Mouth watering Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣶⣶⡿⠇⠀⠓⠆⠀⠀⠀⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣯⢟⡿⣿⣭⣭⣶⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠋⠁⠀⠈⠉⢛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠢⢤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⠀⠀⠀⢀⠀⣀⣀⣾⠈⢠⡟⠚⢈⣏⣿⣿⣿⣿⣿⣿⣦⣴⣤⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣶⣤⣶⣾⣿⣿⣿⣿⣿⣷⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣯⣤⡤⠤⣧⣀⡀⠀⣉⣀⣀⣈⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣤⣴⣶⣶⣤⣤⣀⣭⣤⣤⣶⣾⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⠉⠛⠋⠋⠉⠉⠉⠉⠛⠛⠛⠿⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢿⣿⣿⡇⢠⡀⠀⠀⠀⠀⠀⠀⡉⠒⠀⠒⠈⠁⠀⠈⠉⠙⠛⢿⣿⠿⢿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠻⣿⣇⣿⣷⠀⠀⠀⠀⠀⡈⠁⠛⠦⣀⣤⣤⣤⣀⠀⠀⠀⣸⠃⣀⣤⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠘⢿⣜⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⢻⣿⣶⣾⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠻⣷⣤⡀⠀⠀⠀⢀⡲⣦⣄⠀⠏⢸⣶⣾⡿⢟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣷⣿⣿⣝⣿⣷⣾⡿⢟⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠋⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠉⠻⢦⣀⣴⠶⠛⠛⠛⠻⢿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣀⡾⠃⠀⣀⣠⣤⣤⣬⣿⣧⣤⣄⣀⠀⠀⠀⠈⠛⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠉⠙⣋⣵⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠛⠷⣤⣀⠀⠈⢿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣼⣇⢀⣴⠞⠋⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣸⣏⡙⠻⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⣠⡞⠉⠀⣽⠟⠁⠀⠀⠘⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣏⠙⢻⡎⠙⢿⣿⣿⣦⡀
⠀⠀⠀⠀⣰⠏⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣷⡦⠀⠀⠀⠀⢠⣴⣦⡄⠀⠀⠙⣧⡘⢷⣤⣄⡹⣿⣿⣿⣆
⠀⠀⠀⢠⡿⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠈⢷⡀⠀⠉⢻⡎⢿⣿⣿⣧⡀
⠀⠀⠀⢸⡇⢠⡿⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⢀⣼⠃⠈⢿⣿⣿⣷
⠀⠀⠀⠈⣷⣾⠁⠀⠀⠀⠘⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣶⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠈⣷⡟⠉⠻⣆⠈⣿⣿⣿⣧
⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠃⠀⠀⠀⠀⠸⣧⠀⠀⢹⡆⢸⣿⣿⣿⡄
⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⣼⠃⢸⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠘⠷⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣷⣾⣃⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠿⣿⣿⣿⣿⡿⠿⠋⠁


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

⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀
⠀⠀⠀⠀⢠⣾⣷⡄⠀⠀⠀⠀⠀⠀⠉⣾⣿⣾⣷⡄⠀⠀⠀⠀⠀⢀⣡⣥⣴⣇⡤⠀⠀⠀⠀⠀⠀⢀⣿⣿⡁⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣷⣄
⠀⠀⠀⠀⠀⢻⡟⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢼⣿⣿⡇⠀⠀⠀⠀⠀⠀⣛⣛⣛⣛⣛⣛
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠒⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⣀⣠⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⣰⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⠀⠀⠀⠀⠀⡀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣄
⠀⠀⠀⣭⣭⣇⣿⣼⢼⠂⠀⠀⠀⠀⠐⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠀⠀⠀⠀⠀⠀⡅⠀⠀⣿⣿⡏⠀⠀⠀⠀⠈⣿⣿⣿⣿⣶⣿
⠀⠀⠀⠙⠛⠚⠓⠛⠉⠀⠀⠀⠀⠀⠀⠘⣿⣿⠇⠀⠀⠀⠀⠀⠀⣼⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉


⠀⠀⠀⠀⢠⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀
⠀⠀⠀⠀⢸⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⣴⠟⡱⣆⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡴⠀⠀⠀⠀⠀⣿⣿⣻⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠘⣿⢯⡟⠀⠀⠀⠀⠀⠀⠺⠿⠿⠿⠿⠗⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣰⣿⡿⢿⣿⣦⠀⠀⠀⠀⠀⡇⣠⣴⣦⡄⢾⠀⠀⠀⠀⠀⠀⢠⣾⢿⣷⣦⠀⠀⠀⠀⠀⠀⠀⢀⣼⣥⡄⠀⠀⠀⠀⠀⠀⣀⣀⣼⣋
⠀⠀⠀⢿⡿⠀⠀⡝⣿⠁⠀⠀⠀⠀⡇⣿⣿⣿⣿⠾⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣻⠀⠀⠀⠀⢠⡄⡠⠿⢬⣷⣶⡄⠀⠀⠀⠀⠀⣿⡿⢿⡟
⠀⠀⠀⠐⢾⣿⣿⡿⠇⠀⠀⠀⠀⠀⡇⠈⠛⠛⠁⣿⠀⠀⠀⠀⠀⣿⡽⠿⠟⠛⠋⠀⠀⠀⠀⠀⠣⣁⣀⠼⠿⠟⠀⠀⠀⠀⠀⠀⢸⣷⣾⠇


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⢠⢿⣶⣦⣄⣀⡀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣾⣾⣝⣯⣷⣷⠀⠀⠀⠀⠀⣠⣴⣾⣶⣦⣄⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣷
⠀⠀⠀⠿⠾⠿⠟⠋⠈⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠉⠉⠉⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⡿⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⣀⣀⣀⣀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⣠⠖⠋⢉⡇⠀⠀⠀⠀⢀⡾⠁⠀⠀⡏⠉⠉⠁⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢀⡴⠋⠁⠀⢀⡾⠁⠀⠀⠀⣰⠏⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⣰⠏⠀⠀⢀⣴⠋⠀⠀⠀⣠⡞⠁⠀⠀⣀⣀⣀⣀⠀⢀⣠⣀⣀⡀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⡼⠁⠀⢀⡴⠛⠁⠀⠀⢀⡴⠋⠀⠀⠀⠀⣿⠉⠉⠉⠀⢸⡀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠧⠴⠞⠉⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠘⠃⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⢠⡤⠤⠤⠄⠀⠀⠀⣟⠛⠛⠋⠀⠀⠀⡾
⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠁⠀⢀⣀⣀⣀⡀⠀⠈⠃⠀⠀⢰⠶⠶⠶⠀⠀⠀⠀⢀⣼⣥⣤⣤⣀⡀
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣠⠴⠛⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠈⠉⠛⠶⣤⡀
⠀⠀⠀⠀⠳⣤⣤⠤⠶⠚⠉⠁⠀⢠⡤⠤⠤⠄⠀⠘⠃⠀⠀⠀⣾⠛⠛⠓⠀⠈⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡽⠂
⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⣤⣄⣀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢾⡉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠈⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀⡀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⢀⣀⣤⠖⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠲⠦⢤⣤⣬⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠶⠶⠶⠶⠶⠖⠛⠉⠁⠀⠀⢿⠀⠀⠀⠀⣀⣀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⣿⠙⠷⣄⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⢠⡇⠀⠀⠈⠙⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠒⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠠⡔⠁⠀⠀⠀⠀⠀⢡⠀⠀⠀⢀⠄⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠉⠁⠂⡀⠀⠀⠀⡀⠈⣆⡀⠀⠀⠀⠀⠀⠄⠀⠴⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠠⠊⠀⠀⠀⠀⢨⠚⠁⠀⠀⠀⠑⢆⠀⠀⠀⠀⠀⠐⡄⠀⠀⠒⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠂⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠈⠒⠤⠄⠜⢄⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⣀⠠⠊⠀⠁⠀⠀⠀⠀⢀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠑⠦⠤⠤⠄⠊⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⡡⢂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⡀⠀⠤⠤⠐⠒⠉⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⡔⠀⠀⠱⠄⠤⠊⠑⢄⠀⡠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⢀⠀⡀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢸⠉⠀⠀⠈⠈⢱⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢀⡠⠉⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮
⠀⠀⠀⠀⠀⠀⠀⢀⠄⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⡠⠤⠠⠴⠁⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢄⣀⡀
⠀⡠⠜⠀⠀⡐⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠂⢍⠒⢄
⠸⣄⠑⠤⣀⠁⠤⠒⠀⠠⠜⠑⠂⠤⠄⣀⢀⠀⠀⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⢀⣀⡀⠤⠒⠁⠀⠈⠐⠒⠊⢀⠜
⠀⠀⠈⠳⢄⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠠⠤⠭⠤⠁⠉⠋⣀⡀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⡉⠀⠤⠤⠔⠂⠀⠀⠀⠀⢰⠉
⠀⠀⠀⠀⠀⠉⠉⢹⠃⠢⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠦⠔⠂⠀⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⣊⣀⡀⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠀⣀⠈⠉⣒⡂⠀⠀⠀⠀⠀⠸⠤⠖⠒⣒⣒⣒⣒⣒⣒⣒⣂⣀⣀⣀⣀⣀⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠂⠤⠄⠠⠔⠋


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣭⣬⣯⣤⣭⣽⣭⣽⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⣫⠿⣗⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣴⡾⠟⠊⠁⠀⠀⠀⠑⠽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣋⡽⠖⠒⠒⠺⠿⠿⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠒⠶⣦⣄⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⣀⣠⡤⠤⣤⠤⠖⠋⠉⢹⡀⠀⠀⢸⡈⠳⡄⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⢠⡾⠁⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⢸⣧⣀⣻⣄⣀⣀⣹⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⣰⣯⣧⣤⣤⣤⣆⣿⣷⣤⣤⠤⠾⠓⠚⠛⠋⡩⠟⠛⢋⡥⠐⠉⠀⢨⣷⢦⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣀⡤⠾⠶⡖⠖⠛⠉⠉⠩⠛⠉⠁⠀⠤⠂⠁⠀⠀⠀⠀⠀⠀⠈⠀⣀⠔⠋⠀⠀⠀⠀⢫⣠⡀⣠⣠⣼
⢀⣤⠤⠶⠖⠛⠟⠁⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠄⠤⣒⠉⠀⢀⣀⣴⣨⣶⣀⣠⣤⣶⣦⣴⣿⠟⠉⠉⠉
⢿⣤⣤⣤⣶⣿⣼⣷⣲⣶⣿⣿⣛⣻⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⠾⢿⣖⣿⠿⠉⠉⡽
⠀⠀⠤⠠⠀⠠⠤⠀⠻⣭⠩⠉⠉⠻⣄⢸⡍⠉⢻⠿⠿⢿⢿⣿⣿⠿⠙⠻⡯⠄⠀⣾⣤⠼⠉⠤⠠⠀⣴⢡⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠙⠲⢤⣼⣀⣀⣀⣀⣻⣀⣀⣀⣀⣷⠴⠖⠋⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡖⠛⠛⠛⠒⠒⠒⠂⡐⠓⡄⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢀⡇⠀⠀⠀⠀⠀⠀⢀⡣⠀⠃⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠈⠀⠀⠀⠀⠈⢥⣨⣤⣄⠀⠀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢈⣀⢀⣀⣴⣶⣾⣷⣾⣷⣿⣿⣿⣿⣾⣷⣷⣶⣤⣄⠡⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠁⠼⣹⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠢⡀
⠀⠀⠀⠀⠀⠀⢰⣿⢀⣾⣿⣿⣿⣿⣿⣥⣀⣀⣬⢿⣄⣀⣀⣀⣽⣭⣽⣿⣿⣿⣿⣿⣷⣴⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠿⣿⠋⠻⣏⣉⣹⣿⠿⢿⣟⡯⠉⠙⠋⠛⠛⠻⠿⠹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠘⡿⢟⡿⢿⣿⣶⣿⣶⣾⣿⣿⡟⢸⣧⠊⢹⠛⠆⠀⠀⠀⠀⠀⢀⡈⠍⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢺⣿⣿⣼⣼⣏⣧⠈⡃⢀⡀⠈⡇⠻⢸⡯⠒⠂⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣟⡽⣏⡧⠼⣿⣿⣼⣂⣤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠤⠤⠤⠤⠤⠄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠒⠁⡠⠤⠤⣤⡖⠊⠁⠠⡉⠐⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡀⠀⠈⠁⠀⠋⠀⢠⡎⠀⠀⠀⠁⠙⡄⠀⠀⠀⠠⠖⠠⣈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠁⢀⠈⠀⠔⠀⠀⠒⠀⠀⠀⡆⠀⠀⠀⠀⢀⠇⠐⠁⠀⢀⡀⠀⠀⣀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠁⠀⠀⠲⠄⠀⠀⠢⠀⠈⠢⠤⠤⠔⠋⠀⠀⠐⠆⠀⠁⠀⠈⠀⡀⢠
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠊⠀⠐⠉⠀⠀⠴⠀⠀⠀⠀⠀⠐⠦⠀⠀⠔⠂⠀⠀⠀⠀⠢⠀⠈⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠘⠂⠀⠠⠄⠀⠀⠈⠁⠀⠠⠤⠀⠀⠀⠀⠠⠖⠀⠀⣀⠀⠘⠁⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠂⡀⠐⠄⠀⢄⠀⠠⠂⠀⠀⠀⠀⣀⠀⠀⠐⠢⠀⠀⠈⠁⠀⠀⠀⢸
⠀⠀⠀⠀⢀⡴⠊⡉⢄⠀⠀⠁⠀⠀⠠⠠⠄⢀⠀⠈⠂⠀⠀⡀⣀⠀⠀⠀⠀⠂⠁⠀⢂⠀⠀⢸⢄
⠀⠀⠀⢠⠎⠀⠀⡇⠀⠑⠄⡐⠀⠐⠁⠀⠀⠀⠁⠀⠀⢀⠁⠀⠀⠑⠀⠀⠀⠀⠀⢀⠨⠂⠀⢺⠀⠱⡀
⠀⠀⠀⡎⠀⠀⠀⠉⢂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸⠀⠀⠀⢀⠀⠀⠀⠆⠈⠁⠀⠀⡀⠹⠀⠀⢱
⠀⠀⠀⡇⠀⠀⠀⢡⠀⠑⠠⡀⠀⠀⠀⠀⠀⠀⠑⠄⣀⠜⠉⠉⠀⠈⠀⠀⠀⠀⠀⢀⠄⠊⠀⡄⠀⠀⢸
⠀⠀⠀⠱⡀⠀⠀⠀⠁⠀⠀⠀⠉⠒⠀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠒⠉⠀⠀⠠⠊⠀⠀⢀⠎
⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠑⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠊⠀⡀⠄⠊⠀⠀⠀⠠⠎
⠀⠀⠀⠀⠀⠀⠑⠤⣀⠀⠀⠀⠀⠈⠁⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠁⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠒⠒⠒⠒⠒⠒⠒⠒⠊⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠂⠀⠀⠀⠀⠀⠀⠀⠰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡅⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⣶⠀⠀⠈⠷⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⡞⠳⠊⠀⠘⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠰⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⣄⠀⠀⢠⡦⠀⠀⠀⠘⠛⠟⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⠿⣶⣿⣅⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠈⢯⡙⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⢿⣦⠀⠀⠀⢠⣷⠀⠈⠛⢿⣦⡀⠀⠀⠀⠛⠻⠇⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠈⢻⣧⡀⠀⠀⠁⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠙⢿⣦⡀⠀⢰⣤⠀⠀⠀⠈⠻⣷⡀⠀⠀⠰⡿⠁⠀⠀⠚⠟⠋⠀⠉⠐⠲⠶⠿⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠙⢿⣦⡈⠀⠀⠀⠀⠘⠟⠹⣷⡀
⠀⠀⠀⠀⠀⠀⣸⡿⢿⣦⡀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣤⡀⠀⠀⠀⠀⢹⡇⠀⠀⠉
⠀⠀⠀⠀⠀⢠⣿⠃⠀⠙⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣶⣦⣴⡿⠃
⠀⠀⠀⠀⢀⣾⣇⠀⠀⠀⠀⠈⠙⠻⢷⣶⣤⣄⣀⣀⣀⣤⣶⠿⠛⠁
⠀⠀⠀⠀⣼⡟⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⢉⣩⣿⡿⠟⠋
⠀⠀⠀⢰⡿⠁⠀⠈⠛⠿⣶⣦⣤⣤⣤⣾⠟⠋⠁
⠀⠀⢀⣿⣇⠀⠀⠀⠀⢀⣠⣾⠿⠛⠉
⠀⠀⣾⡟⠛⠿⣷⣶⡾⠟⠋⠁
⠀⣸⣿⣤⣶⠿⠛⠉
⠀⠙⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡄⠀⠀⠀⠀⠀⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⢠⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣷⣦⣤⡀⠀⠀⠀⣠⣤⡀⠀⠀⣀⣀⣀⣠⣤⣿⣿⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠻⠼⠇⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶
⠀⠀⠀⠀⠀⠀⠰⣶⣤⣾⣇⠀⠀⠀⠀⠀⠀⢸⣏⣹⡇⠀⠀⠀⠀⠿⠛⠛⠻⣿⠇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠟⠂⠀⠀⠀⠀⠀⠉⠉⣀⣠⣤⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣸⣿⣿⣶⡆⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡟⠀⠀⠀⠠⠿⠛⠉⠁⠈⠛⠿⣿⠀⠀⠀⠐⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⡽⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⢀⣤⡄⠀⠀⠀⢰⣿⣿⠏⠀⠀⠀⠀⠀⠀⢰⠟⢳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠈⠀⠀⠀⢠⣿⡿⠃⢀⣠⡄⠀⠀⠀⠀⠘⠷⠞⠃⠀⠀⣀⣠⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠁⠀⠸⠿⠟⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣦⡀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⠟⠛⠉⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠉⠻⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⢶⣾⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠈⠙⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⣶⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⢿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠈⠙⠻⢿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⢷
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣷⣦⣄⡀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠤⠶⠶⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠙⠲⠋
