⣿⣿⡿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⣿⢿⣿⣿⡤⠀⣼⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⣨⠏⠀⣿⣿⣅⢀⡘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⣰⣿⣿⣿⣿⣇⠈⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣷⡟⠙⠁⠀⢹⣿⣿⣿⣿⣿⠀⠀⠹⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡀⠀⠀⠘⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠴⠶⠷⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⡖⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⠍⠀⠒⠀⢉⣙⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢱⣤⣿⣇⣼⣀⡔⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⡄⠀⠀⢤⣹⣿⣿⣿⢥⣬⣽⣿⣾⣥⠤⠀⠀⢰⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⣟⠃⠐⠺⢿⣯⣝⣻⠾⠿⣋⣠⣿⠷⠶⠄⢉⡿⢯⡁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣌⣷⡶⠀⠈⠀⠈⠀⠀⠚⢙⣽⣿⢿⣯⣽⣿⣿⠻⢦⠀⠀⠀⠀⠀⠀⠐⣲⣮⠤
⠀⠀⠀⠀⠀⠀⠀⠰⠏⠙⠀⠀⠀⠀⠀⠀⠂⠈⠹⠾⡛⠹⠛⠿⠙⠀⠀⡠⠊⠀⠀⠀⠀⠈⠁⠙⠆⢀⡀⢀⡀
⠀⠀⠀⣈⣣⣞⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⡄⠘⣴⣾⣷⡄⢀⠁⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢿⡯⡤
⠀⠀⠀⠀⠸⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠎⢈⣿⣆⣾⣧⣿⣔⠍⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⣿⣿⣿⣿⣿⣿⡠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⢀⡀
⠀⠀⠀⠀⣑⣾⡴⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣼⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡿⠧
⠀⠀⠀⠀⠀⠘⠇⠀⡀⠀⠀⢀⠔⠒⡤⡴⣾⣿⣝⣛⣛⣻⣏⣿⣿⣿⠟⢿⠒⢀⠔⣦⡀⢠⡀⡤⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠠⢽⣾⣃⠀⠛⠶⠶⣤⣤⣬⢟⣩⡍⣿⣍⣽⣡⠰⠄⠄⢦⡽⠚⠛⠁⠶⢿⡗⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠙⠿⠛⠙⣿⣽⠉⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣀⣀⣀⡀
⠀⠀⠀⢀⠞⠉⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠑⢄
⠀⠀⠀⢸⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⢀⡤⠖⠒⠦⣄⠀⠀⠀⢀⣀⣀⡀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢸
⠀⠀⠀⠀⢣⡀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⢀⠎⠀⢀⣀⠀⠘⣦⠀⡰⠋⠀⡀⠉⢢⡀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠉⢧⠀⠀⠈⠓⠢⣄⠀⠀⢠⠎⠀⠀⠀⢸⠀⢰⣼⣿⣷⠀⢸⡀⠃⠰⣾⣿⡆⠀⢳⠀⠀⠈⢧⠀⠀⠀⡠⠔⠊⠀⠀⢠⠞⠁
⠀⠀⠀⠀⣀⠤⠚⠃⠀⠀⠀⠀⠈⢣⠀⡜⠀⠀⠀⠀⠸⡄⠈⠛⠛⠁⠀⣸⠀⣄⠀⠉⠉⠀⠀⡞⠀⠀⠀⠘⡆⢠⠊⠀⠀⠀⠀⠀⠻⠤⣄⡀
⠀⠀⢠⠊⠀⠀⠰⠂⠀⢢⡀⠀⠀⠀⣇⡇⣠⣴⠀⠀⠀⠈⠢⠤⠠⠤⠖⠁⠀⠈⠒⠠⠤⠔⠊⢀⣨⠷⡄⠀⣇⡇⠀⠀⠀⢠⠒⠒⠦⠤⠀⠉⢦
⠀⠀⠸⡄⠀⠀⠀⠀⠀⣸⣅⠀⠀⠀⡏⡇⠁⠈⠛⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠚⡟⠁⠀⠀⠀⡏⣇⠀⠀⢀⣻⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⢨⠓⠲⠤⠶⠚⠁⢈⢧⠀⠀⡁⢇⠀⠀⠀⠀⠙⢦⣍⡙⠛⠓⠒⠚⠛⠛⠉⠉⣀⣴⡾⠀⠀⠀⠀⢠⠇⡃⠀⢀⣏⠀⠑⠦⠤⠤⠴⢾⠁
⠀⠀⠀⠀⠑⡤⣄⣀⡤⠴⠋⣸⢳⠔⠁⠘⡄⠀⠀⠀⠀⠀⠻⣿⡿⠷⠖⠒⠒⠒⠺⠿⣿⡿⠁⠀⠀⠀⠀⡞⠀⠱⣤⢺⠈⠢⢄⣀⣀⣀⡴⠃
⠀⠀⠀⠀⠀⠣⢄⣀⣀⡤⠖⢁⠜⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠘⢦⣀⡀⠀⠀⢀⣀⣠⡼⠁⠀⠀⠀⢀⡜⠁⠀⠀⠸⣄⠓⢤⣀⣀⣀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠊⠁⠀⠀⠀⠀⠀⠈⠣⣀⠀⠀⠀⠀⠀⠙⠦⣤⣀⣤⠴⠋⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⠑⠒⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠲⠶⠶⠒⠒⠋⠉

