Basketball Emojis & Symbols

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

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣛⠋⠉⠉⠉⠉⠙⠛⠷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠈⠙⠻⢶⣤⡀⠀⠀⠀⢸⡟⠈⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⣠⡿⠁⠀⠀⠀⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣴⠿⢿⣄⠀⢀⣠⡶⠟⠉⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣤⡶⠶⠟⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⢀⣻⣶⠟⠉⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠉⠙⣷⡀⣀⣀⣀⣀⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠉⠀⠀⢀⣠⡾⣿⠉⠉⠉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⠀⠀⠀⠀⢠⡾⠋⠀⢹⣇⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⣠⡴⠟⠋⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠈⣿⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣤⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⣿⡆⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⣿⣷⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣦⣴⣾⣏⣠⣤⣤⣴⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠉⠻⠿⠿⢿⣿⣿
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢀⣿⡿
⠀⠀⠀⠻⣿⣿⣶⣤⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢀⣾⣿⡇
⠀⠀⠘⠛⠻⢿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢠⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣶⣤⣀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣷⣾⣿⣿⣿⣿⣿⠀⠀⠀⢀⣠⣤⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡻⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⠿⠿⠿⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣵⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣻⣯⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⣀⣴⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣉⠉⠉⠉⠙⠿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣇⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠇

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠟⠿⣿⠟⢻⠿⢿⢿⠻⣿⡿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣷⣾⣷⣿⣶⣿⣷⣾⣿⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠛⠉⠉⠉⠉⠛⠻⢿⣿⣿⡿⢶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⣶⣶⣶⣦⣤⣤⣤⣀⣀⣀⣀⣉⣻⣿⣷⣬⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⣿⣿⣿⠛⠛⢿⣿⡁⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⣠⡾⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣧⡀⠈⠻⣿⣄⠀⣘⣿⣿⣦
⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄⣤⣿⣿⣿⣿⣿⡿⣿⣷⡀
⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⡿⠿⣿⣏⠁⠀⠹⣿⣷⡀
⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⠿⠿⣿⡇⠀⠀⢻⣿⣆⣀⣀⠹⣿⣷
⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⡿⠟⠛⠉⠀⢀⢈⣿⡇⣠⣴⣿⢿⣿⡟⠿⣿⣿⣿
⠀⢸⡏⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⡜⢸⣿⣿⡿⠋⠀⠀⣿⣿⡄⠀⠹⣿
⠀⣾⡇⣀⣤⣶⣿⣿⣿⣿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣾⣿⡟⠁⠀⠀⠀⢿⣿⣷⠀⠀⢻
⠀⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢀⣾⣿⡟⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⣸
⠀⢸⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⣴⣿⣿⠟⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⣿
⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣠⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢸⣿
⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⢁⣴⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⣿⡿
⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⣠⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⢀⣴⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣶⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢷⣦⣤⣤⣀⣀⣀⣀⣀⣤⣤⣴⡾⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡾⠛⢁⣠⣴⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠰⣿⣿⠟⢁⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣦⠀⢀⡀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⢿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠁⠰⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣈⠙⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠀⣴⣶⣤⣄⡉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠛⠋⡉⠁⠸⢿⣿⣿⣿⣿⣷⣦⣄⡉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⣠⣾⣿⡏⢠⣶⣄⠙⢿⣿⣿⣿⣿⣿⣿⣷⣤⡈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠀⣼⣿⣿⣧⡈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡉⠻⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡏⢠⣿⣿⣿⣿⣷⡄⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠙⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⢿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣆⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠈⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⡀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠻⢿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣉⠙⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⢿⣿⣿⣿⣿⡿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⡄⢶⣦⣄⡀
⠀⠀⠀⠀⢀⡴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣿⣿⣷⣦⡀
⠀⠀⢀⣴⣿⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⣦
⠀⢠⣾⣿⣿⣿⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣷
⢀⣿⣿⣿⣿⣿⣷⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⢰⡀
⣸⣿⣿⣿⣿⣿⣿⣷⡹⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡟⣸⣇
⣿⣿⣿⣿⣿⣿⣿⣿⣷⡙⣿⣿⣿⣿⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⢡⣿⣿⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣀⣀⡀
⣏⢿⣿⣿⣿⣿⣿⣿⣿⣷⡘⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡿⢣⣾⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⢻⣦⡹⢿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⡟⣡⣿⣿⣿⡟⠈⢳⡀⠀⠀⠀⠀⠀⡾⠁⢹⡆⠀⠈⢙⣿⣿⣿⣿⣷⣤⡀
⠘⣿⣿⣦⡙⠿⣿⣿⣿⣿⣿⣷⠸⣿⣿⣿⣿⢸⣿⣿⣿⠏⣴⣿⣿⣿⡿⠁⠀⠈⢷⡀⠀⠀⠀⣼⠁⠀⠀⣷⠀⠀⣾⠁⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠘⣿⣿⣿⣷⣦⣍⡛⠿⢿⣿⡇⣿⣿⣿⡇⣼⣿⣿⠏⣼⣿⡿⠟⣫⡄⠀⠀⠀⠈⣷⠀⠀⢰⠇⠀⠀⠀⢹⡄⢰⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣶⣶⢠⣬⣭⣍⢁⣍⣭⡉⣨⣭⣴⣶⡟⢹⠃⠀⠀⠀⠀⠸⡇⢀⡟⠀⠀⠀⠀⢸⣇⣼⣿⣿⣿⣿⠿⠿⠟⠛⠛⠉⠉⠁
⠀⠀⣸⣿⡻⣿⡿⠿⠿⠿⢟⣡⣿⣿⣿⠇⣾⣿⣿⡇⣿⣿⠟⢯⡀⢸⠀⠀⠀⠀⠀⠀⢻⣼⠃⠀⣀⣤⣶⣿⣿⡿⣿⠋
⠀⠀⠸⣿⣿⣌⠻⢿⡛⠿⣿⣿⣿⣿⠏⣼⣿⣿⠿⠟⠈⠁⠀⠈⢳⣼⠀⠀⠀⢀⣀⣤⣼⣿⣾⣿⢿⠟⣿⡇⣸⣷⠏
⠀⠀⠀⠈⠛⢿⣷⣶⣿⣦⣽⣆⣀⣀⣀⣀⣙⣿⣆⣀⣠⣤⣤⣤⣴⣿⣶⣾⠿⢿⡿⣿⡉⣽⠋⣸⢿⣤⡏⢹⣿⡟