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣤⣀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⠁⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢠⣿⡿⠉⠻⢿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣦⣄⡀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⣠⣾⣿
⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠈⠙⠿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⣤⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣷⣦⣀⠀⠀⠀⠀⣀⣤⣴⣶⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⠟⠂
⠀⠀⠀⠀⣸⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣶⣾⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠿⠿⢿⣿⣿⠁
⠀⠀⠀⢠⣿⡿⠀⠈⠙⠻⣿⣿⣶⣤⡀⠀⣀⣠⣴⣶⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡿
⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀⣉⣿⣿⣿⣿⣿⠿⠛⠋⠁
⠀⠀⣼⣿⣧⣄⣀⣤⣶⣾⣿⡿⠿⠛⠉⠁
⠀⢰⣿⣿⣿⣿⠿⠟⠛⠉
⠀⠈⠙⠋⠉
⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⡶⠶⠶⠶⠶⣶⡶⠶⡶⣶⠶⣶⠶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⢄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡴⠂⠑⢄⠀⠀⠉⠭⢭⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠈⠁⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣷⡀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠳⢤⣄⣀⣤⡴⠋⠀⠀⠀⢀⡴⠁⠀⢠⠀⠀⣹⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⠤⠖⠚⠁⠀⢀⡴⠁⠀⢀⣿⠓⢮⡻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡶⠾⠿⠟⠛⠛⠛⠉⠉⠉⠀⠀⠀⣀⣠⠤⠚⠁⠀⠀⢀⣾⡏⠀⠈⢷⡘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⡴⠶⠶⠶⠖⠚⠛⠉⠁⠀⠀⠀⢀⣠⣴⡿⠋⣿⠀⠀⢸⣧⢸⡷⢦
⠀⠀⠀⠀⠀⠀⠀⠞⣋⣭⣥⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠿⠿⠛⠁⣠⣾⠃⠀⠀⣸⡏⢸⡇⠈⢧
⠀⠀⠀⠀⠀⢀⣴⡿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣶⠿⠛⢁⡰⠁⣰⡿⠁⣼⠃⠀⢸
⠀⠀⠀⠀⠀⣿⡏⠀⣀⣤⣶⣶⠶⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⠉⢀⣠⠔⠋⣠⣾⠟⠀⣴⠏⠀⢀⡿
⠀⠀⠀⠀⠀⢿⣧⣼⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⠴⠖⠚⢉⣠⣴⡿⠛⠁⢀⡾⠃⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣶⣶⣶⣶⣶⣶⠿⠿⠟⠛⠛⠉⠉⣀⣀⣤⣴⣾⣿⠋⣁⣀⣤⣶⣯⣤⣶⢿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣿⠁⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⣿⠉⠛⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⠟⠋⣹⡇⠀⢸⠇⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠸⡇⠀⢸⡇⠀⠸⣷⠀⠀⣿⠀⠀⢸⡇⠀⠀⡿⠀⠀⣿⠀⠀⡟⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢳⠀⠀⣷⠀⠀⣿⠀⠀⢿⠀⠀⢸⡇⠀⢸⡇⠀⢠⡇⠀⢸⠃⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠘⡆⠀⢸⠀⠀⢹⠀⠀⢸⠀⠀⢸⠁⠀⢸⠁⠀⠸⠀⢀⣦⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣶⣦⣤⣤⣸⣀⣀⣸⣀⣀⣸⣀⣠⣼⣤⣶⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠉⠁

⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠘⠊⠀⠀⠀⠀⠘⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠙
⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠀⠀⣠⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠈⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠙⠃
⡩⠂⠀⢠⠀⠀⠀⠀⠀⠀⠑⠵⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⡄⠀⠀⠀⠀⠀⠀⠶⠖⠀⠀⠀⠀⠀⠒⠀⠀⠀⠠⢦⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢶⣄⠀⠀⠀⠀⢀⣀⡀
⠃⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⠀⠀⢄⠀⠀⠀⠀⢀
⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋
⠉⠀⠀⠾⠋⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⣂⠃⠀⠀⣤⡀⠀⠉⠁⠀⠀⠀⠀⠙⠋⠀⠀⠐⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠏
⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠓⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘
⠀⠀⠀⠀⠀⠠⣖⣠⠀⠀⠀⣤⣄⠀⠀⠰⠙⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠻⠂
⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢀⡀⠀⠀⠘⠁⠀⠀⢀⡀⠀⠀⢠⠀⠀⠀⠀⡀⠀⢀⡀⠀⠀⠰⠀⠀⠀⠋⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠛⠀⠀⢠⡶⠂
⠀⠀⠀⠀⢠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠣⠇⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⡄
⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠀⠀⠀⠀⠀⠀⠀⠀⠎⠕⠀⠀⠀⠀⠤⠀⠀⠀⠀⠖⠀⠀⠀⠠⠆

⠃⠈⢛⠀⠘⠋⠀⠀⢸⢀⣠⠀⠀⢠⡀⢀⡤⠈⠇⠀⡙⠂⢀⡀⠀⢷⠀⠁⠀⠙⠃⠀⠈⠁⠶⠆⠸⠀⡤⠈⠓
⠛⠀⠈⢉⡀⠰⣄⠓⠆⠀⢀⡀⠻⠈⠁⠀⢁⠒⠆⠈⠉⠁⠈⠀⠲⠤⠐⠒⠀⠀⠚⠃⣠⠄⡴⢀⣀⠀⣁⠀⢼
⠿⠘⠇⠙⠀⠤⠄⠀⡶⢠⡀⢉⡀⠠⠖⠂⠘⠃⠒⠃⡶⠀⡗⠀⣤⡀⣀⠸⠆⠀⣠⣤⠁⣀⠴⠦⢀⡀⠈⠃⢠
⡄⠐⠛⠀⣤⠀⡀⢠⠀⠈⠁⠉⣅⡀⠀⡛⠃⠀⣤⠀⠀⠠⢤⠄⠈⠀⠋⡀⢉⠁⠀⣀⠀⣈⡁⠀⠘⣄⡀⠿
⡀⡀⠠⣄⠉⠐⠃⠘⠀⠀⠴⠆⠈⣁⠸⠃⠀⠀⠁⣴⠀⣷⠀⢈⡛⠀⠛⢁⠈⠛⣀⠛⠀⢈⠁⣄⠀⢨⠁
⠁⠗⢀⣬⠄⢠⠉⢃⡄⢶⡀⢠⡆⢉⡃⠀⠉⣉⠀⢀⣀⠀⠀⢉⡀⠰⢃⣘⠃⠘⡁⠀⣐⡋⠀⡋⠀⢙⠐⠛⠃
⠤⠀⣀⢠⡄⠘⢀⠉⠠⣄⠰⠤⠁⠉⡁⠸⡆⠛⠀⢠⣄⠀⠿⢀⡉⠀⠈⠉⢠⠀⠷⠀⢉⣁⠀⠇⣀⡌⠓⠀⡄
⢤⠀⠋⣠⡄⠘⢉⡀⢠⣌⠀⣠⠆⠀⠙⠂⢰⡄⢤⡄⠈⠀⠀⠉⠉⡀⠸⠇⠈⠀⠰⠃⠀⠉⢠⠆⢀⡄⢀⡀⠁
⠀⣠⠀⠠⡄⠀⣜⠃⠀⠀⠀⡀⠰⠶⠀⠴⠌⠁⢦⢀⡀⠛⢁⠸⠆⠙⢃⡄⠐⠒⠂⢰⡄⠐⠒⠀⢈⣀⠈⠃
⣈⠁⢠⠆⠁⠀⢬⡀⠠⠏⠐⠇⠀⢦⠀⡄⢠⡆⠀⠘⢃⣤⠙⠃⠘⠧⠈⢁⣄⡛⠆⠈⠀⠀⡤⠀⢈⡉⠀⠀⠉
⠀⠀⣤⢀⡶⠀⠀⠁⢰⠀⠐⠲⠀⠀⠀⣅⠀⢠⠖⠀⢈⠁⠐⠶⠀⢀⠒⠂⢰⡄⢠⠆⢀⡀⠁⣀⡈⠉⠀⠸
⠄⢀⣉⠀⠀⠷⠀⣀⡀⠀⢤⡀⣴⠀⠀⠉⠀⠀⢰⠃⠘⣃⠀⠒⠦⠘⠃⢀⠀⢁⠀⠀⠚⠀⠀⣭⠀⠀⡄⠰⠋
⠀⢈⡍⠀⢀⡀⢠⡍⢡⡆⢀⣠⠄⢀⠉⠁⠀⠳⠄⠀⢈⣁⠸⠇⠀⠷⠐⠋⠀⠘⠀⠚⠁⢠⠀⠘⢀⠀⠁⠤⠤
⠀⠉⢠⠀⠉⢠⡀⠁⣀⡀⠀⣀⡀⠘⠇⠒⠒⢀⡀⠤⠤⠉⠀⠰⠶⠀⡄⠈⣉⠀⢀⠙⠂⠈⣄⡀⠛⢠⠖⠰⡆
⠆⢀⣈⡁⠀⠸⣅⠀⠀⠀⠀⠁⡤⠀⢠⡆⠠⣄⠙⢀⡀⠸⠄⢀⣀⠘⠁⣄⡙⢃⡘⠃⢠⣄⠀⠁⠀⠀⠐⠒⠂
⠀⢀⠀⠰⢶⠀⠀⠞⠃⠙⠆⠈⢁⡀⠈⢀⠀⣉⡀⣋⠀⠀⣤⡌⠁⠘⠇⠀⠁⠘⠁⢤⡄⠀⠰⠃⠘⠇⠠⠶
⣄⠘⠂⠀⠈⠓⢠⡆⠈⠉⢰⠆⠀⠛⠀⠘⠃⠉⣡⡈⠋⠀⢠⡄⢀⠀⠰⠃⢰⠂⠀⠶⡄⠀⠶⠄⠼⠃⣠⡄⠐
⣈⠁⡀⠚⢁⣀⠀⣀⠘⠓⠀⠈⠛⠀⠀⠸⠇⠀⣀⣀⠰⠦⠈⠀⠈⢃⡐⠦⠄⠀⠳⠀⠀⠀⠰⠶⠀⠀⢀⠀⡇
⠋⠀⠃⢀⡬⠁⠀⠙⠐⠋⠀⢶⠙⠂⠼⠃⠦⠄⠈⢠⠶⠀⠾⠀⢷⠘⠃⠰⠃⠘⠇⠒⠋⠸⠆⠐⠛⠁⠙⠂⡀
⠘⠛⠀⣀⢰⡄⠘⠓⠀⠘⠷⠀⣠⡀⠀⠘⠆⣠⡄⠀⠀⠸⠄⠀⡀⠀⠴⠂⢠⡄⣠⠀⢠⣄⠀⠈⠉⡀⢠⡄⠙
⡁⠀⠀⠃⠀⠀⠀⠾⠀⠠⣄⠀⠁⣀⡘⠋⠀⠁⠀⠉⡋⢠⣀⠀⠃⠀⢠⡄⠈⠀⠉⢀⣀⠀⠐⠋⠀⠙⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⢛⢦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡂⠅⡚⠟⢃⠇⠀⡆⡄⢣⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢊⡔⠈⢀⠤⠊⢀⠔⢠⠁⣰⠛⢍⢣⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡂⠭⢀⣒⠚⠙⠳⠴⠖⠷⠒⠓⢉⠔⡀⠊⠰⢀⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠤⣒⣾⣮⠐⢈⠁⠠⠤⠀⠀⠀⠀⠐⠒⡈⠕⢊⣀⡔⣡⣪⠃⡜⢢
⠀⠀⠀⠀⠀⠀⢸⠭⠬⠉⢉⣙⠋⠥⠈⢛⣉⠨⠌⢚⡋⠭⠑⠋⣉⠠⠐⢉⠤⠊⡠⢊⡇
⠀⠀⠀⠀⠀⠀⠘⣈⢈⠡⠄⢀⣒⠀⠭⠀⠒⠈⣉⡀⠤⠐⢂⡉⠤⠒⣈⠤⠐⣈⣔⠅⠣⡀
⠀⠀⠀⠀⠀⢠⠊⠈⠂⠢⠭⠤⡄⠐⣒⣈⣩⡅⠀⣒⣈⢭⡀⠒⠬⠵⠒⠚⠉⠉⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠸⡖⢢⠄⢠⡀⢀⣀⠀⡀⡀⡀⠀⠀⠀⠀⢀⢀⣀⣀⡀⢀⡠⠠⡤⠀⠶⠈⣿
⠀⠀⠀⠀⠀⠀⡇⠀⡄⠀⡇⠀⠉⠀⢸⠀⠸⠁⠘⠁⠈⠁⠈⠁⠈⠀⠀⠀⠀⠁⠀⡆⢠⡇
⠀⠀⠀⠀⠀⠀⢠⠀⡇⠀⠁⠀⢰⠀⢸⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸
⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢠⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠁⠸⠀⠘⠀⠈⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⠀⠈⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡄⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠀⡃⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢀⣇⠀⡄⢸⠀⠸⠀⠀⠀⠀⠀⠀⠀⢀⡀⣸⡀⠤⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠁⠈⠁⠈⠁⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠛⠿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣶⠛⢿⣷⠀⠀⠀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⣸⡟⠀⠀⢀⡀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢸⡇⠘⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠉⠀⠀⠀⠀⠀⠀⠻⣄⣈⠛⠿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⢦⠉⠛⢿⣷⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣰⡿⠛⠛⠛⠻⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠾⠛⠁⠀⠀⠀⠀⠀⠈⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⢿⣄⣀⡀⠀⠀⢀⣀⣀⣀⣀⠠⠄⠀⢀⣀⣠⣤⡴⠶⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣤⣤⣭⣭⣭⣭⣭⣤⣤⡶⠶⠶⠞⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣼⣿⣄⣀⡀
⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⢉⣠⠾⠋⠉⠉⡙⠻⣷⣦
⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢒⣉⣤⡴⠞⠋⠁⠀⠀⠀⠀⠙⣦⠈⣿⣇
⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠶⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢸⣿
⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⠶⠶⠶⠞⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢸⡿
⣸⡏⣼⠁⠀⠀⠀⠀⠀⣠⠖⢉⣠⡴⠶⠞⠛⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⡿⣧⣤
⣿⡇⢿⠀⠀⠀⠀⠀⣸⢃⣼⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣤⠞⠋⠀⣨⢻
⢻⣷⡸⣆⠀⠀⠀⠀⠟⢸⣯⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠞⠛⠋⠉⠀⠀⠀⢀⠞⣸
⠈⢿⣷⣝⠦⠤⠄⠀⣀⣾⣿⣄⠀⠀⠀⠀⢀⣠⣤⣍⡉⠓⠦⣤⣀⣀⣀⣀⣀⣀⣀⠤⠔⠊⢁⣀⣤⡴⠶⠛⠉⠉⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⠴⠞⠉
⠀⠀⠉⠛⢻⣿⡟⠛⠋⠀⠙⠻⠿⠶⠶⠛⠋⠁⠉⠙⠻⠷⣶⣤⣤⣭⣭⣥⣤⣤⣴⠶⠾⠛⠋⠙⠿⠷⠶⠶⠶⠶⠛⠛⠉⠉⠉⠉⠉⠀⢀⣠⡄
⠀⠀⠀⠀⠘⣿⣿⣷⣤⠶⠻⢿⣶⠾⠿⣷⣦⡴⠿⢿⣦⣤⡴⠿⣿⣬⣉⣥⣤⣄⣀⣠⠶⢶⣶⣄⣀⣤⠶⣶⣄⣀⡴⢾⣦⣴⠟⠿⠶⠾⣻⣿⠃
⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⣤⠀⠀⠀⣷⠀⠀⠀⣷⠀⠉⠁⢸⡆⠈⠉⠉⣴⠈⠛⠛⠁⢰⡇⠉⠛⠋⠁⡖⠈⠙⠉⣴⠈⠉⠁⢸⠇⠀⢠⣿⠏
⠀⠀⠀⠀⠀⠀⢹⣿⡀⠀⢹⡆⠀⠀⢿⡀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⡿⠀⠀⠀⡿⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠈⣷⠀⠀⢸⡇⠀⠀⢹⡄⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⣼⠁⠀⠀⠀⣼⠀⠀⠀⢸⡇⠀⠀⢸⠇⠀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⢹⡆⠀⠘⣧⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⢀⡟⠀⠀⠀⣼⠁⠀⢀⡿⠀⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠈⣷⠀⠀⣿⠀⠀⢸⡇⠀⠀⠸⡇⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⡟⠀⠀⢸⡇⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⢻⡆⠀⢸⡇⠀⠈⣧⠀⠀⠀⣿⠀⠀⠀⡟⠀⠀⠀⠀⣿⠀⠀⠀⣾⠀⠀⠀⢸⡇⠀⢀⡿⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠘⣧⠀⠘⣧⠀⠀⣿⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⢰⡇⠀⠀⢀⡟⠀⠀⠀⣼⠀⠀⢸⠇⢰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⢻⡄⠀⣿⠀⠀⣿⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢀⡟⠀⠀⡿⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠘⣧⠀⢸⡇⠀⢹⡄⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⣼⠀⠀⠀⢸⡇⠀⢸⠇⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⢻⡄⠘⣧⠀⢸⡇⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⢸⠇⠀⢀⡟⠀⠀⠀⣾⠀⠀⡿⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠘⣧⠀⣿⠀⢸⡇⠀⠀⢿⡄⠀⢸⡇⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⢀⡟⠀⢸⠇⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠛⠀⠸⠇⠀⡷⠀⠀⠸⠇⠀⠘⠃⠀⠀⠀⡿⠀⠀⠺⠀⠀⠀⠸⠇⠀⠿⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠶⠾⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡌⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠚⠅⠈⢦⣀⠀⠀⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠱⡀⠀⠈⠑⠲⣄⣑⣱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠸⠂⢀⠠⠀⢸⣿⠋⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢤⠀⣁⡤⢚⣇⡔⢂⣤⠤⠴⣂⣼⠻⣄⠀⠀⢸⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢆⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⣸⠀⣠⠞⠉⠀⠀⠈⣦⣀⣴⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⠀⠀⠀⣰⠏⠀⣏⠀⠀⠀⠀⠀⣿⠻⡿⠛⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⢀⣠⠗⠀⠀⢀⣠⠴⠁⠀⢿⡁⢨⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⢀⣀⣀⣀⣀⣀⣀⠀⠠⠔⠊⢀⣩⠤⠶⠶⠚⠉⠀⠀⠀⣰⣿⣵⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⠻⢄⠀⠉⠀⠀⠀⠀⣠⡤⠞⠉⠀⠀⠀⠀⣠⣴⣶⡾⡿⠿⡿⡿⢊⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠉⠳⠶⠶⠶⣾⣿⣦⣤⣤⣴⣾⣿⠟⠿⠋⠁⠊⣩⢄⣴⣼⣶⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠲⣤⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠂⠠⡠⠀⣀⣀⣧⣶⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢳⠸⡏⠘⡷⠒⢿⠶⣿⠾⢿⠿⣿⠿⣿⠿⢻⠛⢻⠁⣿⡿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⡆⢿⠀⣿⠀⢸⠀⣿⠀⣾⠀⣿⠀⣿⠀⣽⠀⣿⣿⣿⣷⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠐⣸⡇⢸⡆⠸⡇⢸⢄⣻⡀⣹⠀⣿⢰⡿⢰⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣿⣿⢸⣧⠀⣷⣼⣆⣿⣄⣿⢤⣿⣺⣧⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⣠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⣟⣾⣿⡐⣿⣿⣇⣿⡽⣿⣼⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣷⣿⣿⣿⣇⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣽⣿⣧⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣵⠲⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⢗⡚⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠿⠿⠿⠿⠿⠿⠛⠻⠛⠛⠟⠛⠋⠉⠉⠉⠁



⣿⠿⡿⠿⡿⡟⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣻⣿⣛⣿⣛⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡢⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⡉⡅⠀⠀⠀⠀⠈⠗⠑
⠀⠀⠀⠀⠀⠀⠀⠸⢂⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠐⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠐⠤⠀⠀⠀⠁⠀⠑⠀⠐
⠀⠀⢀⠀⢀⠀⠐⠖⠒⠂⠀⡄⠀⡀⠀⠀⠀⠀⠀⠁⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢴
⠀⠀⠀⠀⠀⠀⠐⠁⠄⠀⠀⢀⠀⡀⠀⠀⠀⠀⠊⠠⠀⣾⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠄⠀⠖⠀⠠⠒⠓⠀⠈⠢⡀⠀⠀⠀⠠⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⣀⡴⠇⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⠀⠄
⠀⠀⠐⠀⠈⠂⢀⠀⠰⡀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠐⢁⡄
⢠⠠⣂⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠼⢁⠈⠀⠀⠀⢨⠀⠀⠉⠀⠀⠂
⠈⠰⠀⠀⠀⠀⠀⠀⠀⠂⠀⠉⠀⠀⠀⠀⠀⠢⠶⣥⠀⠀⠄⢺⠛⠋⠀⠀⠐⠀⠻⢯⣚⠏⠈⣡⣖⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠕⠀⠀⠉⠉⠀⠀⠑⣬⣭⠤⡠⠈⠁⠉⢛⠓⠤⠀⠀⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢺⡄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣴⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠭⢪⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⣸⠙⣏⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠦⠀⡀⠈⠀⣠⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⣄⠈⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⢂⡤⢈⣟⣿⡃⠀⠀⠀⠀⠀⠀⠆⠀⠀⠁⠰⠀⠠⠀⠀⠆
⠀⠀⠀⠀⠀⠀⢁⡀⠑⠀⠲⢀⣀⡀⠀⣀⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠛⣕⠈⠘⠃⠁⠀⠀⠀⠀⠈⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⢦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠀⠈⣠⠀⠾⠂⠀⢴⠗⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠘⠃⣠⡀⠂⠀⣴⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠛⠃⣨⡀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⢀⠙⠁⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣍⠕
⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠻⠉⢠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠰⡿⠀⠀⠀⠈⠋⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢀⠀⣀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠀⠀⢀⠀⠀⣶⣶⠄⠀⠀⠻⠿
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠙⠋⠀⠈⠛⠀⠀⠙⠁
⠀⠀⠀⠈⠛⠛⠛⠶⠞⠳⡶⠟⠶⠖⠲⠞⠁⠀⠀⠀⠀⠔⠀⠀⠘⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠄⠊⡁⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠈⠁⢀⣀⠤⠔⢋⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠔⠃⢉⡠⠄⠂⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃

⣿⢿⠿⠿⢿⡟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣟⣛⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠈⠁⠀⢰⠀⠀⣀⠀⠐⠒⠂⠀⡴⠃⠀⠀⠒⠒⠀⠀⠸⠁⠀⠀⡀⠀⠀⣠⠆⠀⠈⠀⠀⣠⠄⠀⡀⠀⠉⠀⢀⡀⠀⠈⠀⠀⢠⠂
⠀⠲⢤⠀⠀⠘⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠠⡄⠀⠀⠈⠀⠀⠘⠁⢀⠀⠀⠘⠀⠀⢠⠆⠀⠈⠀⠀⠘⠄⠀⠸
⡄⠀⠀⠀⠀⠀⠊⠀⠀⠠⠄⠀⠘⠄⠀⠀⠈⠀⠀⠈⠁⠀⠀⢀⠀⠀⠀⠤⠖⠀⠀⠓⠀⠐⠲⠆⠀⠀⠀⠈⠧⠀⠀⠀⠀⠀⠀⠀⠠⠶⠂⠀⢀⡀
⠀⠀⠀⣠⠆⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡔⠀⠀⠐⠃⠀⠀⠀⠀⢀⣀⡀⠀⢀⠀⠀⣀⡀⠀⠠⣄⠀⠀⠤⠆⠀⠉⠓⠀⠀⠀⠀⠀⠁
⠑⠂⠀⠀⠀⠀⡀⠀⠁⠀⢠⡆⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠱⠄⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠋⠀⠀⠀⡆
⣠⠀⢰⡀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠠⠎⠀⠀⠈⠂⠀⠀⠀⠀⠀⠰⡀⠀⢀⡄⠀⠑⠄⠀⠰⠶⠂⠀⠀⠞⠀⠀⠃⠀⠀⠀⢤⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠒⠂⠀⠀⠀⠁⠀⠀⠀⢀⡄⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠈⠂⠀⢀
⠀⠚⠀⠀⠀⣀⠀⠀⠀⠀⢤⠀⠀⠀⠀⡄⠀⠀⡇⠀⠀⠘⠀⠀⠀⠑⠤⠀⠀⠀⠘⠄⠀⠀⠸⠁⠀⠀⢦⡀⠀⠀⠁⠀⠀⠈⠳⠄⠀⠀⠀⠀⠀⠐⠃
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠦⠄⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠀⠀⠀⠀⠀⠤⠆
⠀⠠⠖⠀⠀⠠⠂⠀⠸⠀⠀⠀⠸⠁⠀⡄⠀⠀⡆⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⠀⠁⠀⠐⠒⠀⠀⢰⡄⠀⠀⢠⠤⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⢀⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠉⠀⠀⠃⠀⢠⠖⠀⠀⠀⠀⠀⠀⢆⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠀⠀⠈⠀⡀
⠊⠀⠰⠃⠀⠀⠒⠂⠀⡄⠀⠀⢠⠴⠀⠀⣰⠂⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠀⠀⠈⠁⠀⠘⠄⠀⠀⠘⠁⠀⠀⠰⡄⠀⠐⢦⠀⠀⠀⣠⠀⠀⠐
⣀⠀⠀⠀⠀⡀⠀⠀⠰⠃⠀⠀⠀⠀⢀⠀⠁⠀⠀⢹⠀⢀⡔⠀⠀⠀⠉⠲⠀⠀⠴⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠘⠁⠀⣠
⠀⠉⠁⠀⠀⠳⠀⢀⠀⠀⡰⠃⠀⠀⠘⠂⠀⠀⠀⠀⠀⠈⠀⠠⠴⠀⠀⠀⠀⢀⡀⠀⠀⠱⠀⠀⠀⠋⠀⠀⠃⠀⠀⠋⠁⠀⣠⠂⠀⠀⠀⠀⠃
⠃⠀⣠⠀⠀⠀⠀⢸⠀⠀⠁⠀⠐⠦⡀⠀⠀⠸⠀⠰⠦⠤⠀⠀⠀⠀⠴⠁⠀⠀⠉⠒⠀⠀⠀⠀⢠⠤⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠀⠔⠀⠀⠐⠋
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠰⢤⠀⠀⠐⢄⡀⠀⡠⠀⢀⠴⠂⠀⠰⡄⠀⠀⠀⠀⢀⡠⠄⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⢀
⠂⠀⠀⠋⠀⠀⠈⠉⠁⠀⠈⠃⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⢀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠀⠀⠛
⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢄⡀⠀⢸⡆⠀⢀⡀⠀⠀⠐⣄⠀⠒⠒⠀⠀⢠⠄⠀⠈⠀⢀⡠⠀⠀⠀⠀⢀⡄⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠐⠉⠀⢀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠈⠀⢀⣀⡀⠀⠈⠀⠀⠀⡄⠀⠀⠀⠊⠀⠀⠀⠈⠁
⠈⠓⠀⠀⠀⠀⠀⠃⠀⠀⡠⠀⠘⣆⠀⠀⡆⠀⠀⠖⠃⠀⠀⠞⠀⠀⠀⠴⠂⠀⠀⠀⠃⠀⠀⠈⠁⠀⠠⠤⠀⠀⠀⠃⠀⠤⠀⠀⣠⠀⠀⣀⠤⠀⢀
⠀⠀⡀⠀⡴⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠙⠀⠀⣀⠴⠀⠀⠀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⢠⠄⠀⠀⠀⢀⣀⡀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⡀⠀⠘⠆⠀⠀⠠⠤⠄⠀⠲⢄⡀⠀⠀⠀⠀⢰⡀⠀⠙⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠠⠴⠆⠀⢀⡀
⠀⠀⠤⠂⠀⠈⠃⠀⠀⢀⡀⠀⠀⣀⣀⠀⠀⠀⢠⠆⠀⠀⠀⠀⣀⠀⠀⠀⡰⠀⠀⠐⠒⠀⢀⡀⠈⠃⠀⠀⠀⠳⠀⠀⠠⠞⠁⠀⢠⠂⠀⠀⠀⠃
⠀⠀⠀⠀⠀⢤⡀⠀⠐⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡄⠀⠈⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠖⠂⠀⠀⡀⠀⠀⠠⠤⠀⠀⠀⠀⠖⠂⠀⠠
⠀⠀⠑⠆⠀⠀⠈⠀⠀⠞⠀⠀⢀⠀⠀⠋⠀⠀⣠⠀⠀⠀⠀⠰⠋⠀⠈⠃⠀⠀⡇⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⢠⡄⠀⠀⢄⡀
⠁⠀⠀⡀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠁⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡠⠖⠀⠀⢀⠀⠀⠒⠉⠀⠀⠀⠀⠀⠀⡀⠀⠠
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠚⠁⣀⠀⠀⣄⠀⠀⠀⣀⠀⠀⠘⠀⠀⠀⠉⠓⠀⠈⠳⡄⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠈⠃⠀⣀⠀⠀⠐⢄⠀⠀⠉⠁
⠓⠀⢠⠀⠀⠈⠲⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⡄⠀⠐⠢⡄⠀⠀⠀⠀⢄⠀⠸⠆⠀⠀⠉⠉⢀⠀⠀⠀⠛⠀⣠⠀⠀⠀⠀⠰⡄⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠋⠉⠉⢑⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⣠⣶⣿⣿⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣤⣤⣶⣿⣿⣿⠟⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣿⣿⡟⠿⠟⠋⠀⠀⠀⣠⣾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠉⠀⠀⠀⣽⠉⠀⠀⠀⠀⢀⣠⣾⣿⣿⠶⣶⣶⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⢾⡿⠋⠉⣲⣄⠀⠀⠀⣰⠃⠀⠀⣀⣴⣿⣿⣧⢀⣀⣤⣾⣿⣿⠟⠁⣾⣀⠀⠀⠀⠐⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⣀⠀⠀⠀⠈⠛⠳⡄⠀⣷⣶⣾⣿⣿⣿⠟⠋⠀⠙⢿⡿⠟⠉⠀⢀⡜⢻⡿⠂⠀⣠⣄⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢽⣿⠆⠀⢰⣿⣦⠀⢻⠀⣿⡿⠛⠋⠁⠀⠀⠀⢀⣴⣿⠀⠀⠦⣶⣯⡀⠀⢀⡀⠀⢿⣿⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡀⠀⠀⢠⡄⠈⠛⠋⠀⢈⡆⢡⠀⠀⠀⠀⢀⣤⣾⣿⡿⡟⠀⣠⠀⠙⣿⡇⠀⠈⠁⠀⠀⠀⢀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⠀⠈⠁⠀⠀⠀⠐⣿⡇⠀⠣⣤⣶⣾⣿⣿⠟⠋⣰⠁⠀⠀⠈⠀⠉⡀⠀⠀⣶⣦⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢏⠀⠀⠐⣿⡇⠀⠀⣠⠇⠀⠀⠙⠻⠛⠉⠀⢀⡴⠃⠀⠀⢀⠃⠀⠀⠑⠀⠀⠙⠋⠀⢀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀⣀⣀⡀⢀⠟⠀⠀⠀⠀⠀⠀⠙⢚⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠙⢷⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠃⠀⠀⠀⠀⠀⠀⠠⠢⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠄⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⢿⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠖⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⢀⡄⠀⡀⠀⠀⠀⠀⠀⠂⠀⠈⠁⠀⡀⠀⠀⠀⢰⡆⠂⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠈⠁⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠂⠀⠈⠀⢀⠄⠀⢀⠄⠀⣁⠀⠀⠀⡀⠐⠷⠀⠀⠀⠀⠀⠐⠀⠠
⠀⠀⠀⠴⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡄⠀⢀⢂⡄⠉⠀⠀⠉⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠔⠁⠀⢀⣌⠁⠀⠀⠀⠀⠀⠀⠠⠄⢠⣔⠋⠓⡀⠠⣤⡄⠦⢘⠀⠀⠀⠀⠀⢠⠄⠐⠀⢀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⢀⠀⠛⠃⢀⠀⣀⠐⠘⠀⣄⡀⠀⢀⡄⠁⣄⠈⠋⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⢋
⠀⠀⠀⠀⠀⠀⠈⠀⢠⡄⠚⠀⠀⠒⠈⠀⠀⢰⡏⠁⠀⣤⢾⠣⣀⠐⠃⠊⠁⠀⢀⡀⠈⢄⠻⡠⠀⠀⠀⠀⡀⠀⠀⠀⣴⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠰⠆⢀⠀⢄⡊⠁⠠⢂⠘⠂⡬⢫⣿⠀⠀⠠⠞⣋⣀⡀⠠⠀⠁⠀⠀⠀⡄⠁⠀⠀⠀⡄⠀⠀⣠⠄⠀⠠
⠀⠀⠀⠀⣠⠄⢠⠶⣀⠤⠀⠀⠴⠲⠄⡀⠉⠁⠀⠀⠃⠶⠇⠀⠈⠀⡉⠀⠧⠀⠁⠉⠄⠀⠁⠀⠂⠀⠀⠤⠀⠤⠂⠀⠋
⠀⠀⠘⢁⠰⡄⠀⠀⠀⠉⠀⠀⢶⠄⢙⣀⠀⠀⠰⠦⡄⠱⠄⠀⠊⢹⣁⠊⠐⢀⡀⠳⠀⡀⠀⠁⠄⡀⠀⠀⠄⠀⠀⠒⠦⣄⠀⠀⠀⠃⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠉⠁⣀⠀⠄⠒⠀⠠⠀⠀⡀⣻⡇⠰⠂⠀⠙⠳⣀⠄⠀⣤⣆⠀⠀⠀⠔⠀⠀⠀⠀⠙⠀⢠⡀
⠀⠀⠘⠓⠀⠀⠀⠀⠀⠠⠠⠀⢀⠈⠠⡿⠉⠀⣲⡀⠆⠀⠀⠂⢀⡄⠀⠀⠀⡀⠀⢶⣌⠁⠀⢶⢀⣤⠄⣄⠀⢄⡀⠀⠀⠲⠀⠈⠃
⠀⠀⠀⠀⠃⠀⠋⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⠘⠋⠈⠃⠴⠞⢻⡄⠀⢠⡄⠈⠛⠀⠉⠋⡄⢐⡮⠅⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢀⡁⠠⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠁⢴⣶⢶⡍⠀⠀⠀⢀⠑⠠⠀⠚⡰⠚⠿⠙⠚⠀⠈⠉⠂⠘⠀⠀⠀⡀⠀⡀⣤⠈
⠀⠘⠀⠀⠀⢠⣤⠀⠀⠈⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⣀⡀⠸⠆⡀⠛⠋⠷⠀⢤⠤⠀⠓⠤⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀
⠀⠀⣰⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠚⠖⠀⢠⣴⠀⠈⡉⠁⠀⠀⠀⢄⡀⠀⠶⠀⠂⠀⢦⠀⠀⠀⠀⠤⢀⠘⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢰⠃⠀⠀⠁⠀⠲⠁⠀⠀⠙⠁⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⣀⣠⠀⠀⡸⠃⡀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠄⡀⠈⠀⠀⠐⣦⠂⠀⠀⡈⢹⡄⠈⢧⣈⠃⠐⠀⠀⠀⠀⠉⢠⡀⠁⢠⡀⠁⠈⠁⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠁⠀⢀⠀⠀⠉⠐⢒⣘⠇⠒⠡⠆⠈⠇⠤⠀⠐⢀⠀⠀⢁⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠉
⠀⠀⠀⠦⠀⠈⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢸⠦⠐⠉⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠙⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⡄⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⡀