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠈⠉⠀⢀⠈⠀⡁⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⡀⠄⠈⠀⠀⢠⡄⠀⡌⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠶⠀⢀⣠⣅⠀⠀⠀⠀⢀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠘⠀⡀⠩⢄⣩⠥⣔⠃⠀⢠⣀⠂⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢡⠀⠈⢠⡖⣤⢰⡆⣁⢀⡄⢀⠠⠂⡄⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢐⣤⡑⠀⢰⣇⠃⠀⠅⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠰⠋⠈⣴⠀⡦⠈⢡⠞⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠀⠀⣀⠶⠀⠄⠚⠠⡶⢶⡉⠁⠀⢂⡢⣤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡄⠁⠈⠓⠒⢤⠸⡏⢠⠈⣧⢠⠖⠉⠁⠈⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢠⠀⠀⠐⠀⠀⠀⠢⠀⡆⠀⠀⠀⠉⣠⠀⠤⠁⠀⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠐⠀⠀⠀⠀⠀⠈⢇⡀⠀⠀⢠⡜⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⡀⠀⠀⠀⢀⣠⠸⠟⠸⠁⠀⠀⠀⢀⠀⠀⠈⢀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⣀⢞⠁⠀⠀⢠⠁⠈⠀⠀⠀⢳⠀⠀⠀⠈⠳⡄⠀⣟⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠂⠀⠀⠀⡂⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣤⠀⣀⣠⡀⢸⡀⠀⠀⠀⠀⢰⠂⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠃⢸⠃⠈⠙⡏⢙⠁⡃⠀⠀⠀⠀⠀⣄⡀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡆⢻⣄⠀⠀⢿⣨⡀⡇⠀⠂⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⡇⠈⢦⠀⠈⣿⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡚⡽⠢⡶⠀⣸⠀⣛⡇⠀⢀⣠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠆⠀⣀⢄⡴⢛⠃⡜⠀⡰⠃⣰⣿⠇⡀⢏⠉⢁⡀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠃⠡⠀⠴⠦⠀⢀⠀⠐⢁⣨⡃⠐⡇⠀⣿⢸⣣⠀⠀⠁⠸⣇⠠⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠐⢃⠀⠐⣤⠔⢂⠁⠛⣪⠀⠖⠋⠉⠁⢰⡿⠄⠈⠚⠃⠒⠂⡰⠓⠘⠣⠀⡄⠀⠀⠀⣠
⠀⠀⠀⠀⠠⠆⠀⠀⠀⠈⠁⢾⠉⡇⠀⡀⠂⠐⠤⠄⠘⢘⠛⣿⠀⠶⠖⠚⠻⣅⠀⠈⠳⠉⢡⠄⡂⠉⠁
⠀⠀⠀⠀⠀⠀⡂⠐⠀⡀⠀⢠⠜⠁⡌⣡⡬⠿⢲⠲⠖⡰⠀⢻⣰⠖⠀⠀⠀⠄⡆⠀⣄⢂⡀⠈⠶⠤⣠⠐
⠀⠀⠀⠀⠀⢄⢡⡀⠀⠀⢃⠀⢲⡤⠴⢋⡔⠀⠀⠨⠐⠤⠤⠀⠉⢅⠀⢆⠀⢂⠙⠁⣤⡀⢋⣀⠀⠀⡡⣀
⠀⠀⠀⠀⠀⠀⠈⠉⠘⠇⠀⠠⠪⠁⠀⠈⠄⠀⠀⡄⠈⠂⠀⢋⠀⣎⠁⡴⠉⠉⠀⠦⠈⠁⠀⠀⠀⠀⠀⠈

⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣦⣤⣶⣶⣶⣶⣶⣶
⣿⡿⡉⠿⣯⡿⢽⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠋⠉⠁⠀⠀⠀⠀⠈⠉⠙⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⢀⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⡀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⢺⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠙⢷⣦⣀⡀⠀⠀⠀⠀⠀⣀⣤⡾⠋⠀⠀⠀⣠⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠈⠙⠛⠻⠿⠿⠿⠛⠋⠁⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣄⣀⡀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉⠁



⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣛⣿⣟⣿⣛⣻