⠀⠀⠀⠀⠀⠀⠙⢿⡟⣿⠿⣿⣻⠿⣟⢻⡿⣟⠛⠛⣻⠿⣍⠉⣩⠏⠙⢦⣠⠟⠀⢀⡿⢧⣴⠏⢠⡟⢧⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡷⣈⡿⢦⣈⡿⣦⡈⠻⣶⡃⠀⠈⣿⢯⡀⠀⣰⠛⠷⣤⡞⠁⣰⠛⢳⣾⠀⢠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣽⣧⠈⣿⢧⡀⠙⣾⣇⠙⢳⣾⠃⠀⢙⣾⣇⠀⣠⠟⠳⣶⡃⠀⡾⠉⠳⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣻⣇⠀⠙⣾⡃⠙⢳⣞⠉⠛⢦⣞⠁⠈⣻⢯⣀⣼⠃⠙⣾⣅⠀⣸⠏⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⢧⡼⠃⠙⣶⡏⠈⠳⣦⡟⠙⢳⣼⡃⠀⡽⠷⣄⣸⠃⠈⢳⣿⡀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⠛⣆⣴⠋⠙⢦⣴⠋⠙⢦⣾⠉⢛⣾⡁⠀⣸⠿⢦⡀⣼⠋⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⡼⠳⣄⢀⡼⠛⢦⣠⡟⠉⢳⣾⠁⠙⢳⣏⡀⠀⢹⡿⣄⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⢙⣿⡁⠀⣰⠟⢦⣀⡞⠉⠳⢦⡟⠈⠙⢦⣾⠀⠈⠳⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢠⠏⠀⠻⣾⠃⠀⢀⡟⢧⡀⢀⡞⠙⢦⡀⢰⠏⠳⣄⢠⠏⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡽⢇⠀⢀⡜⠉⠣⣀⠞⠀⠀⠙⣾⡀⠀⠀⠈⡿⣄⠀⠀⢹⠦⡀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠈⢳⡞⠀⠀⢠⠟⢦⡀⠀⡼⠁⠙⢦⡀⣸⠁⠈⠑⢤⡟⠀⠈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣠⠏⠹⣄⢠⠏⠀⠀⠳⣼⠃⠀⠀⠀⠙⣯⠀⠀⠀⢈⣷⡀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠙⣏⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⡟⢦⡀⠀⣸⠁⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⣠⡾⠻⣦⠀⠀⣰⠇⠻⣆⠀⠀⣸⠇⠀⠙⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠠
⠀⠀⠀⠀⢀⡤⠂⠀⠀⠀⠈⢷⠀⠀⠀⡏
⠀⠀⠀⣴⡡⠤⠒⠒⠒⠒⠲⡾⠤⣄⣸⠃⠀⢀⡴⠦⡀
⠀⢀⠈⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⡟⠙⠲⣾⡅⠀⠸⡀
⠀⠘⠀⠀⠀⠀⠀⣠⠶⠉⠀⠀⠀⣸⠃⠀⠀⡧⠈⠑⢄⢠
⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⢠⡏⠀⠀⠀⢷⠀⠀⠀⢻⡄
⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢸⡆⠀⠀⢘
⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠈⡇⠀⠀⡘
⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⡧⠀⡰⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠠⠀⠀⢀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢀⡧⠞⠁⠀⢀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢
⠀⠀⠀⠀⠀⠀⠒⠄⣰⣋⡀⠀⡀⢀⡀⠤⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠖⠚⠋⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠓⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠡⠈⠓⠲⠤⣤⣀⣀⣀⣀⣀⣀⣠⡤⠖⠊⢁⠞
⠀⠀⠀⠀⠀⠐⠒⠒⠲⠤⠤⠤⣴⣦⠤⠒⠒⠋⠀⠠⡄⠀⠈⠢⡀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣀⣀⣀⣀⣀⠀⠐⠄⠀⠀⠀⠙⠒⠠⠀⠀⠀⠀⠀⠀⠊⠁
⠀⠀⠀⠂⠀⣀⡤⠖⠒⠊⠉⠉⠈⢹⡏⠁⠀⠀⠈⠉⠓⠲⡄
⠀⠀⢠⠖⠋⠁⠀⠀⠀⠀⠀⣀⡤⢴⣷⠦⢤⣄⡀⠀⠀⠀⠈
⠀⠀⠈⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⡧⠀⠀⠈⠙⢆
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⢳⠄⡀
⠀⠀⠀⢆⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⡃⠁
⠀⠀⠀⠀⠇⢰⡏⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢀⠄⠁
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠃
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⢀⠤⠂⠀⠙⢏⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⢄⡀
⠀⠴⠋⠉⠈⠁⠀⠀⠀⠀⢀⡷⡀⠀⠀⠀⢀⣾⣽⣿⣿⣽⣇⣻⠿⣿⣆⠀⠀⠀⠀⣠⡞⠥⠀⠤⠤⢵⡀⡉⠑⣄
⡌⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⢟⣽⣿⣹⣦⣝⣧⠀⠀⡸⠁⠀⠀⠀⠀⣠⠎⢈⠓⠮⡈⢆
⡇⠀⣀⡴⠊⠁⠀⠀⢰⠀⢰⠀⠀⠀⠀⣿⣿⣿⢟⣯⣾⣿⣿⡏⣿⣟⣿⣯⠀⠀⡇⠀⠀⣀⠴⠊⠁⠀⡸⠀⠀⠈⢾
⢣⡴⠁⠀⠀⠀⠀⢠⠏⠀⠀⡆⡰⠀⠀⢹⣟⣵⣿⣿⣿⣿⡿⣹⣿⣿⣿⡟⠀⠀⢧⢀⠞⠁⠀⠀⠀⢠⠇⠀⢠⠀⡼
⠀⠣⡀⠀⠀⠀⣠⠏⠀⠀⣼⠔⠁⠀⠀⠀⠹⣿⣿⣿⣿⡿⣳⣿⣿⣿⠟⠁⠀⠀⠈⢧⡀⠀⠀⠀⢀⠎⠀⠀⣈⡴⠁
⠀⠀⠈⠑⠢⠶⠥⠤⠄⠊⠁⠀⠀⠀⠀⠀⠀⠈⠛⠿⠻⠿⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⣔⣁⣀⡠⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠋⠉⢉⣥⠞⠋⠁⠉⠉⠉⠛⠓⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠺⣷⣄⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⣀⣀⣀⣤⣤⡤⠶⠶⠶⠶⠶⠖⠒⠒⢀⣄⣀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠈⠙⠛⠷⠶⠶⣶⣿⠷⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢮⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⣀⣠⣤⣤⣶⣶⣾⣷⣶⣶⣶⣶⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣡⣴⠾⠟⠛⠉⠉⠁⠀⢸⣿⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠿⢶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠾⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣷⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣦⣄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⣶⠟⠋⠉⠀⠀⣿⡇⠀⠀⠀⠉⠙⠻⢷⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠸⡇⢀⣴⠟⠁⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠐⡇
⠀⠀⠀⠀⠀⠀⠀⣷⣾⠏⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⣤⡀⠀⠀⠀⠀⢀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣆⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣄⣠⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⣦⣄⣀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣬⣻⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣻⣿⣿⣯⣷⣦⣄⠀⠈⢿⣆⠀⢀⠀⠀⣀⣀⠤⣀⡠⣀⣠⣶⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣧⣽⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⠛⠟⢿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠋⠹⠏⠙⠛⠛⠛⠟⠛⠛⠛⠛⠉⠙⠏⠙⠫

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢄⣶⡿⡫⡠⡦⣮⣲⣢⣶⣤⣬⣯⣖⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢟⠙⢡⣾⠃⠀⠀⠀⠀⠈⠠⠪⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠟⠋⠁⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⢟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠁⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠁⢵⢟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⡿⠁⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⢑⢟⢗⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢠⢾⣯⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⠀⠀⠀⢑⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢀⢠⣟⣽⣷⣄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⡟⠀⠀⠀⣀⣀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢐⣽⣿⡿⠈⠿⣦⠀⠀⠀⠀⣿⡄⣀⣠⣴⣿⡷⠶⠟⠛⠛⠉⠉⠉⢽⣕⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢱⣿⣿⢑⢀⣬⢻⣧⣀⣠⣴⣿⡟⠛⠉⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢁⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠆
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣵⣿⣟⠉⠀⢸⣧⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⢀⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⣵⣻⣿⠀⠀⠀⣿⡄⠀⠀⠀⠙⢿⣦⡀⠀⠀⣀⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢴⣐⠀⢻⣷⠀⠀⠀⠀⠈⡹⢿⣶⣴⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣧⢴⣴⣷⢝⣵⢟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣜⣿⣇⣽⣷⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢜⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠜⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⢘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢜⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠖⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⣠⠖⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⢀⠜⠁⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⢠⠋⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⢰⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢧
⠀⠀⢠⠃⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⢇