⠀⢀⠀⠐⠀⠀⠐⠀⠠⠀⠀⠁⠀⠀⠀⠁⠀⠀⠆⠀⠀⠀⠀⡀⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠈⠀⢀⠀⠔⠀⠀⠀⣀⠁⠐⠀⠴⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠃⠄⠀⠀⠀⠀⠀⠈⠄⠀⡄⠀⠀⡀⠀⠄⠀⠀⠀⠀⠈⠀⡀⠈⠀⡀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠈⠀⢄⠀⠀⡀⠀⠈⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠐
⢀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⣈⠀⠀⠀⠀⢠⠀⠁⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⠈⠀⠀⠂⠀⢐⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢀⠌⠀⠀⠀⠄⠀⠂⠀⢀⡀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠈⠀⠂⠌⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⢀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠐⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⢀⠀⠄⠀⠀⠀⠀⠦
⠀⢀⠐⠀⠀⠀⠀⠂⠀⠀⠀⠓⠈⠀⠀⠀⠀⠀⠀⠚⠀⢁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠂⠀⠀⠀⠈⠀⢀⠀⠀⠒⠀⠀⠀⠀⠰⢀⠀⠉⠀⠐⠀⠂⠁⠀⠀⠀⠀⠈
⠀⢀⠃⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠄⠂⠀⠀⠀⢠⠀⠐⠈⠀⠀⠀⠀⠆
⠀⠂⠠⠀⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠀⠀⠀⠓⠀⠈⠀⠀⠀⢰⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡀⠀⠂⠀⠀⡀⠀⡀⠀⠀⠂⠀⠦⠄⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄⠀⠀⠀⢀⡀⠀⠀⠀⠸⠀⠀⠤⡀⠀⠀⠀⠄⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⠆⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠄⠀⠀⠀⠈⠃⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⢄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠫⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠭⠀⠀⠂⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠄⠀⠀⠀⠂⠀⠠⠖⠀⠀⠀⠔⠀⠀⠠⡀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠰⠂⠀⣠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠃⠀⡀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⡆⠀⠐⠐⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⠈⠙⠂⠀⠀⠀⢐⠀⠀⠈⠀⠀⠀⠀⠰⡀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠰⠆⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠐
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣀⣀⣀⣀⣀⣀⣂⣀⣀⣠⣀⣀⣸⣀⣀⣀⣃⣠⣃⣀⣄⣈⣗⣤⣀⣀⣁⣀⣀⣀⣀
⣿⡯⠭⣟⡛⣛⣛⡛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⡇⠀⠀⠀⠀⠀⠘⠒⣆
⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠧⠽⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⢴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⠀⠀⠀⠀⠀⠀⢀⠤⡀⠀⠀⠀⠀⠀⠀⠀⢰⡲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠠⠶⠛⠹⣆⢀⣠⣤
⣀⣠⡏⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠘⣧⡴⠞⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠉⠉⠀⠀⠀⠀⠀⠀⢀⡰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⢠⠖⠋⠈⠀⠀⠀⠀⠀⣤⣤⣀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠢⠎⠂⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠚⠋⠁⢻⣤⡴⠾⣆⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⢠⡤⠶⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠹⠶⠋⠹⣆⠀⠀⠀⠀⠀⠀⠀⠣⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠶⠚⣧⠀⠀⠀⠀⠀⠀⠀⠘⠷⠄
⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡄⠀⠀⠀⠀⠀⠀⠀⠻⠶⠞⢿⡀
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠠⣲⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠶⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠛⠶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⣾⠷⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡄
⠀⣼⠛⠳⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠉⠀⠀⠀⠀⠀⣀
⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢆⣀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡄⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠛⠲⢶⡄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣶⣶⣾⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣾⣀⣀⣀⣀⣀⣀⣀⣤⣤⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⡚⣧⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠉⠇⠀⠀⠀⠀⠀⠀⣀⠤⣶⠂⠛⣀⠒⢤⡀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢫⡬⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⡀⠉⠠⠀⠉⠀⠀⠋⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡔⠂⡂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠛⠀⠀⠈⠀⠐⠗⠀⠀⠂⣠⣷
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⢸⠑⠊⠁⠀⠀⠀⠀⣴⠄⠀⠀⢸⠀⠂⠆⠀⠀⢴⠄⠐⠀⡀⢀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⡠⢄⠀⠀⠀⠀⠀⠀⠀⠘⡜⠃⠀⠀⠄⠀⠀⠀⠈⢁⢮⠐⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠘⠑⠒⡢⢄⡀⠀⠀⠀⠀⠀⠈⢺⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⣔⠷⠀⠀⣶⠀⠀⠒⣥⢄⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡁⠀⠀⠸⠇⠀⠈⠀⠉⢦⡀⠀⠀⠀⠀⠀⠢⡀⠀⢈⢈⠇⠀⠀⠀⠀⠀⠈⠑⠦⣄⣀⣀⣀⡥⠖⠋⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠘⠟⠀⠀⠀⠀⠀⣀⠀⠠⣤⢧⠀⠀⠀⠀⠀⠀⠈⠀⠚⠣⠄⠀⠤⠆⠀⠀⠀⢠⠖⡸⠻⡽⡀⠀⠀⠀⠀⠀⠀⠎⡨⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠐⠀⠀⢠⡄⠀⠀⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠙⠓⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣇⢄⠀⠁⠀⠀⠀⠠⠀⢠⣄⠀⡸⠀⠀⠀⠀⡀⠑⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⡰⠆⠀⠀⣴⡆⠀⠈⠁⡴⠃⠀⠀⠀⠘⠄⠉⠀⠀⠀⠐⠟⡸⠀⠀⠀⠀⠧⣹⠴⠂⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢤⣆⣀⣀⡠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⠿⠀⠀⠀⠠⢤⡜⢳⠖
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣸⠟⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⠒⠦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠙⠄
⠀⠀⠀⠀⠀⠀⢴⢁⡦⠀⠀⠀⠀⠈⣓⡛⠁⠀⠀⠀⠀⠀⠀⠀⡰⠋⡀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠣⡎⣀⡽⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⡀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠈⡃⡇⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣜⢀⡸⠀⠀⠀⠀⠀⠀⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠐⠿⡗
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠛⠀⠀⠘⣆⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⢣⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠛⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⡀⠀⠀⢀⣠⠔⠁⠀⠀⠀⣠⠲⡀⠀⠀⠀⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢉⣿⡿⡟⠒⣄⠀⠀⠀⠀⠑⣄⠃⠀⠀⠀⠀⠐⠠⢀⣰⡂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⠻⣤⠖⠀⠀⠀⠀⠘⠲⠔⠚⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠉⠒⠒⠁
⠀⠀⠀⠀⠀⢮⠈⠆⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣸⠚⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠰⠇⡸⠆
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠁⠀⠂⠀⠄⠀⠀⠠⠀⠀⠉⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀
⠀⠀⠁⠀⠀⠀⠀⠐⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⠀⠈⠀⠄⠀⠠⠀⠀⠀⠀⠈⠀⡀⠀⡁⠀⠀⠀⠀⢀⡀⠁
⠐⠀⠆⠀⠀⢀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠁⠠⠄⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠡⠀⠀⠀⡄⠃