⠀⠀⡜⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠘⡄
⠀⢀⠃⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠃
⠀⢸⡀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⢷⡀⠀⠀⠀⠘⣧⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡌⢳⣄⠀⠀⠀⢻⡆⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⢡⠀⠙⠷⣶⣤⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠈⡆⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⣀⣤⡶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⢈⣷⣤⣴⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡞
⠀⠀⠀⠀⠘⢤⣤⡶⠶⠟⠛⠋⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠞⢋⠞
⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠙⢷⣄⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⡴⠶⠶⠾⠛⠛⠋⠉⠉⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⣴⠟⠛⠿⣍⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣾⠃⠀⠀⠀⠈⠛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⢄⣀⠀⠀⠈⠙⠲⠤⣄⡀⣀⣀⠤⠔⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉
⣿⣿⣿⣿⣻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣿⣿⣛⣟⣛

⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠤⠤⠶⠶⠶⠶⠶⠶⠤⠤⢤⣤⣀⣀
⠀⣠⠤⠖⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠤

⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⡰
⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠈⠀⠀⠀⠀⠀⠀⢁⠒⠠⡀⢀⡇
⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⡁
⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠈⢆
⠀⠀⠘⡇⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⢿⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠂⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠑⠠⢀⠀⠀⢀⠤⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⣇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠐⠂⠉⠀⠀⠀⠉⠁⠀⠈⡉
⠀⠀⠀⠀⢻⣀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⣀⣈⣉⣳⣶⣦⣯⣤⡀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⢀⡔
⡔⠉⢔⠋⠙⢇⣠⠋⠘⢄⣀⠜⠉⠂⣀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⢨⠉⠒⢄
⠸⡐⠒⢭⢶⠞⢙⣢⡤⢼⣽⣦⡤⠴⠡⡬⣰⠶⠤⠤⡤⢤⡶⣖⣃⣚⢳⠮⠅⠒⡺⠁
⠀⠙⢦⡠⠻⣄⢀⡽⣄⠀⠈⣿⠁⠀⢧⡸⠁⠈⣯⠁⠀⠈⣧⠃⠀⣸⣎⠀⢀⠜⠁
⠀⠀⠀⢱⠀⡨⢯⠀⠈⣳⠊⠀⠑⣤⠊⠱⣄⠞⠉⢢⢠⠎⠈⢣⡔⠁⠈⣦⠃
⠀⠀⠀⠀⢷⠁⠘⣆⡜⠀⢆⠀⢰⠛⡄⢠⠿⡀⠀⢈⡇⠀⠀⡸⡆⠀⢀⠎
⠀⠀⠀⠀⠀⢣⠀⡸⣇⠀⠈⢦⠇⠀⢱⡜⠀⠳⣀⠎⠸⡀⡰⠁⠹⣀⠎
⠀⠀⠀⠀⠀⠀⠻⣅⠈⢦⣠⠛⢆⠀⡎⢱⡀⡠⠿⡀⠀⣱⡃⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢆⡴⠹⡄⡠⠻⡀⢀⡟⢄⠀⠘⡞⠀⠱⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢻⠁⠀⢣⡸⠀⠈⡆⣸⠳⡀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠋⠱⣄⠞⢣⡀⠀⡼⡁⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⢠⠟⡄⠀⠳⡜⠁⠘⡞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡠⠀⣤⢠⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠒⣓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⢀⡀⠀⠀⠀⠀⠀⠀⠨⠖⠚⠯⠰⣄⣀⠀⠀⡀⠀⠀⠠⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⢙⠀⢀⣘⡿⢀⡙⢣⢬⡏⠙⠳⣶⣤⣤⡌⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣄⣀⣬⣷⡐⣦⣤⣼⣿⣿⣠⣼⣿⣎⣿⣛⠔⣋⢸⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⡟⠛⠛⠿⣷⣿⣿⣿⣿⣿⢻⣿⣷⣄⣀⠀⡘⢟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣩⣿⣿⡿⠟⠛⠓⣦⣀⣠⣧⣀⣠⡞⠛⠛⠿⣿⣿⣿⠏⠟⣻⠇⢀⣠⢁⣸⠓⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠋⡠⠔⠚⠉⡿⠀⠀⡇⠀⢸⡍⠙⠒⢤⡘⢿⣿⣷⠄⡄⣀⠈⣴⣮⡍
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠇⠊⠀⠀⢀⡼⠁⠀⠀⡇⠀⠀⢻⡄⠀⠀⠈⠂⣿⣧⣿⣿⣿⣷⣿⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⠻⡿⣿⡿⠀⠀⠀⢀⡞⠁⠀⠀⠀⡇⠀⠀⠀⠹⣆⠀⠀⠀⢸⣿⣟⣹⡟⣉⣉⡷⠒
⠀⠀⠀⠀⠀⠀⠠⡮⠿⣍⡝⠿⢧⣴⣿⡇⠀⠀⢠⠟⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⣆⠀⠀⢸⣿⣏⣛⡹⠉⡈⡧⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠀⠀⣹⣿⣿⡀⠀⡟⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠸⡆⠀⣸⣿⣧⣟⠐⠆⠈⠐⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣧⡘⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⣰⣿⣶⣿⣿⢀⡠⣀⠈⠁⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⡟⣻⣿⣿⣷⣧⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣸⣾⣿⣿⡻⠟⢿⠏⢍⡍⠈⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣣⠏⠻⠟⣿⣿⣿⣦⣄⣀⡀⠀⡇⠀⣀⣠⣴⣾⣿⣻⡬⣿⢧⣤⠄⠀⠀⡠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠇⠀⢀⡾⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠳⢿⠀⠚⠀⠀⠀⠀⠀⠀⠒⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠚⣋⡭⣿⡿⠿⠻⢬⡟⢻⡿⢻⣿⣿⣷⢚⣉⣀⡀⠺⠆⠂⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⡀⢹⠃⡞⠀⠈⣿⠖⡇⠹⡿⢿⠍⣼⡟⠟⠃⠀⠀⠀⠀⢀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⡀⡄⠀⠼⢻⠀⠓⢲⡄⣀⠸⣎⡇⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠠⠠⢸⡗⠃⠀⠀⢼⠀⠀⠘⡇⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⠀⠠⠄⠀⢾⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⢸⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢶⣶⡚⠿⠭⣭⣭⣉⡀⠒⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⡫⠓⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⠈⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠤⠘⠒⣂⣀⠩⠭⠥⠤⠀⠀⠐⠒⠀⠒⠒⠂⠀⠐⠒⠀⠀⠤⠬⠭⢉⣀⣒⠲⡇⢰⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡡⠄⠒⢉⡉⠤⠤⠐⠒⣒⣀⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣐⣒⠒⠀⠤⠄⣹⠀⡞⠠⡉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠣⠴⣊⣁⡤⠒⠂⢉⣁⠤⠤⠤⠀⠐⠒⠒⠒⠒⠒⠒⠒⠀⠤⠤⠤⠄⣈⡉⠒⠲⠇⢠⡓⠤⠜⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣅⣉⠒⠂⠤⠄⣉⣉⠁⠒⠒⠒⠓⠂⠠⠤⠤⠤⠤⠤⠤⠤⠄⠒⠒⠒⠒⠒⠈⢉⡋⠀⣈⠖⠒⠉⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠬⣉⡓⠒⠂⠤⠤⢈⣉⣉⠉⠙⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠉⣉⣉⣉⠠⠬⠍⠒⠒⣋⡉⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡒⠦⠤⣉⡑⠒⠲⠦⠤⠤⠈⣉⣉⣉⣉⣉⠉⠉⠉⠉⣉⣉⣉⣉⣁⠠⠤⠤⠴⠒⠒⣊⡉⠤⢶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡒⠤⢄⣀⡉⠉⠒⠒⠂⠤⠤⠤⠤⠄⢀⣀⣀⣀⣀⠤⠤⠤⠤⠤⠀⠒⠒⠂⠉⣁⣠⠤⠔⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⡑⠢⠤⣀⣉⠉⠀⠒⠒⠒⠀⠠⠤⠤⠤⠤⠤⠤⠤⠀⠀⠐⠒⠒⠂⠉⠉⣁⣀⠤⢒⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⢑⠒⠤⠤⢉⣉⣙⠉⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⢈⣉⣉⡉⠥⠤⢒⡪⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠐⠒⠒⠂⠉⠉⠉⠉⠉⠍⠉⠉⠉⠉⠀⠒⠒⠒⠒⠂⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠄⠀⠒⢒⣒⡒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⢉⠠⠔⠒⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⢮⡠⠠⢤⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡴⠚⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢳⠄⣀⢱⣄⠀⠈⢧⠀⠈⠱⡍⠁⠐⢴⠒⠒⢤⠖⠛⠢⢞⠉⠁⠑⢏⠀⠉⠙⢄⡀⡀⣡⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⢸⠀⡏⠉⠀⠑⠒⠀⠘⠒⠀⠠⠒⠠⠤⡵⠶⠀⠤⠓⠒⠒⠒⠉⠉⠉⠉⠀⡇⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠉⠉⠚⠃⠐⠀⠠⢤⠤⡤⠤⠀⠠⠤⠀⠠⠄⠤⠤⠤⠤⠤⠀⠤⠤⠐⠐⠒⠈⠉⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠑⠲⠶⠤⠤⠤⠄⢠⣀⣆⣀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡶⠤⠤⠄⠒⢐⠂⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠠⠴⢠⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⡁⢸⠀⠀⠀⠀⢀⣀⣀⡀⠀⠤⠘⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠤⣀⣀⠀⠀⠀⠀⠈⠀⠏⠉⠉⠁⠀⠀⠉⠁⠈⠉⠉⠉⠁⠀⣩⢨⠀⢀⠀⢤⠴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⣈⣹⠉⠉⠀⠐⠒⠒⠃⠐⠒⠒⠒⠒⠲⠖⠶⠂⠀⠀⠂⠀⠉⠉⠁⠀⠀⢸⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠃⠐⠒⠒⠠⠤⠤⠤⠤⠤⠠⠰⠄⠥⠤⠤⠤⠄⠀⠀⠐⠒⠋⠉


⡶⠶⠶⠶⠖⠲⠶⠶⠶⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⢶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠄⠐⠢⠴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠪⡖⠀⠀⠀⠀⠀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠑⠁⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠵⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⠸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⢀⠠⠄⠐⠀⠋⠀⠀⣤⠤⠚⠁⢠⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⢿⠀⣠⣠⣤⠒⠒⠛⠛⠉⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⢀⡀⠀⡄⠢⠐⢀⡂⠀⣟⣁⣁⣀⣯⣠⣄⠀⠀⠀⠀⠀⠀⠀⢐⠄⠀⠀⠀⠀⠀⣸⠲
⠀⠀⠀⠀⣰⠘⠃⠐⡇⠀⠀⠈⠃⠀⠘⠁⠀⠀⠁⠉⠠⡀⠀⠀⠀⠀⠀⠀⡾⠖⠁⠄⠀⠀⠀⣰⠁
⠀⠀⠀⣼⢠⠀⠢⠄⠈⠄⠂⠀⠀⠀⠀⠐⡂⠀⠀⠀⠀⢰⠉⠀⠀⠀⡀⢀⡷⢤⠐⡐⠀⠘⡀⠇
⠀⠀⠀⠏⠙⠃⣄⣁⠀⢄⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡂⡥⡪⡿⠀⠖⠉⡄⠁
⠀⠀⠀⠈⠲⣀⠈⠠⠃⡰⢄⡤⣀⠄⠄⠀⠈⡥⠀⢉⠍⠁⠰⣾⠉⠠⡆⠀⠓⢉⠀⢀⠁
⠀⠀⠀⠀⠀⢹⣄⢟⠀⠂⢀⡀⠁⠀⠀⣄⠄⠉⢠⡎⠀⠒⢀⡆⠀⠀⡇⠀⠀⠀⠀⢘⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠹⣖⢆⠀⠀⢻⡀⠀⠀⠸⡀⠀⠀⢿⠀⠀⠀⠇⠀⠀⣥⠀⠀⠈⠀⢨⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠈⢯⢄⠀⠈⣗⠀⠀⠈⡆⠀⠀⢸⡆⠀⠀⢇⠀⠀⣿⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣤⠀⢸⣆⠀⠀⠳⠄⠀⠀⣷⠀⠀⠰⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠃⠀⠀⠑⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠆⠐⠂⠄⠠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⢀⡀⠀⠀⠐⠄⣀⣁⡀⠀⠂⠀⠁⠀⠁⠄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠮⠄⠀⢀⡤⠄⠉⠉⠀⠀⠀⠀⠀⠀⠉⠲⠠⠀⠀⠀⠀⠣⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠀⠀⢠⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⠀⠀⢡⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠀⠀⣀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⡀⠀⠈⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡀⠀⠘⠢
⠀⠀⠀⠀⠀⠀⠂⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂
⠀⠀⠀⠀⠀⠰⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠌⠀⣀
⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠀⠀⠠⢀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠜⠀⡘⠂
⠀⠀⠀⠀⠀⡁⠀⣀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠰⠴⢀⡇
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⠐⠂⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⠤⠀⠄⠀⠐⠈⠁⠀⠀⠄⠀⢁
⠀⠀⠀⠀⠀⠐⠠⠄⣀⠈⡉⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠁⠀⣀⡠⠄⠒⠂⢉
⠀⠀⠀⠀⠀⠐⠄⠀⢀⠀⠉⠀⠈⠀⠀⠂⠀⠀⠠⠤⠤⠤⠤⠤⠤⠠⠤⠤⠤⠠⠀⠀⠀⠐⠒⠀⠀⠁⠀⠈⠀⢀⡀⠀⠠⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠲⠒⠀⠀⠄⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠉⠀⠀⣀⣀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠐⠀⠠⠄⠀⠀⠀⠀⣀⠀⠀⣀⠀⢀⣀⠀⣀⣀⣀⡀⣀⠀⠀⠤⠄⠐⠂⠀⠒⠈⠉⠁⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠈⢢⠠⠄⠀⣀⠀⠀⡀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠤⠀⠒⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠠⠀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠄⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⣀⠀⠀⠀⠀⠀⠁⠉⠉⠁⠀⠁⠀⠈⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⠀⡀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠉⠉⠀⠂⠒⠂⠀⠐⠀⠠⠀⠀⠄⠀⠀⠀⠐⠒⠂⠐⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡈⠉⠐⠀⠀⠀⠠⠀⠠⠄⠠⠄⠀⠠⠀⠤⠤⠠⠔⠂⠐⠀⠐⠀⠀⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠒⠀⠀⠄⠠⠄⠤⠄⠀⠠⠄⠤⠀⠀⠀⠀⠒⠒⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣯⣭⣭⣭⣭⣭⣥⣄⣒⣒⣒⣒⣒⣒⡒⠒⠶⠶⠦⠤⠤⠤⠤⠤⢤⣤⣤⣤⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠿⠶⠶⠶⠶⠶⠶⢶⣶⣶⣬⣭⣭⣉⡓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣦⠙⣆
⠀⠀⠀⠀⠀⠀⠀⢸⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⣼⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢸⡆
⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠃
⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢸
⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⣀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⠀⠀⣿⡀⣇⣤⡶⣿⣿⡟⢂⠒⠀⠙⢫⡖⠚⠒⠛⡇⠀⠼⢦⠄⠀⠐⣶⣖⠒⠒⢶⣤⣀⣀⣤⣤⣀⣀⣀⢀⣀⠀⠀⠀⣀⠀⢸⡇⢸
⠀⠀⣀⣀⣄⡶⢿⣶⡄⡸⠏⠙⣸⣿⣿⣶⣷⣶⣾⠿⡿⠶⠦⣤⣿⣤⣤⣤⣷⣄⣀⠀⣷⡄⠀⠀⢨⡍⠉⠁⠉⣧⠀⠒⠊⠹⡛⠛⠁⠘⣃⢺⡇⣼⠰⣆
⣰⣯⣹⣿⣛⣠⣾⣿⣼⣿⣾⣿⣿⣿⡇⣿⡟⠈⠈⠀⡀⠀⠀⠀⠀⡎⣿⠈⠉⠉⠉⠉⠉⡻⠛⠛⢻⠟⠓⠒⠒⠛⡿⠶⠖⠲⣿⣶⠖⠒⠿⢿⡇⣿⢴⣿
⣿⡇⠀⠀⠈⠟⠄⠀⠀⠙⠿⡇⠉⠉⢻⡿⠛⠛⠛⢿⣧⠄⢀⣀⣠⣄⣉⣁⣾⣀⡀⠀⠀⠃⠀⠄⢸⠄⠀⠀⠀⢰⠃⠀⠀⠰⠼⠃⣀⣤⣴⣏⡛⢣⣼⢿
⠉⡻⠤⢄⠀⢘⣾⣄⡀⠀⠐⣴⡀⠀⠀⢂⣀⠀⠀⠀⠉⣢⠀⠀⠀⠛⣂⠀⠀⠙⠟⠁⠁⠻⡿⠒⠛⠒⢷⣖⠒⠒⠒⢾⢧⣴⣿⣿⣿⣿⣿⣟⣡⡌⣿⣿
⠀⣧⢠⡆⠀⢰⠉⠉⠉⠉⠛⠙⢻⠛⠛⠛⠛⠒⠒⠲⠶⠿⠶⢤⢤⣤⣼⣧⣀⣀⣈⣶⣄⣀⢡⣤⣀⠀⠀⢢⣤⠀⠀⢀⣸⣿⢿⡿⢿⡿⣿⢻⡍⣿⣿⡿
⠀⣜⡀⠃⠀⢘⣄⡀⠀⠀⠀⠀⠸⠀⠀⢀⠀⠥⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠈⠉⠙⠙⠙⠩⡭⠉⠉⠛⠛⣋⠛⠹⠋⠀⣾⣿⣿⢳⣿⡐⣢⡿⣏⡗
⠀⣯⠩⠉⠉⠉⢹⡟⠛⠻⠛⠛⠛⠒⠒⠛⠿⣷⣶⣤⣴⠾⠦⠀⢀⣤⣄⡀⢀⣀⣠⡂⢠⠀⢀⠀⠑⠀⠀⠀⠀⠹⠀⠀⢀⣄⢙⣓⣿⠼⠛⣿⡏⠀⡟⠃
⠀⣿⣀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠃⠁⠀⢠⠀⠉⠀⠀⠀⠉⠉⠉⠉⠉⡉⠉⠉⠙⠿⠶⠶⡶⠲⢟⡚⠀⠓⠚⠛⡟⣿⡏⠀⢰⣿⣿⢶⣿
⠀⠘⢿⠻⠛⠛⠛⠿⠤⠤⠼⠿⢷⣦⣶⣴⡶⠧⠁⠀⢼⣤⣄⣀⣀⣀⡄⠀⠀⢀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⡒⠀⠀⠀⢀⠣⣿⣷⣤⣿⠏⠀⢸⡟
⠀⠀⡇⣀⠀⢄⡀⠈⠀⠀⠀⠀⢸⠈⣹⠹⠀⠒⠀⠀⠀⢈⠿⠛⠛⢹⠁⠌⠀⠚⠛⣿⣷⡶⡾⣷⠧⠤⠤⠷⣦⣶⣤⣤⠶⡿⠋⠉⢹⢸⢿⣤⣤⣬⡇
⠀⠀⡌⠛⠛⠛⢷⣾⣤⣤⣤⡶⠿⠾⠴⠾⣦⣤⣤⣤⣤⣎⣀⣀⠀⢸⣄⣁⡀⠀⢀⠇⠈⠀⠇⣠⠉⠀⠀⠀⠘⠁⡏⠙⠀⣇⠁⢀⡼⠛⠙⣿⠃⣿⠇
⠀⠀⣧⠀⠀⠀⢰⠌⠉⡏⢿⠀⠋⠀⠀⠀⣿⠉⠉⠉⢈⠀⠌⠉⠀⠉⡍⠛⠛⠛⠉⠒⠓⠒⠓⢿⣬⣥⣤⣤⣶⣤⠤⠔⠲⢻⡟⣿⠇⠀⣸⢻⣠⠿
⠀⠀⠹⢶⣶⣤⣼⠤⠀⠤⣼⣄⣀⣀⣀⣠⣿⣀⡀⠀⢸⣄⠀⠀⠀⠀⠁⠀⠀⠀⡀⢐⠙⠂⠀⠀⠏⠉⠉⠁⡇⠀⠀⠀⠀⣿⣇⣿⢶⣾⠏⠉⢡⡞
⠀⠀⠘⣿⠁⠀⢹⠸⠀⠀⠀⠩⡟⠛⠛⠉⠇⢀⠀⠈⠉⠉⠻⡿⠿⠿⠒⠒⠒⠚⠳⣮⣤⣤⣤⣧⣁⡂⠀⢀⣦⣀⣀⣠⣼⠛⠉⠀⢸⣸⡆⢁⣸⣁
⠀⠀⠀⣿⢀⣀⣼⣄⣀⣀⣀⣴⠁⠀⠀⠀⡆⠈⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠀⠀⠀⠈⠨⠙⠀⠀⠄⠉⠈⠉⡋⠙⠉⠁⢸⡆⠁⢀⣼⠟⢹⢻⣿⡇
⠀⠀⢸⡇⠀⠀⠀⠈⠙⢙⠉⠛⠛⠛⠛⠚⠻⠷⣶⡶⢾⠗⠓⠒⠂⠾⣤⣤⣠⣤⣥⠤⣤⡀⣴⡀⠀⠀⠀⠀⠀⢠⠸⠀⣼⣥⣶⢿⡇⠀⢸⠸⣿⠃
⠀⠀⠈⢷⣀⡀⢀⣀⠀⠸⠀⢰⣬⡄⠀⠀⠀⠀⠀⠁⢸⡤⠄⠀⠀⠀⠁⠙⠉⠉⠀⢄⠀⠀⠈⠙⠛⠿⠿⠛⠃⠀⠐⢒⠙⢡⠀⣸⣀⣠⡾⠛⠁
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠛⠛⠿⠷⠖⠛⠒⠲⠶⠶⢾⣥⣄⣀⣴⣦⣀⣀⣀⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⣼⣿⡿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠒⠶⠶⠾⢦⣤⣤⡴⠞⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢲⠃⣀⠘⠉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢣⡠⠚⠁⠀⠉⠙⠢⡔⠛⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠈⠲⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠒⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠂⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠯⢉⡒⣿⣉⣩⣉⣉⣉⣉⣹⣋⠁⠒⢒⠶⠼⠒⢾
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠁⣀⠄⠚⠛⠉⣉⠀⠀⠀⠀⠀⠀⠐⠈⠉⠉⠙⠓⢴⡒⠤⡗⠦⣀
⠀⠀⠀⠀⠀⠀⡠⠊⠀⢀⠴⠋⠀⠀⠀⠀⠀⣀⠀⠁⠀⠀⣀⠀⠐⠒⠀⠀⠤⠀⠀⡃⠒⢗⠲⢌⡱⢦⡀
⠀⠀⠀⠀⠀⡐⠀⠀⡄⠁⠀⠁⠀⠐⠂⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⡒⠀⠀⠈⠐⠀⣏⠑⢾⠀⠀⠑⣄⠁⡀
⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠨⠀⠀⢀⠒⠂⠀⠀⠤⠀⠀⢀⠀⠀⠰⠤⠖⠀⠔⠂⠀⣏⠙⢺⠍⣂⢁⡿⠁⡇
⠀⠀⠀⠀⠀⡟⣄⠀⠙⢄⠀⠀⠀⢐⠒⠂⠀⠀⡈⡀⠀⢍⢁⠀⠈⢡⣤⠄⡢⠉⠀⡏⠑⢾⡒⣬⡵⢁⡰⡇
⠀⠀⠀⠀⠀⣷⡈⠢⢄⠀⠙⠢⠤⣐⡭⠅⠀⠀⣀⡀⠀⢀⣀⠄⠰⠐⢂⣀⠂⢉⡴⠭⠠⢾⣿⣁⠼⢋⡴⡇