⠂⠀⢀⠀⠀⠀⠀⠀⠀⠍⢠⠀⠈⠀⢀⠠⠀⠒⡀⠁⠀⠀⠄⠀⠁⡀⠤⠁⢂⡀⠄⡀⠐⢠⠀⠈⡀⠀⢀
⢈⠠⠘⡌⠀⠀⠈⠡⢒⠀⠦⠀⠀⠠⠊⠀⠈⠀⠠⠠⡀⠀⠀⠀⡌⠀⡀⠀⡈⠀⠀⠐⠄⠀⠀⠁⠀⡒⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠼⣷⠒⠶⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⢹⡀⠀⠀⢀⡙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠚⠛⠀⠀⠈⢱⡌⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⢳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠛⠉⠙⠶⣄⣀⡀⢀⣠⡴⠚⠁⣠⠏⠀⠙⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⣤⠤⠶⠒⠛⠋⠉⠁⣀⣤⠞⠁⠀⠀⢠⡏⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣠⠀⠀⠀⠀⠀⠀⠠⠶⠖⠚⠛⠉⠁⠀⠀⠀⠀⢀⡞⠀⠀⠀⢸⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣰⠋⠁⣀⡴⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⣼⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡿⠁⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⣴⠃⠀⠀⢸⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢃⡞⠁⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠋⠁⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⡾⢿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⠁⢀⡴⠋⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⢀⡼⠁⣸⡟⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⡞⣠⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠚⠁⠀⠀⠀⠀⠀⣠⣞⣠⡾⠿⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡉⢿⣿⣷⣧⡇⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⢀⣀⣀⣤⣾⠟⠛⣿⠃⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡈⢿⠛⠉⢻⣭⠴⠒⣆⣀⡴⢦⡀⢀⣠⢿⣤⣤⡴⠶⣶⣿⡏⠉⠻⢿⠟⠀⠀⡟⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠘⣇⠀⠈⣇⠀⠀⢸⠁⠀⠈⣿⠋⠀⠀⢹⡏⠀⠀⠈⣿⠀⠀⠀⣸⠀⠀⢸⠃⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢹⡄⠀⢿⠀⠀⢸⡄⠀⠀⢿⠀⠀⠀⢸⡆⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⡟⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢷⠀⢸⡆⠀⠸⡇⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⡇⠀⢸⠇⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⣇⠀⣧⠀⠀⡇⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⢀⡇⠀⠀⢰⡇⠀⡾⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡈⠀⢻⠀⠀⣿⠀⠀⢸⡆⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢸⠁⠀⣡⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠉⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠈⠁⠀⠀⢈⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠉⠉⠉

⡀⠛⢟⠀⠀⠀⠘⠂⠘⠃⠀⡀⠈⠁⠀⠀⠀⣀⡀⠀⠉⠶⡆⠀⠈⠀⠀⠒⠀⠀⣀⠀⠄⠦⠀⠀⠰⠆
⠋⠀⠀⠀⠠⠄⠒⣼⠃⠀⠈⢁⣀⠐⠀⠀⠀⠛⠁⠐⠃⠈⢠⣄⠀⠛⠠⢄⠀⠈⠁⠀⠀⠀⠀⣠
⠃⠀⠀⠀⢀⠠⠄⠀⠀⣠⡀⠈⠉⠀⠀⠀⠀⠐⠒⠘⠀⠀⠈⠁⠀⢠⡄⠈⠀⡀⢙⡃⠰⠆⠀⠋⠀⠰⠀⢀⡀
⠈⠀⣄⠀⠀⠠⠀⢄⠀⠀⠀⠀⠄⠀⣀⠀⣦⠀⠀⡦⠀⠀⠐⠀⠰⠆⢤⠀⠀⠁⠐⡀⠀⠀⠀⠁⠀⠀⠤
⠀⠀⠉⠀⠀⠀⠀⢀⠀⣀⠀⡄⠀⠀⠉⠀⠀⠈⢠⣄⡀⠾⡆⠰⠆⠀⠀⠰⠆⣤⠘⠃⠀⠀⠁⠀⠐
⠀⠘⠟⢀⠀⠀⠀⠨⡅⠴⠴⠀⠒⠀⠠⣤⠀⠀⡄⠀⠁⠀⠀⠀⡄⠘⠣⠀⠀⠀⠀⠉⠀⠛⠀⠘⢃⠀⠐
⠀⠀⠀⠈⠁⢠⣄⠀⠀⠀⠀⠰⡄⠀⠀⠈⡀⠀⠀⠀⠶⠀⠀⠷⠀⠀⡤⠀⠀⢴⠄⠈⠀⣀⠀⠀⠈⠁⠰⠀⠠
⠆⠀⠄⠀⠀⠀⡀⠀⠀⠿⠀⠀⠀⠀⠀⠠⠉⠀⠆⠀⠃⠀⠀⣀⠀⡄⠀⠀⠀⠁⠀⠀⠀⠉⠀⠀⠀⠀⢶⠂
⠀⠐⠀⠆⠀⠂⠀⠈⠁⡀⢀⠀⠘⠃⠀⠀⠀⠈⠛⠀⠀⠀⠄⡄⠀⠀⠀⠂⠀⠀⠀⠀⠶⠀⢀⡀⠀⠀⠀⠐⠟
⠀⠠⠀⠀⠀⠆⠀⠂⠀⠁⠀⠀⠀⠐⠂⠀⠀⠀⠀⠶⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠈⠁⠀⠀⠀⠠⡄
⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⠐⠷⠀⢀⣄⠀⠀⠘⣃⠀⠀⢀⡀⠰⠆⠀⠀⠀⠘⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠆⢀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠃
⠂⢀⡀⠀⠀⠒⠀⠄⠈⠀⠀⡿⠀⠀⠀⠀⠀⣶⠄⠀⠀⠀⠀⠀⠘⠂⠀⢀⡀
⠀⠘⠃⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠠⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡤⣤⡄⢠⡄⡤⣤⣠⠀⡤⢤⢤⣤⡤⡄⣤⢠⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣇⣼⣧⣇⣼⢷⠀⡟⢸⢻⣿⣇⣧⡿⡞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠞⠁⠀⠀⠀⠀⠀⠙⠊⠁⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠰⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡝⠀⠀⠀⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁
⠚⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡙⣄⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠋⠀⠀⠀⠰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠘⠧

⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⠶⠆⠀⠀⠀⠀⠀⠀⠴⠆⠀⠀⠀⠀⢠⣦⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢴⣤⡀
⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠿⠿⠗⠀⠀⠀⠐
⠀⠀⠀⠲⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡾⠋
⡶⠆⠀⠀⣠⢞⠆⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠓⠁⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⢞⢢⡀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢡⠃⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠈⠿⠀⠀⠀⠀⠀⠀⢶⡀
⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣀⡀⠀⠀⠀⣠⡀⠀⠀⠀⠀⣶⠭⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠱⣼
⣐⡤⠀⠀⠀⠀⠀⠀⠉⠛⠚⠁⠀⠀⠀⠈⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡆
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⠇⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠄⠀⠀⠀⠁⠀⠀⠀⠀⠚⠃⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠿⠃⠀⠀⠀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⢶⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠈⢆⣳⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣠
⣄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣙⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢰
⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⣀⣀⣀⣀⣠⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣷⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣊⣼⣁⣀⣀⣀⣀⣀⣤⣄⣀⣀⣀⣀⣀⣾⣀⣀⣀⣀⣀⣰⣆⣀
⣿⣿⡿⠻⣿⠛⡿⠿⣿⢻⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡤⠀⡆⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⠤⣀⣄⡉⠀⣁⣀⡴⡚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠐⠠⠇⠀⠀⠀⠀⠀⠀⠀⡜⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠲⠆⢠⡄⠠⠄⠀⠙⠉⠀⠀⠀⠠⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡀⢴⡶⡀⠙⠀⠀⠀⢀⢀⣀⡠⠥⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠑⠀⠀⠊⠀⠀⠈⠂⣀⣠⣀⣀⣦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⣀⣀⣀⣤⡤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠓⠤⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⢀⡀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⣀⣤⣄⠀⠰⠶⠒⢀⠀⠀⠀⢀⠠⢴⠄⠀⠀⠀⠀⢈⠉⠀⢤⡴⠀⠀⠀⠀⠀⠛⠋⢀
⠀⠀⣀⡚⢃⠉⡄⠄⠀⠀⠀⠀⠀⠀⠀⠾⠃⠈⠉⠀⠀⢁⠔⠁⠀⠀⡠⢠⠀⠀⠘⠄⢁⡀⠆⠀⠀⣄⠈⠁⠀⠄⠀⠀⠄⡀⠀⠈⠓
⠠⠬⠛⠅⡭⠀⣰⡏⠀⠀⠀⠀⠀⢸⡇⠚⠂⠀⠀⠑⠿⢆⠀⠂⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠸⠠⠚⠁⠀⠀⠀⠀⠀⠀⢸⠄⠀⢤⠴⠃⠒⠒⠚⠉⠙⠂⣠⡔⠛⠀⠀⠀⠀⠀⠀⠀⡤⣄⠠⠤⠀⠀⠀⣀⣠⠤⠒⢠⠀⠀⠀⡰
⠈⠳⠦⣀⢀⣀⠤⠐⢳⡀⠀⠀⠀⠀⠢⣤⠄⠠⠈⡀⠀⠐⠀⢲⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠒⠐⠀⠒⠒⠐⠐⠀⠀⠀⠀⠀⢡
⠲⠤⠤⣀⠠⣀⣠⣔⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⡆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠐⠂⠠⠆⠐⠒⠀⠉⠁⠀⠠⡀⠐⠂⢂⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠃⠀⠀⠀⠀⠀⠀⠀⡎⠆⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠁⢤⣰⣀⣤⠷⠜⠂⠀⠀⠀⠀⠀⠀⠀⠲⠷⡄⠈⠀⠀⠀⣀⣀⡠⠤⠖⠋
⠂⠤⣤⣤⡤⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⣀⠀⠠⠄⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⠲⠐