⠀⠀⠀⠀⠀⢓⠦⠀⣄⠉⠒⠢⢤⣀⡈⠉⡖⠒⠒⠦⠤⠬⡭⡥⠤⠤⠤⠴⠖⠚⠛⢷⠖⣤⣈⡇⠐⢐⣠⡇
⠀⠀⠀⠀⠀⢹⠀⠠⡌⢑⠀⠀⠠⠠⢉⠉⠛⠓⠲⠤⠤⠤⠧⠤⠤⠤⠄⠐⠘⠀⠘⠛⠚⢁⡠⠀⠀⢰⢺⠇
⠀⠀⠀⠀⠀⢸⠦⠐⣢⡀⠀⠀⠨⢄⠂⠀⠀⠀⠁⠒⠂⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⢺⢹
⠀⠀⠀⠀⠀⢸⠭⠀⢁⠊⠄⡀⢈⠠⢌⡁⠀⠀⠡⠒⠆⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢼⣿
⠀⠀⠀⠀⠀⢸⠓⠀⡾⠄⡀⠀⢘⣑⠠⠄⢀⠀⠀⣀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠀⠀⢺⣿
⠀⠀⠀⠀⠀⢸⡒⠂⡆⠑⠤⠤⠐⠢⠍⠠⠙⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡌⠁⠀⠀⠅⠐⠠⡿⡇
⠀⠀⠀⠀⠀⣨⣯⠤⡂⠑⠄⠀⠠⡝⠤⠀⠀⡐⠠⠄⠀⠐⠒⠈⠉⢀⠀⠀⠀⠐⡂⠀⠀⠨⡇⠀⡀⣿⣧⡀
⠀⠀⠀⠀⠀⠡⡘⣥⡬⢍⠢⠀⠈⠭⢉⡉⠀⠀⠈⠀⠀⢀⢀⣃⣀⡠⠄⠀⠀⢨⡥⠀⠀⠺⢶⡺⠓⣅⠔⠃
⠀⠀⠀⠀⠀⠀⠙⠣⣈⣹⠶⢤⣀⣩⣐⣒⡀⠄⡀⠀⠀⠀⠀⠀⠠⠐⠲⠤⠤⢚⣑⡤⠴⢚⡩⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠮⠬⠉⣙⠒⠓⠒⡖⠒⠑⢺⠏⠓⠒⣒⣊⡉⠽⠆⠒⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣀⣀⣈⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣿⣿⣿⡿⢛⣩⣴⣶⣿⣿⣿⣿⣿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡟⢠⣿⣿⣿⣿⣿⠟⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠏⣰⣿⣿⣿⣿⠟⢁⣾⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠋⠉⢉⣉⡉⠛⠛⠿⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⠿⠛⠃⠘⠛⠛⠻⠟⠁⢰⣿⣿⣿⣿⣿⣿⡿⠋⢁⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣮⣝⡻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣫⣵⣶⣾⠟⣠⣿⣿⣿⣿⠗⠀⣴⣤⣤⣈⡉⠙⠛⠋⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣯⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⢃⣼⣿⣿⣿⣿⡟⠀⣼⣿⣿⣿⣿⣿⡿⠀⢠⣄⡈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠏⣠⣾⣿⣿⣿⣿⡟⠀⣸⣿⣿⣿⣿⣿⣿⠁⢠⣿⣿⣿⣷⣦⣄⡈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⣸⣿⣿⣿⡟⢁⣴⣿⣿⣿⣿⣿⡿⠀⣰⣿⣿⣿⣿⣿⣿⡟⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⣰⣿⣿⡿⠋⣠⣿⣿⣿⣿⣿⣿⣿⠁⢰⣿⣿⣿⣿⣿⣿⣿⡇⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⢀⣿⣿⠟⢡⣾⣿⣿⣿⣿⣿⣿⣿⠇⢀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⣸⣿⠏⣴⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⣿⠏⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠹⣿⣿⣿⣿⣿
⠀⠀⠀⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠘⢿⣿⣿⣿⠇
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠀⣚⣛⢛⣛⡛⠻⠟⠿⠯⠿⠯⠭⠭⠭⠥⠤⠬⠭⠉⠍⢉⣉⣛⣛⣛⡛⠛⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣧⡈⢿⣿⣿
⠀⠀⠀⠛⠛⠉⠉⠉⠀⠀⢐⣀⣤⡤⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⠀⠈⠉⠀⠐⠒⠀⠀⠀⠈⠉⠉⠁⠘⠛⠿
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⢋⣩⡀⠀⠀⣠⡿⠀⠀⠀⠀⠀⣠⣤⠀⠀⣼⣿⣃⡀⠀⢀⣀⡀⠦⣴⣿⣥⣤⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⣴⡟⠁⣠⢟⣿⣇⣤⡾⠋⠀⣴⡾⢛⡇⢀⣿⣧⠀⣰⣿⣿⡿⢣⣾⣟⡽⢃⣼⡿⠁⣠⣿⡿⢺⣷⠄⢀⣤⣤⣄⠀⠀⣠⣿⠇⣠⣾⠆
⠀⠀⠀⠀⠀⣾⡟⢀⡼⠋⣿⡿⠛⠉⢹⣷⢸⣿⠁⣾⣏⣞⢀⣿⢷⣿⠻⣏⣠⢾⣿⣋⣴⢾⣟⣠⠾⣿⠃⣠⣾⣿⣴⡿⠋⣰⡮⢀⣾⠟⢁⣾⡿⠃
⠀⠀⠀⠀⠀⠛⠗⠋⠀⠀⣿⡇⠀⣠⡿⠋⠈⠛⠋⠙⠋⠈⠉⠥⠤⠭⠦⠾⠷⠶⠾⠷⠶⠶⠿⠧⠤⠽⢿⣯⣉⣀⡹⠷⠺⣿⢴⣿⣫⣴⡿⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣦⣀⣤⣶⠿⠋⠀⠀⠀⠀⠀⠀⠐⠒⠂⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠒⠒⠶⠶⠤⣭⣉⣑⠒⠢⠬⠀⠙⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠂⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⠃⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⢁⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠐⠀⢉⡀⠀⠄⢀⠀⠄⠀⠌⠁⠐⠀⠠⢄
⠀⠀⠑⠢⢀⠉⠢⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠧⠄⠀⠈⠉⠉⠁⠉⠀⠈⠀⠀⠢⢄⡀⠀⠈⠐⠄⡀
⠀⢂⠀⠀⠀⠀⠀⣀⢰⠂⠈⠉⢖⠉⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢁⠀⠀⠒⢄
⠀⠀⠑⠀⠀⠀⠀⢀⠌⢂⢀⡀⠄⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠂⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠳⠀⠈⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⢢
⠀⠀⠀⠄⠀⠀⡀⠔⠩⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠉⠀⠰⠃⠀⠀⠸⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠈
⠀⠀⠀⢀⠊⠔⠰⠁⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⡀
⠀⠀⠀⡀⠀⢀⠀⢀⡀⠐⢀⠀⠀⠀⠀⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰
⠀⠀⢀⠀⡀⡆⠀⠈⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⡀
⠀⠀⠈⢐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠁
⠀⠀⠃⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⢸
⠀⢰⡉⠉⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⢉⡆
⡌⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠒⠋⠉⠉
⠑⢠⠀⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⡄
⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠒⠒⠒⠒⠒⠒⠊⠈⠓⠒⠈⠉⠉⠉⠁⢈⠀⢀⠀⠀⠀⡇
⠀⠀⡀⠁⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⡀⣀⠀⢀⠀⠀⣀⠀⡠⠀⠠⡀⢠⠄⠀⢰⠀⢸⠀⠉⢉
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠰⠄⠀⠘⠐⢪⠀⠀⠄⠀⠄⠀⠰⠀⠈⠂⠀⠚⠀⠈⠉
⠀⠀⠆⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢨⠀⠀⢤⢀⡤⠀⠀⢰
⠀⠀⠃⠐⠀⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠁⠉⠇⠸⠁⠉⠱⠀⢌⠉⢈⡉⠉⣁⡀⠨⠀⠸⠄⠀⠄⠀⠐⠀⠒⠘
⠀⠀⢦⠠⠀⡀⠀⢀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠉⠉⠉⠀⠀⠀⠀⡁⠀⠅⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠄⡴
⠀⠀⠀⠄⠄⠸⣀⣊⠀⠉⢆⠀⠀⠀⠀⠀⢀⠐⠃⠂⠀⠆⠀⠰⠄⠠⠂⠀⠰⠀⠐⠀⠐⡇⠀⡃⠀⠰⠍⢬⠁⢀⣇⠀⠧⠄⠠
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠁⠠⠀⠀⠀⠐⠚⠂⠀⠒⠀⠃⠀⠐⠂⠐⠂⠀⠂⠀⠐⠀⠀⠃⠀⠁⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠈⠉⠀⠐⠒⠐⠂⠀⠒⠂⠀⠀⠠⠠⠤⠤⠀⠤⠄⠀⢄⡠⠠⠤⢄⣀⡠⠤⠤⠤⠤⠄⠒⠒⠀⠐⠒⠛⠋⠈⠉
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠒⠒⠒⠚⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠒⠒⠖⠶⠦⢤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⣠⡴⠖⠋⠉⢤⡄⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠉⠁⢲⡆⠀⠂⠠⠁⠉⠙⠓⠖⠦⢤⣀⡀⢀⣀⣀⡤⣄⡤⠤
⠀⠀⠀⣠⠟⢁⠀⠀⠀⠀⠀⡓⠄⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⣵⠂⠀⠀⢀⠙⠲⣄⠀⠀⡀⠉⢒⣤⣀⣀⢠
⠀⠀⢠⡇⠰⡏⠀⠀⠀⠀⠀⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢀⠞⠉⠀⠀⠀⢠⠓⡄⠘⣧⠁⠁⠀⠈⠀⢹⠌
⠀⠀⠀⠣⡀⠙⠻⢤⣀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠂⠀⢀⡔⠁⠀⠀⠀⠀⣠⣧⠞⠁⣰⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠈⠳⢦⣄⡈⠉⠓⠺⠦⢤⣀⣘⣆⣀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⢸⣶⠃⠀⣀⣀⣥⠴⠞⠉⠀⣠⣾⣿⡇⠂⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢦⣤⣀⣀⠀⠉⠉⠙⠒⠒⠒⠚⠳⠶⠶⠶⠾⠷⠶⠖⠒⠒⠒⠚⠛⠉⠉⠉⠉⣀⣠⡤⠖⣻⣷⡿⢻⡇⠀⠀⠀⠀⠀⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠈⢂⠉⠉⠙⠒⡶⠶⠴⠴⠤⣤⣤⣤⣤⣤⣤⣤⣤⢤⡤⠤⠶⠒⠒⢻⢏⠉⠩⠀⠀⠘⣛⣩⠵⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠰⣸⠀⠀⢱⣄⠀⠀⠃⠈⢢⠀⠀⠀⠀⢨⠀⠀⠀⠀⢠⡞⠀⠀⠁⠀⠀⡀⠸⠶⠲⠖⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢹⡄⠀⠀⢩⠓⣠⡄⠀⠀⢱⣤⠀⠀⠀⠀⠀⠀⠀⠎⠁⠀⠀⢀⠀⢰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⢨⠓⢄⠀⠀⠉⠑⣤⡀⠀⠀⢠⡆⠀⠀⠀⠀⢈⣠⠏⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢸⡄⠀⢼⠀⠀⠳⠂⠀⠀⠙⢣⠀⠀⢈⠓⠀⠀⠀⢀⣈⡟⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⡎⢶⡞⠀⠀⠠⣠⡂⠀⠁⠀⠈⠀⠀⡀⠀⠈⢿⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢀⠏⠱⡀⠀⠀⠙⠓⣄⠀⢸⣇⠀⠀⢸⣶⠀⡆⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠘⢦⣀⠀⠀⠈⢠⡇⠈⠢⠄⡀⠻⣴⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⢦⠀⢨⠛⠢⣀⢠⠊⠙⢄⠀⠘⠃⠐⢼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢱⠟⠄⠀⢈⠋⠀⠀⣠⠷⠀⠀⣠⢃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