⠀⠀⠀⠀⢀⠠⡲⠂⠀⠀⠀⠀⢀⠁⠀⠤⠖⠀⠀⠀⠀⢀⠁⠁⠠⠀⠀⠀⠀⢀⡀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⣀⡤⠤⡄⠀⢒⠟
⠔⢠⠀⠀⠈⠂⠠⠄⠃⠀⠀⢦⠀⠁⠐⠂⠀⠀⠂⠄⠀⠀⠁⠀⠀⠀⠀⢀⣠⡋⣁⠀⠄⣆⠀⠀⠀⠀⠀⠀⣠⢟⠁⠈⢁⡀⡊⠤⠂⠁
⠠⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠋⡂⠔⢀⣰⠏⠀⠀⠀⠀⠀⢸⠇⠁⠀⠀⠀⠈⠛⢅⡀⠉
⡞⠙⠀⠀⠀⠀⠀⠀⠀⣴⠤⠄⠒⠀⠀⠀⠠⠤⠖⠊⢠⠀⠀⠀⡰⣄⢀⡀⠀⠘⠐⠋⠀⠀⡀⠀⠀⠀⠀⢸⠂⠀⠤⠚⠉⠙⠛⠉⠁⠉⣁
⣥⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣬⣭⣥⣤⣭⣤⣭⣨⣥⣠⣤⣤⣤⣥⣤⣌⣿⣦⣤⣤⣤⣴⣤⣭⣤⣤⣤⣤⣄⣴⣶⣤⣤⣤⣤⣤⣴⣤⣯⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣠⡤⠶⠒⠛⠋⠉⠉⠛⠓⠲⢤⣀⠀⠀⠀⢀⣠⠴⠖⠚⠛⠛⠛⠒⠲⠦⣤⣀⡀
⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄
⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣀⣀⢀⣀⣠⡴⠋⠁⠀⠀⠀⠈⢳⣤⣀⡀⠀⢀⣀⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣩⣏⣹⣽⠇⠀⠀⠀⠀⠀⠀⠻⠴⣏⣽⣹⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣁⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠠⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠁⠀⠀⠄⠀⠀⠠⠄⠀⠀⠠⠀⠀⠀⠀⠔⠀⠀⠀⠉⠀⠀⠁⠀⠀⠄⠀⠀⠠⠄
⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⢠⠄⠀⠐⠀⠀⠀⠂⠀⠀⠠⠄⠀⠀⠀⠁⠀⠀⠂⠀⠀⠁⢠⠄⠀⠐⠀⠀⠀⠂
⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠂⢀⠀⠀⠠⠆⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠂⢀⠀⠀⠠⠆
⠀⠈⠀⠂⢀⠀⠀⠴⠀⠀⡀⠀⠀⠀⠀⠀⠖⠀⢀⡀⠀⠀⠀⠈⠀⠂⢀⠀⠀⠴⠀⠀⡀⠀⠀⠀⠀⠀⠖⠀⢀⡀
⠀⠀⠘⠁⠀⠀⠂⣀⠀⠈⣀⠀⣀⠀⠀⠠⠀⡀⠀⠀⠀⠂⠀⠀⠘⠁⠀⠀⠂⡀⠀⠈⣀⠀⣀⠀⠀⠠⠀⡀
⠀⠐⠀⢉⠀⢀⠀⠀⣀⠀⠀⠀⠀⠠⠀⡀⠀⠀⡀⢀⡀⠀⠀⠐⠀⢉⠀⢀⠀⠀⡀⠀⠀⠀⠀⠠⠀⡀⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡈⠀⡀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠐⠀⠀⠁⠀⠀⠁⠀⠀⠁⠀⣀⠀⠀⠁⠐⢀⠀⠠⠀⠀⠀⠐⠀⠀⠁⠀⠀⠁⠀⠀⠁⠀⣀⠀⠀⠁⠐⢀⠀⠠
⠄⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠀⠐⠀⠄⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠀⠐
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠂⠀⠀⠀⠈⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠈⠀⠐
⠀⠀⠀⠀⠆⠀⠈⠀⠠⠀⠀⠘⠀⡀⠀⠠⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠠⠀⠀⠘⠀⡀⠀⠠⠀⡀⠀⠐
⠀⠠⠀⠀⠀⠀⠐⠀⠀⠀⠉⠀⠀⠁⠀⠀⠄⠀⠀⠠⠄⠀⠀⠠⠀⠀⠀⠀⠐⠀⠀⠀⠉⠀⠀⠁⠀⠀⠄⠀⠀⠠⠄
⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⢠⠄⠀⠐⠀⠀⠀⠂⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⢠⠀⠀⠐⠀⠀⠀⠂
⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⠂⢀⠀⠀⠠⠆
⠀⠈⠀⠂⢀⠀⠀⠴⠀⠀⡀⠀⠀⠀⠀⠀⠖⠀⢀⡀⠀⠀⠀⠈⠀⠂⢀⠀⠀⠴⠀⠀⡀⠀⠀⠀⠀⠀⠒⠀⢀⡀
⠀⠀⠘⠁⠀⠀⠂⣀⠀⠈⣀⠀⣀⠀⠀⠠⠀⡀⠀⠀⠀⠂⠀⠀⠈⠁⠀⠀⠂⡀⠀⠈⣀⠀⣀⠀⠀⠠⠀⡀
⠁⠐⠀⢉⠀⢀⠀⠀⣀⠀⠀⠀⠀⠠⠀⡀⠀⠀⡀⢀⡀⠀⠀⠐⠀⢉⠀⢀⠀⠀⡀⠀⠀⠀⠀⠠⠀⡀⠀⢀⡀⢀⡀
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⡀⠀⠁⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⡀⠀⠁⠀⠀⠀⠀⠄
⠀⠀⠐⠀⠀⠁⠀⠀⠁⠀⠀⠁⠀⣀⠀⠀⠁⠐⢀⠀⠠⠀⠀⠀⠐⠀⠀⠁⠀⠀⠁⠀⠀⠁⠀⣠⠀⠀⠁⠐⢀⠀⠠
⠄⠀⠀⠠⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠀⠐⠀⠄⠀⠀⠠⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠈⠀⠐
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠈⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠂⠀⠀⠀⠈⠀⠐
⠀⠀⠀⠀⠄⠀⠈⠀⠠⠀⠀⠘⠀⡀⠀⠠⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠠⠀⠀⠘⠀⡀⠀⠠⠀⡀⠀⠐

⠀⠀⠀⠀⢀⣀⣠⣤⣀⡀⠀⠀⢀⣀⡤⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⢠⠖⠋⠀⠀⠀⠀⠉⢳⠖⠉⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠈⠙⢦⡀
⠀⢰⠋⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⡟⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠉⢢⡀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⢧⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠘⣆⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠈⠳⣄⡀⠀⠀⠀⢀⣸⠦⣀⡀⠀⠀⢀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠉⠛⢲⣻⡉⠀⠀⢼⣽⠉⠉⢯⡀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⣸⣻⠒⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢹⡀⠀⠀⢸⠀⠀⠀⣴⣳⠦⣄⣀⣀⣀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢸⡀⠀⢠⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢸⡇⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢸⡇⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢸⠁⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⡾⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢶⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠
⠀⠀⠄⠀⠀⠐⠂⠀⠀⢠⡄⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠠⠀⠀⠐⠂⠀⢠⠀⠀⠀⠀⠁⠀⢀⡀⠀⠀⠀⠀⠀⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠀⠀⠄⠀⠀⣤
⠀⠀⠐⠓⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⡤⠀⠀⠀⠀⠉⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡀⠀⠀⠂
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢴⠄⠀⠀⠈⠁⠀⠀⠀⠀⠰⠆
⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⣤⠀⠀⠃⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⣤⠄⠀⠀⠀⠈⠁⠀⢀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀
⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠆⠀⠀⢀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠂⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠰⠆⠀⠀⠀⠃
⠀⢠⡄⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠈⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠘
⠀⠀⠀⠀⠠⠦⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⣀
⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠚⠂⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠛⠀⠀⠀⢠⡄⠀⠀⠀⡀
⠆⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣀⣀⣀⣀⣀⣀⣀⣰⣇⣀⣀⣀⣠⣀⣀⣀⣀⣀⣉⣀⣀⣀⣀⣀⣆⣀⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣤⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⡴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⡰⠆
⠀⠀⠀⢘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠈⢄
⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⢪⠂⠀⠀⠀⠀⠀⢠⠔⣺⠃⠤⡀⠀⠀⠀⠀⠀⣀⣠⣷⠆⠀⠀⠀⠀⠀⠀⡤⢒⣒⠰⠤⠄
⣠⡖⠢⢿⡿⠖⢀⣄⠀⠀⠀⣤⣶⣿⣿⣿⣦⡀⠀⠀⠀⠠⠀⠉⠤⠀⠈⠂⡀⠀⠀⡸⢅⡁⠠⠴⠚⠉⢦⠀⠀⠠⡎⠉⠘⠛⠃⠙⢄⠀⠀⠀⡞⠉⠒⠙⠒⠂⣛
⠿⢿⣶⣶⣶⣶⡿⠿⠀⠀⢜⠉⢀⠀⠀⡀⠀⢸⡄⠀⠀⡁⠀⠀⠀⣁⣠⡤⡍⠀⠘⣆⢲⣄⣀⣀⣠⣤⢤⠃⠀⢸⡀⠀⣀⣀⣀⣤⢤⠇⠀⢾⣉⠉⠑⠒⠒⠊⠉
⢸⡼⡇⣿⢹⢰⣇⡇⠀⠀⠈⡟⣿⣿⢻⡏⡞⡿⠀⠀⠀⢸⢹⡿⡇⣿⢸⢳⡇⠀⠀⠘⡏⣇⣿⢸⣇⡇⡏⠀⠀⠀⣯⣿⢸⣿⡇⡿⣸⠀⠀⠀⢻⢳⢲⡖⣿⣿⢹
⠀⢇⣇⣿⣿⢸⣻⠃⠀⠀⠀⢻⣿⣸⢸⣷⣇⠇⠀⠀⠀⠘⣟⡇⡇⣿⣾⡸⠀⠀⠀⠀⢇⣿⣿⢸⣿⣷⠇⠀⠀⠀⠸⣹⢸⣿⡇⣇⡏⠀⠀⠀⠸⣸⣿⡇⣏⣿⡾
⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⢠⣶⣴⣶⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⣴⣴⣤⣷
⠀⢀⡀⣤⣧⣄⠀⠀⠀⠀⠀⠀⢘⣿⣿⣏⠀⠀⠀⠀⠀⠀⠰⡶⠀⠐⣠⡄⠀⠀⠀⢀⠴⣙⠛⠁⣓⢄⠀⠀⠀⠀⢀⡴⢿⣿⣷⣀⠀⠀⠀⠀⢀⣎⡛⠋⠛⠋⣢
⣴⣇⣈⠛⠛⣁⣨⣧⠀⠀⢀⠾⠟⠛⠒⠓⠽⢆⠀⠀⠀⡄⠀⠀⠀⠀⠙⠁⢄⠀⢀⠀⠒⠄⠀⠉⠁⠀⠱⡀⠀⢈⠇⠀⠀⠀⠀⠈⠱⡀⠀⢀⣯⣀⣈⣉⡁⣀⣬
⢹⢻⡿⣿⣿⠿⡟⡏⠀⠀⢲⣀⣠⣄⣠⣄⣀⣸⠃⠀⠀⢦⣀⣠⡤⣤⢲⡏⡇⠀⠈⢳⣬⡦⣤⢴⡖⡿⣿⠀⠀⠘⣦⣄⢴⣤⡴⣶⢹⠃⠀⠻⣶⣀⣀⣉⣉⣁⣠
⠘⡟⡇⣿⣸⢸⣧⡇⠀⠀⠀⣇⣷⣻⢸⡇⡏⡏⠀⠀⠀⢸⣼⡟⡇⣿⢸⢹⠃⠀⠀⠀⡇⣧⣿⢸⣷⡇⡇⠀⠀⠀⢷⣿⢸⣿⡇⡟⡾⠀⠀⠀⢹⢹⣹⡏⡿⣿⣸
⠀⠳⢧⣿⣽⡼⠞⠀⠀⠀⠀⠘⠿⣼⣼⡿⠷⠃⠀⠀⠀⠀⠣⢧⣧⣿⠿⠞⠀⠀⠀⠀⠱⠿⣿⣼⡧⠟⠃⠀⠀⠀⠘⠾⣼⣿⣧⠷⠃⠀⠀⠀⠈⠾⢿⣧⣯⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣔⣦⡄⠀⠀⠀⠀⠀⠀⠀⢀⠔⠄⠀⠀⠀⠀⠀⠈⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠤⢀⡀
⢀⡠⢀⣀⣀⡤⣀⡀⠀⠀⠀⢀⣿⣿⣿⡿⣅⠀⠀⠀⠀⢀⣀⠁⢠⡈⠤⣄⠀⠀⠀⢠⠚⠝⠛⣛⡭⠢⡀⠀⠀⠀⡀⠂⠀⠁⠀⠤⡀⠀⠀⠀⣠⠿⠅⣤⠈⢤⣵
⣾⣧⣤⣉⣉⣥⣴⣷⠀⠀⠠⠛⠋⠉⠉⠙⠛⢣⡀⠀⠀⠆⣠⠀⡄⠖⠀⣑⡦⠀⢠⡃⢉⠂⠀⠀⠀⣀⣘⠄⠀⢨⠃⠀⠀⠀⠀⠀⣘⡆⠀⣠⡷⠦⠤⠴⣀⡤⠶
⢸⣹⡏⣿⢿⢛⡏⡇⠀⠀⠹⡤⡴⣤⢴⡦⣤⣾⠁⠀⠀⢳⢤⣴⡖⣶⢹⢧⡇⠀⠀⠹⡖⡟⣶⢻⡏⡏⡿⠀⠀⠈⡷⣶⢺⣶⡞⣿⢹⠁⠀⠉⣿⢤⣤⣴⣦⢤⢴
⠈⡇⡇⣿⣼⢸⢷⠇⠀⠀⠀⢧⣿⣻⢸⡇⡇⡇⠀⠀⠀⠸⡾⡎⡇⣿⣸⢸⠁⠀⠀⠀⡇⣿⣿⢸⣧⣇⡇⠀⠀⠀⢻⢿⢸⣿⡇⡏⡿⠀⠀⠀⢸⢸⣼⡇⡿⣿⣼
⣀⣙⣳⣿⣿⣾⣋⣀⣀⣀⣀⣈⣻⣾⣼⣿⣋⣁⣀⣀⣀⣀⣙⣷⣷⣿⣟⣉⣀⣀⣀⣀⣈⣻⣿⣼⣿⣋⣁⣀⣀⣀⣈⣻⣾⣿⣷⣟⣁⣀⣀⣀⣀⣙⣿⣧⣷⣟⣁
⣿⣿⡏⠉⠙⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