⢄⠀⢱⠆⢀⣤⠊⠁⠙⠢⣞⠁⡜⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠙⢃⠀⠊⠉⠀⠠⠖⢀⡛⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢂⠀⠀⠀⠸⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠠⠤⠤⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠀⡉⠄⠀⠀⠒⠀⠀⠒⠀⠀⠤⢉⠐⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⡀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠢⢀⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢨⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠄⠀⠐⢂⣈⠉⠩⠥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡬⠍⢉⣀⡐⠂⠀⠠⢀⠀⠰⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡜⢁⠄⢒⠈⢁⣀⠀⠠⡄⢰⠀⠀⠀⠀⠀⠰⠆⠃⠀⠀⠀⠀⠀⢰⠀⡴⠀⠤⠄⣈⡹⠒⠆⡈⢣⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢦⣗⠈⡭⡅⠀⠀⠀⠀⢣⠘⠒⠀⠀⠀⠉⠉⠉⡏⠉⠉⠀⠀⠀⠙⢠⠉⠀⠒⠀⢠⣈⠛⢄⢈⡴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣈⠐⠓⠲⠶⠤⠄⣀⣘⣚⡃⠀⠀⠀⠀⢸⡄⡗⠀⠀⠀⠀⢀⡁⣈⣀⣀⡀⠠⠶⠐⠛⠊⣁⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣍⡐⠂⠠⡄⡄⠤⠤⠈⠉⠉⣁⣀⡀⣈⣉⣁⣀⣀⣀⣀⡉⠉⠁⠤⠤⠠⠤⡄⢀⣂⠩⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠈⠉⠁⢡⡟⡀⢀⣀⠀⠀⢰⠀⠄⠀⠀⠀⠀⠀⠇⠰⠀⠀⢀⣐⢂⡞⡸⠁⠀⠐⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⣐⡀⠀⢆⢱⡄⠀⠀⣀⣉⣀⣏⠉⠀⠀⢀⣈⠋⣏⡁⡀⢀⠀⠴⠴⣀⠠⠄⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠈⠉⠆⠗⠐⠂⠀⠀⠄⢤⠄⠀⠀⠀⠸⢠⠃⠐⠂⠀⠉⢉⠃⣀⠀⡤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠩⠁⢙⣚⠂⠀⠀⠀⢄⠘⠄⠀⠀⠀⠲⣘⠀⠤⠀⠢⡏⠼⠀⠐⣐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡀⠀⢥⠙⡄⢉⠉⢹⢀⣏⡈⠁⠀⡅⡥⠠⠄⠀⠐⣚⠃⠩⢥⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠀⡈⣆⣋⣉⠀⢐⠂⠒⠒⠒⠒⠃⠋⠉⠉⢀⢁⣃⠀⣤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡍⣁⠐⡒⡆⠀⠘⡃⢸⠉⠉⢹⠻⠋⠉⠉⡛⡘⢉⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡈⠉⠁⠀⠐⠛⠚⠒⠒⠚⠛⠒⠀⠀⠉⢁⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⢸⣿⡇⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠸⣿⣿⣶⣿⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⡿⢿⣿⡟⠁⠀⣸⣿⣿⠀⠀⠙⠻⠟⠁⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠋⠁⠀⠀⣿⣿⣧⣤⣴⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠴⢶⣾⣿⣿⣷⣦⢲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣶⣭⣟⡻⠿⣧⢻⣿⣷⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡆⣷⣶⣿⣆⠀⣿⣿⣿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⣼⣿⠿⣛⣛⣯⣭⣭⣿⣶⣶⣶⣶⡆⣭⣭⣟⡻⠄⠻⠿⣿⣤⣤⡄
⠀⠀⠀⠀⠀⠀⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣛⡁⣙⡻⣿⣿⡇⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⢛⣵⣾⣿⣿⢧⣿⣿⡞⣿⠇⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡿⣫⣾⣿⣿⣿⣿⡿⣸⣿⣿⡇⡟
⠀⠀⠀⠀⠀⠀⠀⠘⠿⣛⣵⣾⣿⣿⣿⣿⣿⡿⣳⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⢟⣵⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠂⠀⠀⣉⣀⠈⠀⠈⠀⠒⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⢁⣀⠤⠄⠀⠉⠉⠁⠀⠀⠈⠁⠐⠂⠠⢀⡈⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠦⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠋⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⢀
⠀⠀⠀⠀⠀⠀⠆⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠆
⠀⠀⠀⠀⠀⠠⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⡀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘
⠀⠀⠀⠀⠀⠄⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠄⠆
⠀⠀⠀⠀⠐⠳⠬⠅⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠭⠴⠓
⠀⠀⠀⠐⠄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠔
⠀⠀⠀⠀⠀⡀⠀⢨⠀⡋⠉⠉⠒⠒⠒⠲⠀⠶⠒⠲⠶⠒⠒⠲⠂⠲⠒⠲⠶⠒⠖⠒⠂⠐⠒⠒⠓⠋⠉⠉⠇⠈⠀⠀⡀
⠀⠀⠀⠀⠀⡇⡀⠹⠀⡗⠒⠂⠠⠤⠤⢴⠀⢠⣀⣀⣀⣀⣀⣠⠀⢠⣀⣀⣀⣀⡀⢠⠄⡤⠤⠤⠄⠐⠒⠒⠆⠜⠀⡀⡇
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠃⠓⠂⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠐⠂⠂⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⡉⠀⠐⠆⠦⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠠⠄⡤⠀⠀⠀⠀⠀⢠⠤⣄⠀⠀⠀⠠⠄⠰⠂⡏⠉⢉⡁
⠀⠀⠀⠀⠀⣀⠀⠀⡀⠈⠀⠀⠀⠀⠐⠐⠁⠙⠁⠀⠀⠀⠀⠨⠁⠡⠀⠀⠀⠀⠀⠐⠀⠖⠀⠀⠀⠀⠀⠸⠀⡃⠀⣀⡄
⠀⠀⠀⠀⠀⠈⡉⡐⡇⠸⠀⠐⠒⠀⠀⠠⡄⢠⠀⠀⠀⠀⣀⢠⡀⣤⠀⠀⠀⠠⠤⢤⡀⡧⠀⠒⠒⠒⠒⢺⠀⡋⡉⡩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠂⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠃⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠒⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠛⠋⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡤⠴⡒⣉⠝
⠀⠀⠻⢍⣉⣉⡉⠻⢷⡿⠿⣟⣿⣝⣗⣦⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢀⣶⣫⣿⣿⣛⡿⠭⠥⠿⠗⠒⣲
⠀⠀⡤⠤⠬⠟⠶⢚⣋⣽⡭⣳⣯⣯⣞⡄⣧⠴⠚⠋⠉⠉⠉⠉⠻⢗⠦⣄⣸⠹⣻⢯⣿⢭⡯⣟⣁⠒⠾⠯⢥
⠀⠀⠙⣒⡲⠶⠚⣅⠵⢚⠟⣼⣏⣇⣇⢒⠸⡖⠦⢤⣀⠀⠀⠀⠀⠀⠱⡀⠙⢴⣰⣽⣼⠳⡈⢢⣴⣙⠛⢿⠉
⠀⠀⠈⠳⢶⡾⠞⣱⡶⡏⣠⠋⡿⢸⢹⢻⣰⣮⡆⠀⠈⠙⠢⢄⠀⠀⠀⠐⡀⠈⣿⡏⣏⢳⣈⡢⣷⣽⣫⠉
⠀⠀⠀⠀⠈⠒⢻⣋⣴⡷⣣⡜⢃⡜⡾⡟⡏⢿⠃⠀⠀⠀⠀⠀⠑⠢⢀⡀⣃⣠⠂⣿⢋⢿⣌⣟⠺⠇
⠀⠀⠀⠀⠀⠀⠀⠁⠸⠗⢫⣇⣿⡇⣧⣳⣽⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢸⠞⠚⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢘⠉⠉⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⡖⠠⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⣀⡰⠀⣀⣠⠔⠊⠀⠀⡴⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢶⡒⠚⠛⠫⠩⠂⠀⠀⢀⢜⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⠤⠤⠴⠶⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠂⠀⠀⠉⠉⠉⢉⣩⣭⠶⠶⠶⠠⠦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠂⠁⠀⠀⠀⠀⠀⢀⡠⣐⠝⠊⠉⠀⠀⠀⠀⠀⠀⢀⣀⢨⣭⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠁⠀⠀⠀⠀⠀⠀⢀⠠⠐⠕⠈⠀⠀⠀⠀⠀⡀⠠⠀⠒⠙⠀⠉⠀⠀⠀⠀⠀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⡵⠋⠀⠀⠀⠀⠀⠀⢀⠔⡡⠊⠀⠀⠀⠀⢀⠠⢂⠥⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠞⢁⡞⠁⠀⠀⠀⠀⠀⣠⠞⡡⠊⠀⠀⠀⠀⡠⢐⡡⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⢦⡀
⠀⠀⠀⠀⠀⢀⡼⠁⢀⡟⠀⠀⠀⠀⠀⣠⠞⡡⠊⠀⠀⠀⢀⡤⢊⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⢠⠊⠀⠀⡞⠁⠀⠀⠀⢀⠞⡡⠊⠀⠀⠀⢀⡴⢉⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢡⡈⢧⡀
⠀⠀⠀⡰⠁⠀⠀⡸⠰⠀⠀⢀⠔⢁⠞⠁⠀⠀⠀⡠⢊⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠄⠱⡀
⠀⠀⣰⠁⠀⠀⠀⡇⡆⡠⠞⢁⠔⠁⠀⠀⠀⠀⡸⢡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⢰⡟⢆⡀⠀⢀⠇⣉⠠⠊⠀⠀⠀⠀⠀⠀⢰⢡⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠀⠀⠒⠒⠀⠀⠠⠀⠈⢀⣒⣷
⢀⡏⠘⠢⠥⠤⠐⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠐⣂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⢰⠁⠀⠀⠀⠀⠀⢀⡃⠀⠀⠀⠀⠀⠀⠀⢠⠀⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⡂⠨⠅⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣼⡆⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠠⠀⡆⢇⠠⠀⡂⠈⠀⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⡟⣿⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠄⣀⢡⠠⡆⠁
⡇⢹⡄⠀⣀⡔⠀⠀⣻⠧⠄⢂⡡⠄⠂⣀⡄⠀⢧⡘⣄
⡇⠘⣿⠀⠁⡠⠐⣈⢤⣰⡈⠀⠀⠀⠤⡞⠠⠀⠀⠱⣌⢢⡀
⢰⠀⡸⠓⡩⢔⠉⠀⠈⢇⣇⠀⢠⠆⠴⠀⠀⠐⠀⠀⠈⠑⢌⡢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠸⡞⡰⣾⡀⠀⠀⠀⠀⠈⢾⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢉⡑⠂⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⢯⠀⢹⣇⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠤⢉⣁⠒⠠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠇
⠀⠘⠆⠀⢿⡄⠀⠀⠀⠀⠀⠈⣿⡄⢀⠀⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠒⠂⠠⠄⠈⠁⠐⠒⠒⠀⠀⠀⠀⢀⡀⠦⠜⠊⡟
⠀⠀⠰⡄⠸⣇⠀⠀⠀⠀⠀⡠⠚⣉⣤⠀⠒⠒⠒⠀⠠⠌⠁⡒⡀⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠘⣆⢻⡄⠀⠀⢀⠎⡴⠁⠈⢎⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠨⠍⣒⠂⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠘⢮⣧⠀⠀⢈⣸⠀⠀⠀⠈⢣⡳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠬⠁⠐⠒⢀⣀⣀⠀⠀⢀⣀⣀⠀⠀⠒⠒⢉⠋
⠀⠀⠀⠀⠀⠀⠻⣇⠀⢸⣿⠀⠀⠀⠀⠀⠑⢜⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⢻⣇⠀⠀⠀⠀⠀⠈⠣⣕⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢿⣆⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢄⡀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⢀⢀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠐⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣐⣒⣀⣠⣤⣤⣤⣤⣭⣍⣛⣛⣛⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⣠⣾⡟⠛⠙⠻⣟⣷⣦⡀⠀⠀⣠⣶⠟⠋⠙⠻⣟⣳⣦⡀⠀⠀⢀⣴⠾⠛⠉⠛⢯⢻⣶⣄⠀⠀⠀⠀⠐⠒⠦⣬⡇⣀
⠀⠀⣼⣯⠉⠉⠙⠓⢒⣻⣧⠽⣷⠀⣰⡏⠉⠉⠙⠓⠒⣛⣧⠽⣷⡀⢠⣿⠍⠉⠉⠓⠒⢚⣻⡤⢿⣆⠀⣀⡤⠶⠖⠚⣩⠿⣧⡶⢄
⠀⠀⣿⡇⢀⣠⠴⠚⠉⣡⢾⡟⣿⡇⣿⡇⠀⣠⠤⠒⠋⢡⠾⣟⣾⡇⢸⣿⠀⢀⡠⠔⠚⠉⡴⢿⢳⣿⠀⠁⠀⠀⢠⡞⠁⢸⡏⢳⡀
⠀⠀⢿⣿⡋⠀⠀⠀⣰⠃⠀⣷⣿⠁⢻⣿⣏⠁⠀⠀⢠⠏⠀⣿⣿⠃⠸⣿⣞⠉⠀⠀⠀⡼⠁⢸⣼⡟⠀⠀⠀⡴⠋⠀⠀⢸⠀⠀⠇
⠀⠀⠈⠻⣿⣦⣄⣴⣋⣤⣾⠟⠁⠀⠀⠻⣿⣷⣦⣤⣯⣶⣿⡿⠃⠀⠀⠙⢿⣷⣤⣀⣼⣡⣤⣾⠟⠀⠀⠀⠈⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⡿⠟⢉⣠⣴⣾⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡀⠻⠿⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠂⣠⣤⣤⣤⣈⣉⣉⣉⣉⣉⣉⣉⣉⡉⠛⠻⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡍⠁⡘⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠁⣾⣿⣿⣶⣦⣌⡙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⢉⣠⣤⠀⣀⠙⢿⣿⣿⣿⣿⣿⣷⣤⣈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣰⣿⣿⡏⢠⣿⣷⣄⠙⣿⣿⣿⣿⣿⣿⣿⣷⣦⣈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠃⣼⣿⣿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡉⠻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣷⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠻⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⡄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣦⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠄⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡉⠻⠿⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠖⠒⠛⠛⠛⠒⠒⠶⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⣉⣀⡤⠴⠖⠒⠛⠛⠛⠛⠓⠒⠶⢤⣀⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢁⡤⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⡀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢀⡼⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠙⣆
⠀⠀⠀⠀⠀⢀⡞⠁⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠹⡄
⠀⠀⠀⠀⠀⢸⠃⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢷
⠀⠀⠀⠀⠀⣿⠀⣿⣀⣤⠤⠶⠶⠒⠒⠚⠛⠛⡛⠛⠛⠛⠛⠛⠛⠒⠖⠒⠶⠶⠤⢤⣤⣀⣸⡇⢸
⠀⠀⠀⠀⢀⡿⠋⢉⣤⣤⠴⠶⣒⣛⠛⠛⡛⠽⠏⠉⠩⠭⠍⠉⠛⠿⠟⡓⠛⢒⣶⠶⠦⣤⣽⡇⢹⡄
⠀⠀⠀⠀⢸⡁⠘⠯⠅⣊⣀⣒⣀⣠⣌⣉⣠⡤⠈⠉⠠⠤⠈⠉⣁⣠⣄⣐⣒⣀⠴⠦⠬⠖⣻⢁⣿⠇
⠀⠀⠀⠀⠀⡟⡛⠲⠶⠶⠤⣤⣤⣤⣥⣤⣤⣬⣅⣀⣤⣍⣁⣀⣤⣍⣤⣤⣤⡤⠤⠴⠖⠒⣛⡋⢹
⠀⠀⠀⠀⠀⢷⠈⠉⢄⣀⡐⠒⢂⣀⡀⠒⠒⢀⣀⠒⠒⠀⠀⠐⠒⠂⠀⠒⠒⣀⣀⠉⠡⠤⠀⠐⢻
⠀⠀⠀⠀⠀⢸⡄⠂⠀⠀⠠⠤⠄⠀⠀⠤⠤⠀⠀⠤⠤⠉⠉⢀⣀⠀⠀⢀⡠⠄⠀⠠⢄⣀⠒⢂⡿
⠀⠀⠀⠀⠀⠀⢳⡠⠬⠉⠁⣀⣈⠉⠁⣀⣀⡒⠂⣀⣀⠉⠉⠠⠤⠌⠉⠀⠀⠈⠉⣀⡀⠠⠄⣽⠃
⠀⠀⠀⠀⠀⠀⠀⠹⢤⡐⠒⠠⠤⠐⠒⢀⣀⡐⠒⣂⣀⠐⠒⢀⣀⠐⠂⣀⡀⠉⢉⡀⠈⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠯⣤⣈⣉⣀⣤⠈⢉⣠⣤⣈⣉⣡⣤⣈⣉⣤⣀⣩⡤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠒⠒⠒⠢⠠⣄⠀⠀⠀⠀⠀⢸⢧⠄⠀⠀⠀⠀⡀⠰⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⢀⠄⠃⠘⠂⠦⠀⠙⢆⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠆⠀⠀⠀⠀⠀⠘⠄⠀⠳⡴⠂⠉⠣⡀⠀⠀⢀⣴⡏⠀⠀⠀⢀⡀⠀⠀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⣼⠄⢌⠀⠀⢰⠇⣄⠀⠀⠈⠆⠀⢳⠀⠀⠀⢀⡔⠉⠉⠙⡄⠀⠀⠐⠋⣀⠴⠛⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠑⠺⡄⢹⡄⠀⠀⢸⠀⠀⡄⠀⢀⠏⠀⠀⠀⠀⡁⠔⣠⡴⢊⣁⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⡰⠒⠉⠑⠢⡄⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠠⣼⡄⡏⠀⢡⠠⠯⣤⣄⠀⠀⡔⣡⡾⡋⠔⠉
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠞⡉⠃⢰⠀⠘⠀⠀⠈⠀⡠⣫⠚⣩⠊⠀⠚⠀⠈
⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⠁⠀⢼⡄⠐⠇⢀⠀⢀⣏⠵⠋⠁⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡴⢿⢀⡂⠀⠀⠀⠈⠣⠀⠀⠀⠀⣠⠔⠊⠁⠀⠘⠀⠀⠀⠀⠀⠀⡆⠀⠶⡀⠈⠁⠑⢄⠀⠀⠀⠀⣀⣤⠒⠁
⠀⠀⠀⠀⠸⠁⢻⡞⠀⡤⠀⠀⠀⠀⡇⢀⠀⡜⠁⠀⠄⠀⠀⠀⠄⠀⠁⠀⠀⠐⡇⠀⡀⠘⡄⠀⠀⢘⢷⣀⡴⠋⢁⡎
⠀⠀⠀⠀⢱⡀⠸⣇⠀⠀⠀⠀⠀⡰⠄⢾⡂⠁⠐⠠⠀⠀⢀⠆⠀⠀⠀⠀⠂⠀⠃⠀⢁⠀⡃⠀⢀⣠⠞⠋⢀⡤⢋
⠀⠀⠀⠀⠈⢦⡄⢙⠣⣄⡀⢀⡞⠀⠀⠈⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰⡂⠀⣸⠤⠷⠊⠉⢀⣠⢴⠋⠐⠔
⠀⠀⠀⠀⠀⢸⢽⡓⢦⣄⣀⠙⠛⠀⠤⠄⠠⡤⠀⡠⠤⡀⠼⠠⠄⠠⠴⠀⠐⠊⡃⠀⡁⣀⣠⠶⠚⡉⠀⠄⠀⠅⡉
⠀⠀⠀⠀⠀⠘⡏⡆⠈⡅⠉⢹⡓⠒⠶⡦⠤⠤⣤⣤⣤⣤⣤⣤⠤⡤⠤⠤⠶⠖⠓⢊⠉⠀⠀⠀⠀⠂⠀⠄⢐⢡⠁
⠀⠀⠀⠀⠀⠀⢷⢫⠀⣓⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈
⠀⠀⠀⠀⠀⠀⠸⡟⡆⠸⠀⠀⠅⠀⠀⠅⠀⠀⠠⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⢻⣺⠈⢆⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢐⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢳⣧⠸⡄⠸⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⢁⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡫⡀⢅⠀⠐⡂⠀⠈⠀⠀⠰⠀⠀⠀⠀⠀⠈⠀⠀⡠⠀⠈⠀⣠⡤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠾⠦⣀⣐⡀⠀⣂⠀⠈⠀⠀⢀⠀⠀⠀⢀⣠⠤⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠒⠒⠒⠒⠛⠊⠉⠉


⣶⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣦⣶⣧⣶⣴⣶⣴⣾⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠐⣀⣤⣤⣤⣤⣄⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤
⠀⠀⠀⠄⠀⣠⡶⠛⣏⣠⠊⠁⠀⢀⣩⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⣠⠴
⠀⠀⠀⠀⣴⣋⣠⣤⡼⢽⣖⣒⠚⠉⠀⠀⠈⢷⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠐⠋⠀⠀⠀⠀⢀⡀
⠀⠀⠆⢰⡏⠁⠀⡼⠀⠀⢀⠈⠉⡒⠦⣀⠀⠸⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⣠⠔⠀⠀⢀⠴⠚⠉
⠀⠀⠀⢸⣇⡴⠚⡏⠉⠓⢤⡀⠀⠀⠀⠈⢣⢀⡇⠀⠉⠀⠀⠀⠀⠀⠀⢠⠖⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠁⢻⡄⠀⣇⠀⠀⠀⠹⡄⠀⠀⠀⢀⣿⠃⠀⠲⡀⠀⠀⠀⠀⠀⢁⡀⢀⡴⠀⠚⣡⠞⠁
⠀⠀⠀⠀⣆⠻⢦⣘⡄⠀⠀⠀⢳⠀⢀⣠⡞⠁⠀⢀⠀⠙⣆⠀⠀⠀⣠⠏⠀⠎⠀⠀⠀⠁
⠀⠀⠀⠀⠈⠁⠀⠉⠛⠲⠾⠶⠶⠛⠋⠁⠲⣄⠀⠀⠳⡄⠘⠆⠀⣰⠃⠀⠀⡤⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠒⠒⠀⠀⢦⡀⠀⢠⡀⠘⠆⠀⠰⠃⠀⠀⡼⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠓⠀⠀⠙⠆⢀⡞⠰⣠⠎⠀⡁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠓⡠⠀⡀⣆⠀⠉⠀⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣢⠈⠠⠈⣘⠡⢚⣡⢠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⣤⣤⢤⣤⣤⡤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣚⣻⡿⠟⠛⠛⠿⠶⠮⠽⠷⣮⣛⣗⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠿⡿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣝⢷⣦⡀
⠀⠀⠀⠀⠀⠀⢀⡴⣫⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⡝⢆
⠀⠀⠀⠀⠀⢠⢟⣵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣎⢷⡀
⠀⠀⠀⠀⢀⣷⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡞⣷⡀
⠀⠀⠀⠀⣸⢃⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⣧
⠀⠀⠀⠀⣿⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣻
⠀⠀⠀⢸⡧⣼⠶⠒⣒⣛⣛⡛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⣒⣒⣒⡒⠶⢬⡗⢻⡆
⠀⠀⠀⠸⣷⣇⡔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⣆⣿⣾⠁
⠀⠀⠀⠀⢻⡟⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⣹⠏
⠀⠀⠀⠀⠀⢷⡀⠉⠙⠛⠶⠶⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⡤⠴⠶⠚⠋⠉⠀⢠⡟
⠀⠀⠀⠀⠀⠈⣷⢤⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿
⠀⠀⠀⠀⠀⠀⣿⡅⢺⣉⠓⢲⠦⠤⠤⣤⣤⣤⣤⣄⣀⣠⣠⣤⣤⡤⠤⠤⠶⠖⣺⠏⣹⡧
⠀⠀⠀⠀⠀⠀⢹⡆⠽⡆⠈⣹⠅⠈⢩⣕⠂⠀⠀⣺⠥⠀⠀⠬⣝⡂⢀⣭⡃⠈⢽⠁⢼⡇
⠀⠀⠀⠀⠀⠀⠈⣧⠀⣯⠀⢒⣇⠀⣒⡺⠥⠈⠥⢼⣏⡂⢀⣻⡶⠂⢐⡺⠀⣐⡗⠠⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣇⠐⣂⠨⢗⡀⠀⣾⠉⠀⠉⢽⣒⠒⠐⢲⡭⠀⠤⠯⠀⠴⠄⣺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠹⠀⠹⡆⠈⢿⣗⡀⢐⣸⠯⠅⠨⣿⠭⠀⢭⠂⢨⠏⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠧⣄⣻⡄⠩⣶⡀⠀⢸⠯⠅⢬⡯⠁⢨⣓⣠⡿⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠓⠒⠛⠛⠛⠋⠙⠛⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⠀⠀⠀⣀⣤⣤⣶⡆⢰⣶⣤⣤⣀⠀⠀⠀⣿⡇⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠁⢀⣤⢸⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⡇⣤⡀⠉⠀⢸⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⢀⣴⣿⣿⣆⢿⣿⣿⣿⡇⢸⣿⣿⣿⡿⣰⣿⣿⣦⡀⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣎⠻⣿⣿⡇⢸⣿⣿⠟⣰⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷⣬⣛⠃⢘⣛⣥⣾⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡃⢘⣛⣛⣛⣛⣛⣿⣟⣛⣛⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡐⣶⢆⣴⣶⣶⣶⣆⢲⣶⢂⣶⣶⣶⣶⣆⢲⡖⣰⣶⣶⣶⣶⣄⢶⢂⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⠀⢾⣿⣿⣿⣿⣿⡧⠡⣿⣿⣿⣿⣿⣿⢆⠸⣿⣿⣿⣿⣿⡿⢂⠺⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣎⢿⣿⣿⣿⡟⣱⣷⡙⣿⣿⣿⣿⢃⣾⣷⡙⣿⣿⣿⡟⣱⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⠻⣿⠏⣼⣿⣿⣿⣌⢿⡿⣡⣿⣿⣿⣷⡜⢿⠟⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⠉⣾⣿⣿⣿⣿⣿⡆⢰⣿⣿⣿⣿⣿⣿⢆⢺⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢡⣶⡜⢿⣿⣿⣿⢏⣼⣧⡹⣿⣿⣿⡿⢣⣾⣦⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣎⢿⣿⢃⣾⣿⣿⣷⡙⣿⡟⣱⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡆⠡⣿⣿⣿⣿⣿⣿⠌⢰⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡟⠁⠀⠹⣿⣿⣿⣿⠏⠀⠈⢻⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠏⠀⠀⠀⠀⠘⢿⡿⠃⠀⠀⠀⠀⠹⣿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠂⠀⠐⠀⠀⠂⠀⠒⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠀⣀⡀⠐⠒⠒⠛⠀⠒⠂⠒⠠⠢⠄⣀⠀⠑⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⢀⡀⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠁⡀⢁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⢀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢈⠈
⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠐⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠂
⠀⠀⠀⠀⠀⠀⠰⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠆
⠀⠀⠀⠀⠀⠀⠄⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⢀⢀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠸⠁
⠀⠀⠀⠀⠀⢨⠀⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠄⡆
⠀⠀⠀⠀⡀⠬⠤⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠤⠬⢀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠉⠉⠓⠒⠀⡶⠤⠤⠤⠤⢤⣀⡤⠄⣄⣀⠀⢀⠀⠀⢀⡀⢀⡀⢀⣀⢀⣀⣀⣠⠀⢤⣤⠤⠤⠤⠤⠶⢶⠀⠒⠚⠋⠉
⠀⠀⠀⠀⠀⢰⠀⣀⡄⠀⣇⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣀⡀⢸⠀⣅⡀⠠⠆
⠀⠀⠀⠀⠀⠰⠀⠀⠼⠀⠇⢀⠀⠈⠉⠉⠉⣡⠠⡗⠒⠒⠒⠒⠒⠒⠦⠼⠒⠒⠒⠒⠒⠀⢘⡁⣋⠉⠁⠀⠀⡀⠀⠨⠤⠇⠀⠂⠂
⠀⠀⠀⠀⠀⠰⡄⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠆
⠀⠀⠀⠀⠀⠰⠀⠀⢹⠀⢓⢀⠀⠀⠀⠀⠀⢍⠀⣆⠀⠀⠀⠀⠀⠐⡆⢰⠀⠀⠀⠀⠀⠀⠰⠛⠻⠀⠀⠀⠀⣀⡀⡉⠈⠅⠀⠀⠆
⠀⠀⠀⠀⠀⠠⡄⠀⣀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠃⠀⠀⠀⠀⠀⠒⠂⠐⠂⠀⠐⠀⠀⠀⠘⠀⠉⠈⠀⠀⠀⠀⠀⡀⠀⣀⣀⣠⠄
⠀⠀⠀⠀⠀⠀⢣⠁⣈⡂⢚⠀⠁⠀⠀⠀⠀⠆⠀⡇⠀⠀⠀⠀⠀⢐⡆⢴⠀⠀⠀⠀⠀⠀⢴⠀⠶⠒⠒⠒⠈⠉⠉⡗⢰⡁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠐⠓⠂⠂⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠒⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠐⠒⠒⠒⠂⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠀⠒⠒⠒⠒⠒⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢦⡄⠀⠀⠀⣠⣴⣾⠿⠋⠙⣷⡀⠀⠀⠀⣀⣴⣤⣭⣟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠁⠀⠀⠀⢿⣀⡴⠋⠉⠀⠀⠀⠀⠀⢸⣇⢀⣠⣾⣿⡏⠀⠁⠉⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⣀⣀⠀⠀⠀⣨⣿⡿⠛⣿⣿⠐⠀⠀⣠⠊⠙⠿⣤⣀⡴⠛⠳⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⣠⣿⡿⠋⢀⠴⢾⠿⠛⢹⣦⣠⣾⠿⠋⠠⣾⣿⣿⣴⣧⠜⠁⠀⡆⠈⠀⡙⠓⢦⣄⠀⠙⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⣿⣿⣀⠌⠀⣠⠃⠀⠀⠀⠨⣿⡅⠀⠀⠰⣿⣿⣿⣿⠏⠀⢐⠻⢀⠲⠀⠀⠀⢸⡏⠣⠀⠀⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣄⣉⣿⣿⣿⣦⣶⣅⠀⠀⠀⠀⠀⢀⣷⡀⢠⣾⡏⣼⣿⠏⠀⣀⠈⢀⡈⡰⠈⠀⠀⣸⣦⠃⢠⡞⢩⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣯⣄⠉⠐⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠈⢻⡿⣿⣷⣿⠏⠠⠀⠶⣮⠀⢉⠉⡘⠁⢠⡿⢃⣴⣏⣔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠻⣿⣿⣿⣷⣦⡀⠉⢻⣿⣿⣦⡄⠀⠀⠀⠀⠀⠙⣿⣿⡏⠀⢀⠀⠀⡀⢀⡙⠦⠀⢠⣿⣵⣿⣿⡿⡋⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣴⢉⣏⡟⣹⡻⠳⢢⠬⣿⣿⣧⣀⣀⣀⠀⠀⠀⠈⣹⣥⡀⠀⢨⣤⣹⣎⣋⣇⣀⣾⣿⠿⠻⣹⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠿⣿⢷⣿⣿⣷⣾⣾⣾⣆⣇⣇⣯⡏⡏⡉⡉⠏⣻⠋⡏⡟⢹⡛⢻⣉⡏⣏⣌⣧⣾⣿⣷⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⣻⣸⡇⢻⣿⠍⣹⣟⣟⢻⣿⣿⠛⣿⣿⣷⡷⠿⣾⡷⣷⣿⢷⣿⣿⢿⣿⠛⣿⢿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡼⡿⡇⢸⣿⡖⠠⣯⣷⠨⣿⣿⠤⢤⣿⣿⡁⠀⣹⡇⣿⠆⠀⢛⣿⢿⡏⢀⣾⣿⢹⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⣏⠀⣿⡇⠀⣿⣿⡤⣾⣿⠄⠀⣿⣿⡄⠈⣿⡏⡟⠉⠉⠉⣿⣼⡏⢀⣿⡿⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡦⣿⣧⠀⢸⣿⣇⣹⣿⡃⢈⣿⣿⠄⠈⣻⡇⣗⠀⠀⢺⣿⣿⣃⣰⣿⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡸⣿⡄⠸⣿⣇⢈⣿⡇⠀⣿⣿⠉⠉⢻⡗⣿⠀⠀⢻⣟⡿⠉⣼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢿⣿⣷⣤⣿⣿⣄⣿⣧⠀⣿⣻⠃⠐⣿⣿⣿⠂⠐⣾⣷⣏⣸⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⠿⢷⣿⣿⣷⣦⣾⣿⣿⣶⣾⣿⣿⡿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠄⠠⠀⣀⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠠⠖⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠠⠀⡈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠈⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠊⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠂⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⣘⡈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣃
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠉⠙⠒⠂⠖⠂⠦⠤⠤⠤⠄⠤⠤⠄⠀⠀⠀⡀⢀⠀⠀⠠⠤⠤⡤⠠⠤⠤⠤⠖⠒⠲⠐⠒⠋⠉
⠀⠀⠀⠀⠘⠀⠰⡀⡦⠤⠄⠀⠀⢀⠀⢀⠀⣀⣀⠀⣀⡀⢀⣀⣀⣀⡀⠀⣄⢠⠀⠀⠀⠤⠤⠴⠠⠆⠂⡃
⠀⠀⠀⠀⢈⠀⠀⠁⠁⠀⠀⠀⠀⠀⠃⠛⠀⠀⠀⠀⠀⠅⠨⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠨⠀⢐⠇⠦⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⠀⠀⣄⣠⠀⠀⠀⠀⠀⡤⢴⠀⠀⠀⠀⠀⡒⢘⠉⠈⡅
⠀⠀⠀⠀⠠⣀⣀⡀⢀⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠂⠘⠀⠀⠀⠀⠀⡁⢀⣀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠅⠩⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠆⠰⠀⠀⠀⠀⠀⠆⢘⠀⠉⠉⠉⠉⠇⠪⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠈⠁⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡠⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠁