Wheeze Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⣘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⣀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣷⣶⣦⣄⠀⠀⠀⠀⢀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣶⣶⣦⣤⡀⠀⠘⢿⣦⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣠⣿⠏
⠀⠀⠀⠀⠀⠀⢶⣶⣶⣦⣼⣿⡀⠀⠈⠉⠀⠀⠀⠈⠻⣿⣦⡈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃⣠⣾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⢀⣀⣤⣶⡶⠀⠈⠙⠿⣷⣤⣄⣈⡉⠉⠉⠉⠉⣉⣀⣤⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠛⠉⠁⠀⠀⠀⠀⣀⠀⠉⠛⠛⠿⠿⠿⠿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⣦⠀⠀⠀⠀⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠿⠟⠋⠉⠀⠀⠀⠀⣠⣾⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠃⠀⣴⠟⠁⠀⠀⠀⠀⣠⣤⠶⠶⢶⣤⡀⠀⠀⠀⠸⣦⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠹⡇⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠛⠋⠉⠉⠛⢶⣄⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠈⠻⣦⣀⣀⣀⣀⣴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠖⠀⠀⠀⣿⠀⠀⠀⠉⠉⠉⠉⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠰⠶⢤⣤⣴⣶⠛⠋⠉⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢿⡀⠹⣦⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⢦⣤⣀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠈⠙⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡄⠀⠀⠀⠀⠀⠀⣤⡴⠞⠋⢠⡄⠀⢷⣄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠉⠙⠛⠷⢶⣤⣄⣀⡀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠉⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⡞⠉⣯⠉⠙⠛⠶⠛⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⢸⡇⠀⠙⣧⡀⠀⠀⠀⠀⠀⠉⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠸⣧⠀⠀⠈⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠉⠛⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠉⠛⢶⣤⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣤⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢀⡿⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢀⡾⠁⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢀⣾⡅⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢀⡾⠁⢻⡄⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢻⡄⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣀⣤⠟⠁⠀⠀⠀⠀⠀⠀⠹⢦⣄⣀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⡤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤
⠧⠤⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠣⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀⣀⠀⠀⢀⣀⡀⠀⡀⠀⢀⢀⠀⠀⠀⠀⣀⡀⠀⠀⣀⠀⢀⣀⠀⡀⣀⠀⢀⢀⡀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⢸⠁⠀⡆⢸⠀⢸⠀⣘⣡⠀⣧⠸⠁⢈⠀⠀⡥⠀⠀⠘⠦⡀⠀⡇⠀⡧⢬⠠⠃⠀⢹⠀⡦⡁⠀⠤
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣷⣦⣼⣦⣼⣡⣬⣤⣬⣤⣥⣤⣦⣵⣴⣥⣴⣦⣤⣶⣤⣤⣤⣦⣥⣤⣧⣤⣧⣬⣤⣵⣤⣯⣤⣤⣽⣤⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠋⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣶⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⢹⠶⠒⡆⠀⠀⠀⠀⠠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⣰⠃⠀⠀⡇⠀⢀⡀⠀⠀⡠⠖⠒⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣎⣤⠀⠀⠓⢤⠀⠀⡇⠠⠋⠀⠀⡼⠁⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⣠⢦⠤⡈⢦⠀⠱⣠⠞⠉⠉⢳⡀⠀⠀⠀⣀⣀⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠘⣯⡇⠀⠹⣄⠤⢤⣾⢷⣶⣉⡩⢕⣫⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠴⠖⠲⠾⣿⠀⠀⠈⠭⠟⠁⠀⠀⠐⠒⠉⠉⠉⠉⠉⠉⠉⠁⠀⠈⠉⠉⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠒⠯⠱⠆⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡅⣒⠒⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠄⢀⠀⣀⠀⠀⢀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠰⣨⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢓⡶⠶⠶⠶⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⢳⠀⠘⡆⠀⠀⠀⠀⣀⣤⡴⠒⠋⠉⠉⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⣀⠀⣰⡬⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠘⡄⠀⠸⡄⠀⣠⠞⣥⢼⡁⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⡀⢠⠶⣄⣆⣱⠧⠬⠗⠁
⠀⠀⠀⠀⠀⠀⢠⡶⠋⠀⠀⠀⠀⠀⣇⠀⠀⠹⡜⠧⠤⠤⠄⠛⠀⢰⠧⢵⡂⢴⠋⠀⠀⢎⣁⡹⠤⠋⠈⠁
⠀⠀⠀⠀⠀⣠⠞⠃⠀⡴⠀⠀⢀⠀⢸⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⣠⠴⠚⠙⠶⡇⠀⠀⠀⠁
⠀⠀⠀⠀⡴⠃⠀⢀⡞⠀⠀⠀⢸⠀⠀⠗⠒⠋⠉⢸⣀⣀⡤⡖⠉⠀⠀⠀⠀⠀⠀⠀⢸⡼⡴⢹⢴⢰⣟⢰⡒⠠⡤⣠⠄
⠀⠀⠀⡼⠁⠀⠀⠈⠙⢶⣶⣶⠚⠀⠀⠀⠀⠀⠀⣸⡜⡀⢸⠃⠀⢠⡊⢅⢀⣤⠀⣀⡀⠀⠀⠀⠀⠈⠁⠘⠒⠾⠄⠻⠅
⠀⠀⠸⣇⡀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⡔⠁⠸⡀⠀⠀⠉⠉⠚⠹⢘⣣⣥⣟⡦
⠀⠀⢰⡏⠙⠲⢤⣄⡀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⡜⢲⣶⡖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢣⡀⠀⠀⢠⠫⠻⠂⢖⢚⡦⠴⠖⡖⠚⡟⠁⠀⠆
⠀⠀⠀⠀⠱⣄⠀⡔⢛⠀⢀⠏⠀⠀⢰⠀⡇⠀⠱⡴⠀⠂⠀⠠⠽⡂
⠀⠀⠀⠀⠀⠈⠷⠄⠉⠒⠁⠀⠀⠀⠙⢏⠁⠀⠀⠱⡀⠐⢄⡗⠒⠃
⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⡰
⠀⠀⠀⠀⢠⣏⠀⠀⠀⠀⠀⠀⣀⣀⡤⠃⠤⣤⠴⠃⢤
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠯⠩⠿⠾⠤⠤⠒⠋⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣗
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠷⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⣴⠿⠆⠀⢀⣘⢷⣄⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠶⠟⢋⣤⠙⠷⣯⣛⡉⠀⠀⠈⠉⠉⠀⣀⣤⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⣡⣴⠆⠈⠉⠛⠻⠷⠶⠶⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠐⠛⠛⠉⠀⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⠤⣤⣌⣻⡛⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣀⣀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠛⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠭⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣯⣤⣄⣀⠀⠀⠀⣄⠀⠀⠀⠀⠙⢦⡀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⢛⣉⡁⠀⠀⠈⠙⠒⢤⣘⠆⠀⠀⠀⠀⠀⠑⠏⠙⢦
⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⣀⡤⠖⢫⡥⠴⠲⡆⠀⠀⢀⣠⠤⠶⠒⢲⡇⠈⠓⢦⡀⠀⠀⠀⠀⠀⢤⣞⠃
⠀⠀⠀⠀⠀⢸⢡⣤⡼⣷⣊⠁⢀⡔⠁⠀⡀⢠⠇⣠⠞⣩⡀⠀⠀⠀⠘⡇⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠈⠙⠲⡄
⠀⠀⠀⠀⣰⠚⠛⢦⡄⠛⡏⠀⠸⣄⣀⣨⠷⢣⠞⠁⠀⠉⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠈⢷⢦⣳
⠀⠀⠀⢠⠋⡉⠳⡾⡃⢠⣇⡤⣸⡋⠛⣦⠀⣿⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠘⣳⠆⠀⠀⠀⣤⡀⠈⣧⠉
⠀⠀⠀⠸⡄⠙⠚⡇⡇⠀⣿⣹⠀⠈⠀⠀⠀⢻⣄⠀⠀⣀⣤⠞⠋⠀⠀⠀⠀⠀⠀⡼⠁⡼⠉⠓⠦⣼⡍⠳⣾
⠀⠀⠀⠀⠘⢲⠀⣙⣓⣒⢛⡷⢆⡀⠀⠀⠀⠀⠙⠿⠭⠭⠀⠀⠀⠀⠀⠀⠀⠀⠰⠓⠚⠉⠉⠓⣆
⠀⠀⠀⠀⠀⢸⠀⢻⠀⠉⠉⢁⣀⣉⣓⣶⠤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠤⢄⡀⠚⠻⠿⠓⣠⠏
⠀⠀⠀⠀⠀⠈⢧⡈⠑⠲⢤⣾⣇⠀⠀⠀⢰⠆⠀⠀⠀⠉⠉⠉⠉⠁⣮⣇⠀⠀⠉⠒⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠶⠼⢿⣿⠀⣠⠴⢺⠀⠀⠀⠀⠀⢈⣦⠀⠀⢸⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⣸⠀⠀⠀⠀⠀⠀⡏⠀⠀⢀⣧⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠉⠉⣿⣿⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢷⠸⣄⣠⠗⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡶⠤⢤⣤⣀⣀⣤⣤⣼⠀⠈⠉⠠⠚⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡏⢸⠀⠀⠈⠣⣄⡀⠐⣲⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠘⠒⠦⢧⣼⣄⣀⣀⠀⠈⠉⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠻⣭⣻⠒⡶⢺⡦⣤⣄⣀⣀⣀⣀⣼⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣖⡶⠤⠼⠯⢴⣟⣻⢿⡺⠶⣏⣀⠀⠿⣾⠁⠀⢉⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠉⠓⠒⠫⠭⠭⠭⠭⠭⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣘⣿⢹⡏⡷⢾⣾⣶⣇⣾⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⣠⡀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢹⡏⣶⠜⡾⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⣞⣁⣤⣟⣿⣺⣤⡈⠛⠦⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠚⠉⠀⠀⡞⠁⠀⠀⠀⢹⠀⠀⠀⠀⠹⡄⠀⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡇⢰⠀⠀⠀⠘⢤⣀⣀⣆⣀⣇⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠃⠘⠀⠀⠀⠀⠀⠀⠀⠋⠈⠃⠀⠀⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠛⠦⣿⣿⠀⠀⣰⠀⡀⠀⠀⠀⠀⠀⠀⢠⠯⠭⠭⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡝⢀⠰⠒⣿⣿⠒⠦⣄⢫⡅⠀⠀⠀⠀⠀⠀⢸⡤⠤⣍⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠢⢤⡇⣿⣿⢸⣤⠜⣆⠀⠀⠀⠀⠀⠀⠀⢸⠈⠇⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠤⣾⠋⣿⣿⠙⣷⠤⢸⡄⠀⠀⠀⠀⠀⢀⣼⣏⡛⠉⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠩⠃⣿⣿⠸⠉⠁⢸⡇⠀⢀⣠⢠⡖⢯⠀⠀⠳⠀⢠⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣠⠤⠖⠃⠘⠲⠤⣄⣸⠋⠉⠉⠁⠀⢧⡬⣧⡤⠔⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢲⣠⢤⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠁⠀⣰⠋⠀⢸⠃⠀⠀⠀⠀⠀⠉⣁⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⢠⣇⠀⠀⢸⠀⢀⡴⠃⠀⢠⠞⠁⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠚⠇⠀⠀⠈⢷⠀⠘⣇⠈⣠⠤⠤⣟⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠋⠂⠁⢀⠤⠀⠘⣼⠁⠀⠀⢘⡇⣀⡀⠠⠄⢀⢞⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚⡆⠀⠘⠶⣒⣹⠟⠁⠚⠀⠀⣈⣤⣊⠀⠀⠀⠀⠤⠀⠀⠀⠤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⣉⣀⡀⠁⠇⠀⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠈⠉⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠭⣉⢩⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠦⣄⡀⠐⠄⠠⠀⠤⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢯⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠗⠒⠒⠒⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠘⡆⠀⢻⡀⠀⠀⠀⠀⢀⠠⡤⠒⠈⠉⠁⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⢧⠀⠀⢣⠀⠀⡠⠊⣁⢰⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⣠⠦⣴⡆⢑⠢⠀⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠊⠀⠀⠀⠀⠀⢸⠀⠀⠈⠃⠐⠀⠀⠀⠀⠱⠤⠤⠅⢀⠄⢠⠜⠋⠀⠰⡋⠁⠣⠀⠋⠈
⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠛⠠⢴⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⣰⠋⠀⠀⣠⠁⠀⠀⠀⡇⠀⠠⠀⠀⠐⠀⢠⠀⠀⣀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⢂⣆⠀⢀⣠⢀⠀⢠⠤⢀⣀⢀⣀
⠀⠀⠀⠀⣰⠃⠀⠀⠐⠳⢤⣤⣤⡤⠇⠀⠀⠀⠀⠀⠀⢸⡱⠉⢳⠇⠀⠀⡴⠶⠀⢀⡀⠀⠀⠈⠈⠀⠁⠘⠸⠧⠸⠥⣴⣋⢸⣂
⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠸⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠟⣠⠋⠸⡀⠀⠀⠳⠽⢣⠯⡇⠶⡒⢠⢤⡀
⠀⠀⠀⠈⠓⢦⣄⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣴⣁⣀⣀⠇⠀⠀⠀⠀⠀⠀⠁⠐⠈⠛⠚⠁
⠀⠀⠀⠈⡄⠀⠀⠉⠓⠦⢤⡇⢟⡀⢀⠀⠀⣀⣀⡤⠠⠁⠸⠛⠃
⠀⠀⠀⠀⠐⡄⠀⠀⠈⣬⡁⠀⢨⠄⠘⠉⠁⠘⠀⠐⡁⢀⠀⠀⠠⠀⠀⡀
⠀⠀⠀⠀⠀⠈⢦⡀⠪⢠⠂⡠⠋⠀⠀⢀⣆⢸⠀⠀⠸⡇⠒⢂⠀⡐⠚⣤
⠀⠀⠀⠀⠀⠀⠀⢻⠂⠀⠈⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢹⠀⠈⠂⠋⠈⠁
⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠰⣇⣀⡀⠀⠀⣀⣀⣀⡤⡤⠚⠒⠢⣖⡟⢀⣢
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠁⠘⠒⠓⠒⠒⠊⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠲⠀⠆⠀⠀⠀⠀⠀⠂⠐⠐⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠉⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠿⠛⠋⠄⠀⠀⢀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠈⠴⠀⢀⠄⠠⡐⢂⠬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⡀⠀⠀⠀⡰⠀⠁⠸⠠⡔⠁⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣐⣒⣈⢀⣠⠔⠁⡰⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠴⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠀⢸⣿⣿⣷⣦

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠿⠟⠛⠉⠉⠁⠀⠀⠀⠈⠉⠉⠙⠛⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠃⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠸⣿⠟⠀⠀⣤⣶⣶⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏
⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣃⠀⠀⠀⠀⠀⠀⢀⣀⣙⣿⣿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠏
⠀⣰⣿⡿⠿⣿⣷⡄⠀⠀⠀⠀⠀⠻⠿⣿⣿⣷⡄⠀⠀⢸⣿⡿⠿⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠁
⠀⣿⣿⠀⠀⠈⠛⠁⣴⣶⣶⣶⡄⠀⣠⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢰⣿⡟
⣼⣿⡟⠀⠀⠀⠀⠀⠈⣽⣿⡟⠀⢸⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠀⠀⠀⠀⠀⠀⣿⣿⠃
⣿⣿⡀⠀⠀⠀⠀⠀⢀⣈⠉⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⢿⣿⡆
⠙⣿⣷⣦⣤⣄⠀⠀⢸⣿⡇⠀⠀⠀⢹⣿⣧⣤⣤⣤⣤⣤⣶⣶⣶⣿⣿⣿⡿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇
⠀⠈⠙⠛⢿⣿⣶⣶⣿⡿⠃⠀⠀⠀⠀⠙⠛⠿⠛⠛⠛⠛⣿⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇
⣿⣿⠟⠟⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡾⠿⠿⠿⠿⠿⠷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣶⣤⡀
⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀
⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷
⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇
⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆
⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠈⣿⡄⠀⠀⠀⠀⠀⠀⣶⡶⠶⠶⠶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦
⠀⠸⣿⡄⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣸⣿
⠀⠀⠘⣿⡄⠀⠀⠀⣾⡏⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⠛⠁
⠀⠀⠀⢸⣿⠀⠀⢀⣿⠃⠀⠀⢰⣿⣁⣀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⡏⠀⠀⠀⠀⠀⠀⢀⠀⣀⣤
⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠙⠛⠛⠛⠉⢹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠛⠛⠁⠀⣤⣶⣦⠸⠿⠟⠃⠉⠉
⠀⠀⠀⢸⣿⠀⠀⣾⣇⣀⣀⣀⣠⡀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣉⣀⡀
⠀⠀⠀⣸⡟⠀⠀⠻⠛⠛⠛⠛⣿⡇⠀⣰⡿⠁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⡀⠀⠀⢀⠙⠛⠛⠸⠿⠿⠆⣶⣶
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⠇⣰⡿⠁⠀⠻⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⠃⢀⡀⠛⢿⡦⢀⡀
⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⣼⡟⠁⠀⠀⠀⠈⠙⣿⡿⣶⣤⣄⣀⣀⣠⣼⡿⠁⠀⠘⢿⣦⠀⠀⠙⠿⡶⣀⡀
⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠉⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠰⣶⡄⠀⠀⠀⠙⠻⠷
⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⢾⠟⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣄
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷
⣿⣿⢛⢿⢛⠟⣿⢟⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣷⣄⢀⡏⡇⠏⢧⡆⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠋⠈⢿⣿⡄
⠀⠀⠀⠀⢸⣿⡿⠿⠋⢉⡄⢙⠛⢧⡘⠀⡀⠀⡇⠀⠀⠀⠀⠀⢤⠄⠀⢻⠛⠆⡆⠺⠀⠀⠉⡇
⠀⠀⠀⠀⢸⣿⡃⠈⡦⢖⠛⠚⢤⠁⠑⣄⠥⠤⡇⠤⠤⠐⠒⠒⣒⡒⠀⠘⡄⠠⡒⢢⠀⢠⣿⣿⣂
⠀⠀⠀⠀⠀⢆⣀⣩⠈⣒⠨⢔⠜⠀⠀⢰⠀⠀⠁⠀⠀⠀⠈⠁⠄⠀⠀⡀⢾⠂⠙⡗⠊⡍⠁⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⣉⠴⡖⠒⣩⣆⠀⠐⠚⠀⠀⢸⠀⠀⠀⣠⠀⢀⠴⡪⠂⡼⢄⣀⠏⠉⠀⠀⠀⠐⢄⠀⠘⡄
⠀⠀⠀⠀⠀⡰⠊⠀⠀⠈⢰⠛⠿⡀⠀⠀⠀⢀⡰⠀⠀⠀⣀⠔⠁⠈⠀⢰⠁⠀⡸⢆⠀⠀⠀⠀⣀⣼⡀⢀⠇
⠀⠀⠀⠀⢸⠀⠀⠔⠊⠉⢡⠀⢠⠃⠈⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⠁⢸⠀⠀⠀⣎⣄⣀⡽⠋
⠀⠀⠀⠀⠸⡀⠀⠀⠀⣀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠖⠋⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⣦⠔⠋⠀⠉⠀⠀⠀⠀⠸⠧⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠀⢀⣠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠏⠀⠀⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠀⠀⠀⠈⠀⠧⢤⠀⠀⢀⡤⢄⡀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠸⡄⠀⠀⠀⠀⠀⠘⢦⢀⡏⣖⡀⣷⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠦⣀⠀⠀⠀⠳⡀⠀⢳⢠⡧⠆⠀⠀⠀⠘⠶⠃⠇⣤⡋⠀⠀⠀⠀⠀⡧
⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡄⠀⠀⠀⣸⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⢤⡀⢀⣠⡀⠀⠀⠀⠀⢠⠏⠀⠧⠴⣲⠞⢋⣨⠷⢤⡀
⠀⠀⠀⠉⠓⠲⢤⠀⠀⠀⢀⡤⣀⠙⣩⠞⠁⠀⠀⠀⣰⠃⠀⣀⠴⠋⣡⠖⠉⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠉⡷⠋⠳⣌⠙⡆⠀⠀⡰⣧⠴⠊⢁⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡝⢾⣷⠞⠀⢸⡆⠑⠲⠊⠁⢸⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡙⠒⣿⡀⠀⢸⣇⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⠁⠳⠀⡼⢹⡄⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⠤⠞⠁⢠⣧⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡤⠊⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣶⣶⣤⣽⣿⢿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣇⣇⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠿⠛⠁⠀⠘⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡂⠀⠀⠀⠘⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢛⠹⢷⣤⡀⠐⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠈⠢⣀⢀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠈⠰⡑⣄⠈⠇⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠃⠀⠀⠀⢣⠀⠑⠀⡉⠂
⠀⠀⠀⠀⠀⢀⠀⡞⠀⠀⠀⠀⠀⡎⠀⠀⠀⣙⢰
⠀⠀⠀⠀⢀⡃⢸⡇⠀⠀⠀⠀⣸⣀⣀⡴⠀⠈⠇⡆
⠀⠀⠀⠀⢸⢠⣾⣿⠀⠀⠀⠠⣬⡿⠇⣊⢗⣠⡇⢇
⠀⠀⠀⠀⡟⠈⢸⣿⠀⠀⠀⠀⡟⠙⠿⣷⣟⠁⢻⡇
⠀⠀⠀⠀⢷⢷⠸⣿⡀⢀⣀⡐⢧⠀⢰⣿⠀⠀⢸⡉
⠀⠀⠀⠀⢘⣿⣷⣏⣴⡒⠤⣌⣾⠀⣞⢿⡗⠔⠛
⠀⠀⠀⠀⣼⠈⢻⣿⡗⡥⠀⠈⠃⠀⢹
⠀⠀⠀⠀⢦⣰⣄⣿⣷⣭⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠇⠀⣶⣿⡄
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣧⡀⢹⣿⣇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡧⡄⠙⠿
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⠂⠀⢠
⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣷⣄⡀⠘⠃
⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⢿⣿⣿⣦⣘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢙⡮⠀⠉⠙⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⣀⡤⠴⠖⠒⠚⠛⠉⠉⠙⠛⠓⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⢹⡄⢀⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⢸⠛⠲⠦⣄⣀⣄⣴⠾⣤⠄⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠸⡿⡄⠈⢢⡀⠈⣳
⠀⠀⠀⠸⡆⠀⠀⠀⠉⠳⡍⠀⢹⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢸⠀⠀⠀⠀⠀⢀⡇⢹⣄⣀⣻⡍
⠀⠀⠀⠀⢻⡀⠀⢀⡩⢽⣿⣀⣼⠁⠀⠀⣀⣀⣀⣀⣀⣠⣤⡤⠴⠞⠁⠈⠛⠛⠛⢿⣛⠋
⠀⠀⠀⠀⠈⣧⠀⣠⠞⠋⠩⠿⠁⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠄⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠈⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠰⢣⠖⠛⠛⠶⣄⠀⠀⣠⠖⠛⠛⠒⢦⡈⠳⣄
⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⣿⠀⠀⠀⠀⠈⠳⣼⠁⣀⠀⠀⠀⠀⡧⠀⠈⠳⣄⠀⠀⠀⠀⠀⣀⣤⠖⠒⠒⢦⡀
⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣯⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠹⣎⠉⠀⠀⠀⢠⡇⠀⠀⠀⠈⠳⣄⠀⣤⣴⡃⠚⣿⣛⣧⣨⡇
⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣿⠀⠀⠀⠹⡆⠀⠀⠀⠀⢤⡆⢻⡀⠀⢀⣠⠟⠀⣠⠤⣄⠀⠀⠘⢧⣿⠈⢉⡽⣽⣯⠭⠭⣿⡄
⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⢀⣤⠤⠤⣤⣴⠃⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⣸⠛⠛⠉⠁⠀⠐⠁⣠⠎⠀⠀⠀⠈⣿⠀⢸⠀⢻⣤⡤⠄⣸⠇
⠀⠀⢀⡏⠀⠀⠀⠀⠀⣼⠉⢠⣤⠶⣤⡉⠃⠀⠀⠀⠀⠀⠉⠳⣤⣤⣤⠶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢶⣀⣿⠀⣼⠀⣾⣠⠴⠚⠁
⠀⠀⢸⡇⢀⠀⠀⠀⠀⢷⡀⠀⠀⠁⢀⣡⠔⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⣿⠀⠀⡟⠀⡇⣿
⠀⠀⢸⡇⠘⡄⠀⠠⠀⠈⠙⠒⠒⠛⠉⠀⠀⠀⣀⣽⡶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣟⡿⠲⠶⠓⡞⠃⡏
⠀⠀⠈⠛⠉⢳⠀⠀⣷⡀⠀⠀⠀⣀⣠⡤⠖⠋⠉⢸⠃⠀⠈⡉⠓⠶⠦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⣶⠞⠉⠀⠀⢀⡼⠃⣸⠃
⠀⠀⠀⠀⠀⠈⢧⣀⣹⡙⠶⠞⠋⠉⠀⠀⠀⠀⠀⣾⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠈⣯⠉⠉⠉⠁⣸⣧⣯⣤⣤⡤⠶⠛⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠘⣷⢄⡀⠀⣿⣤⠤⠤⠤⠶⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡶⢶⣶⡞⠛⠀⠀⠀⠀⠀⠀⠀⠘⣆⠉⠲⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡏⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡚⠛⠓⠶⡇⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣈⣁⣂⠀⠀⢸⡗⠲⠶⢶⡶⢶⠶⠖⠒⠚⢻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⡤⠴⠚⠁⠀⠀⢸⡇⢸⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⠀⣸⣀⣀⡀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢧⣀⠀⠀⠒⠒⢛⣟⣉⣉⣠⣤⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠉⠛⠮⣽⠛⢙⣋⣿⣉⠙⠷⠶⠚⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠤⠶⠖⠚⠋⠁⠀⠈⠙⠳⠦⠤⡤⠴⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠤⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣶⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⢀⡴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡏⠑⠒⠤⢄⣀⣀⣲⡆⠴⠖⠒⡖⠒⠋⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠉⢙⣛⠛⠿⠿⠏⠙⠋⠉⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡇
⠀⠀⠀⢡⠀⢠⠖⠒⠤⠔⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡏⠈⠙⠋⠀⠀⠀⠀⠠⠶⠄⠀⠀⡀⢠⣤⠀⡇
⠀⠀⠀⠀⢇⠘⢄⠀⠀⠀⠀⠀⠀⠀⡠⠠⣆⠀⠠⠂⠈⠁⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⠀⠀⠀⠀⠀⠀⢀⡾⠛⢻⣤⣜⡁⠀⠀⢰⠃⣀
⠀⠀⠀⠀⠀⠳⢎⠀⠀⠀⠀⠀⠀⠐⣇⣀⣘⠈⠑⠒⠤⣀⠞⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠈⠿⣦⠾⣿⣿⣿⣿⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢄⣀⠀⠀⠀⠉⢈⡹⠂⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⣲⣤⣤⢤⣤⣴⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⣸⡓⠩⣹⣏⢧⠀⢀⡠⠊⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣾⣿⣿⣧⣙⣺⣿⣿⣿⡿⢟⠁⠀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⢰⡡⠒⡀⢹⠈⠑⠉⠈⠆⠗⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⡇⢸⠀⠀⠀⠀⠸⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⢸⠀⠐⢾⣀⡎⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⣛⣩⣹⢛⣿⣿⡛⣟⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢱⠢⢤⡋⣘⡅⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣛⣛⣃⣞⣛⣛⣛⣛⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢦⡏⠉⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣟⠛⠻⠿⠿⠿⠛⣛⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠒⠂⠀⠀⠒⠒⠚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⣿⣿⣯⣿⣽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⢸⢧⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣗⣿⢙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⢀⠎⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣟⡵⠃⢸⣿⣝⣾
⠀⠀⠀⠀⠀⠀⠀⠀⣼⢓⡒⡴⠋⠀⢨⣑⣒⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⡟⠀⠀⠸⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠃⠀⠀⠈⠙⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡀⢰⣟⡛⠃⠛⣿⡟⠃⣿⣀⣀⣿⢰⣿⣧⢰⣿⡇⢀⣾⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⢾⣷⣠⣍⣻⡷⠀⣿⡇⠀⣿⠋⠙⣿⢸⣿⢻⡿⢹⡇⣼⡷⢾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠉⠉⠀⠀⠈⠀⠀⠉⠀⠀⠉⠀⠁⠀⠁⠈⠁⠉⠀⠀⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⢀⣀⣀⡀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣴⠟⠉⠉⠻⣦⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢹⣿⡏⢠⡿⢻⡆⢹⣿⡟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⡿⠛⠁⠹⣧⡈⢻⡟⢁⣼⡟⠀⠛⢿⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣤⣀⣰⣦⣶⠟⠋⠀⠀⣀⣠⡿⠛⢿⡿⠛⢻⣆⣀⡀⠀⠉⠻⢷⣤⣶⣄⣀⣤
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣿⠷⠟⠛⠋⠉⢀⣤⡴⠾⠟⠛⠋⠙⠻⠶⢾⣷⠶⠟⠛⠙⠛⠃⠰⠆⢀⡀⠉⠉⠛⠻⠷⢾⣧⣀⣀
⠀⠀⠀⠀⢠⣶⡾⠋⠁⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠈⠙⠻⣦⣄
⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣀
⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⢰⡆⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟
⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⣶⣤⣤⣤⣾⣷⣤⣤⣿⣦⠄⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧
⠀⠀⠀⠀⣽⣷⡀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡘⠋
⠀⠀⠀⢀⡀⢈⣿⣶⣄⠀⢸⣧⣼⣿⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠉⠋⠙⠛⠉⢻⣧
⢠⣄⠀⠘⣷⡀⠀⠀⡹⠛⢸⣏⣹⣿⠀⠀⠀⠀⠀⣼⠏⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⢛⣿
⠈⠙⠷⣦⠈⠀⠀⣀⣠⣤⣼⣏⣹⣿⣤⣄⣀⡀⠀⠀⣤⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠛⠛⠛⠛⠻⣿
⢶⣶⣤⠀⢀⡄⠘⠋⠉⠀⢹⣏⣹⣿⠁⠉⠙⠛⢷⣄⠀⢠⣴⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡶⠶⠶⠶⠶⣶⠀⠀⠀⣿
⠀⠀⠀⣠⡄⠀⠀⠀⣦⠀⢸⣟⣹⣿⠀⣰⡄⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠰⣶⣶⠀⣿⠀⠀⠀⣿
⠀⠀⣰⡟⠠⣶⢶⣶⡟⠀⢸⡟⢻⣿⠀⢘⣷⣶⢶⡄⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⣦⠀⣿⠀⠀⠀⣿
⠀⢠⡿⠀⠀⠀⢀⣬⣿⣶⢿⡇⢸⣿⢷⣾⣯⡀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣿⠀⠀⠀⣿
⠀⣼⡇⢀⣴⠶⢿⡏⠀⠀⢸⡇⢸⣿⠀⠀⢈⣿⠶⢶⡄⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣧⣀⡀⠀⠀⠀⠀⠀⠀⠟
⠀⣿⠀⠀⠀⣤⡾⢻⣆⠀⢸⡇⢸⣿⠀⢠⡿⠻⣦⡄⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠛⠁⠈⠉⠻⣦⠀⠀⠀⠀⠀⠶
⠀⣿⠀⠀⠀⠁⠀⢸⠏⠀⢸⡇⢸⣿⠀⠘⡷⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢀⣤⠀⣴⡶⠟⠛⣷⠀⠀⠀⠀⠀⠻⡇⠀⠀⠀⣰⡆
⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⡃⢴⣤⣤⣶⠶⢿⠇⠀⠹⣧⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟
⠀⢿⡄⠀⠀⣀⣠⣤⣶⠟⠋⠀⠀⠈⠻⢶⣦⣤⣀⡀⠀⢀⣿⠃⠀⠀⠈⠉⠀⠀⠀⠀⠀⢻⣇⣀⣠⣿⣆⣀⣠⣴⡶⠟⠛⠉
⣤⣬⣽⣿⣯⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣿⣿⣿⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣯⣭⣭⣿⣯⣭⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡏⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣠⠖⠉⡙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢠⠎⠁⠀⣰⡟⠁⢀⣼⠔⠊⠉⢉⡹⠆⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡎⣿⠁⠀⠀⠀⠙⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢷⡇⠀⠀⠀⢰⠀⠀⠠⠀⠀⠀⢀⠀⠀⠉⠀⠀⠀⠈⠉⢩⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠁⠀⠀⡀⠸⠆⡀⢴⣦⠔⠈⠏⢠⠄⢐⣆⡄⠀⠀⠶⠃⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠀⠀⠄⠀⠛⠚⠀⠋⠈⠉⠀⠘⠋⠀⠀⠈⠙⠀⠀⠀⠀⢀⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠳⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⣤⠖⠓⠂⠀⢰⠇⠀⠀⠀⠈⢩⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠠⠞⠻⠶⠀⠀⠀⠁⠀⢀⠀⠀⠈⠻⡆⠀⠀⣀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡈⢣⠀⢀⣀⡀⠀⠀⠀⠀⠞⠋⠉⠀⠀⠀⠀⠁⠚⠡⠄⢱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⢾⣄⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢂⠀⠀⠦⠀⢉⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡠⠆
⠀⠀⠀⠀⣀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⠀⠀⠀⣿⠀⠀⠞⠓⡄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠙⠟⠛⠶⠀⠀⠀⠀⠀⣤⠖⠀⠈⠉⢦⡘⣄⠀⠀⠈⠲⠆⠀⡨⠃⠀⠀⠀⢀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⣹⠉⠲⣤⣀⠀⠁⠈⠀⠀⣠⠔⢶⠟⡗⠂⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠘⢄⡀⠀⣀⣐⠒⠉⠙⠀⢀⠴⠛⡿⢶⠀⠐⠊⠀⠀⢀⠀⡇⠀⠀⠀⠁⠲⡄
⠀⠀⠀⠀⠀⠀⠾⠟⠉⠉⠁⠀⠀⠀⠈⢳⠒⠉⠉⠒⣤⠛⡰⠃⠀⠀⣱⢄⣢⡄⢤⠒⡖⠠⠔⠀⢀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢈⡓⠒⠒⠀⣀⣠⠁⢀⡀⠄⠳⣤⣁⠘⠻⠆⢹⠁⠀⠀⢸⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠋⠀⠀⠀⠀⡌⠁⠚⠓⠀⠙⠇⠀⠸⠋⢠⣤⠄⠀⠀⠀⠀⠀⣦⠠⡤⢤⣇⠀⠀⢀⠄⠀⠸
⠀⠀⠀⠀⠀⠠⠐⠛⠉⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⠀⠀⡿⠠⣴⠦⠀⠀⠀⠀⢀⡷⠀⡀⠀⠙⠳⠶⠦⣄⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠘⠂⠀⡇⠀⠉⠘⠃⠈⠛⠛⠛⢄⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⢀⣠⢶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠄⠀⠴⠊⠉⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠆⢀⣀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣭⠙⣒⣢⣤⡤⠤⠴⠒⠒⠛⢓⣂⡈⣭⡥⠒⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠈⠉⠁⠐⠒⠒⠒⠒⠒⠉⠉⠉⠁⠘⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠲⢄⣀⡠⠤⠄⠀⠀⠀⠀⠀⠀⠂⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣋⣀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠠⠀⢀⡀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣶⣤⠤⠴⠒⠫⠝⠷⢦⣤⣤⡤⠖⠺⠟⣁⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣭⡶⠖⠀⢠⠐⠲⠆⢸⠒⢤⠃⢀⣀⡟⣉⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠴⠞⡉⢧⣟⣻⠇⠀⠀⠀⠸⣧⣷⡾⢏⣉⣁⣸⡟⡞⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠈⢶⠩⠤⠀⠀⢀⣀⢰⡮⠟⠋⠈⠉⠉⠉⠛⠃⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣜⣀⡤⣤⣤⣼⣠⣀⣙⡃⠴⠾⢿⡁⠀⠀⠀⢀⡀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠸⢎⡁⠀⠋⠀⠀⠈⢋⣡⠞
⣤⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣴⣦⣶⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣤⣤⣴⣦⣤
⣿⣿⣿⡟⡏⠛⢿⡟⠙⡿⠛⢿⡛⠟⣻⣻⡿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣷⣶⣷⣶⣷⣶⣾⣿⣶⣿⣷⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄
⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠁
⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⠙⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⢠⠞⠋⠁⠐⢄⢠⣿⣦⣄⡀
⠀⠀⠀⢀⠀⠀⢀⣤⠀⠂⣀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⡐⠀⢀⣤⠀⠶⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠈⢶⡉⠙⠛⠛⠋
⠀⠀⠀⣆⠀⠀⢿⡟⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⡇⠀⣿⡿⠀⠀⠀⠺⠇⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⣰⣦⠸⠟
⠀⠀⠀⢿⡀⠀⠀⢀⡴⢢⡀⠀⠀⣰⠇⠀⠀⠀⠀⠈⠉⠉⠀⠈⠁⢀⡴⣄⠀⢀⠠⠦⠀⠀⠀⠀⠀⢻⡄⠀⠀⠻⢿⡄⠀⠀⢀⣰
⠀⠀⠀⠀⠙⠒⠒⠉⠀⠀⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⠴⠋⠈⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣴⣶⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⠀⣀⣄
⠀⠀⠀⢀⣾⠿⠋⢄⠀⢘⡿⣿⣦⣀⠀⠀⠀⠀⠀⠀⢰⠟⠁⠀⢀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⢸⠿⣿⣿⣷⣤⣴⣾⣿⣿
⠀⠀⢾⣏⣀⣤⣤⠦⠿⢥⣄⡀⠙⠻⠿⠂⠀⠀⠀⠀⠻⠁⠀⠀⣤⣱⡄⣴⠾⣟⣛⠁⠀⠀⠀⠀⠀⢠⠂⠀⣠⣍⠛⠛⣍⠀⠈⠃
⠀⠀⠸⡟⠉⢿⣿⠀⠀⠀⣿⠟⠳⡼⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⣿⠟⡇⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⡌⠀⠀⢿⠏⠀⠘⠿
⠀⠀⠀⢱⣄⠈⢁⣠⠶⣀⣀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⡰⠓⢄⠀⠔⠃⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⣠⠞⢂⡀⠀⢀⡐
⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠉⠁⠀⠀⠈⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⣶⣶⣤⡀⠀⠀⠈⣦⣾⣿⡿⠟⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠉⠉⠛⣦⡀
⠀⠰⠛⠻⢿⣿⣦⡄⠀⠙⠋⠁⠀⣀⡀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⠿⣿⢿⣿⣶⣦⣄⠀⠀⠀⠀⢀⡤⠚⠁⠀⠊⠀⠀⠀⠀⠀⠈⢿
⠀⠀⡌⠉⢲⣬⡛⠁⢀⡤⣶⣾⡆⠈⣿⠀⠀⠀⠀⠈⣛⠟⢻⣿⣧⠀⠀⠀⣸⣿⠿⣿⡗⠀⠀⠀⣞⠀⣠⣿⡇⠀⠀⠀⢰⡆⠀⠀⠸
⠀⠀⡇⠀⠘⠟⠈⢹⣏⠀⠸⢿⠇⢀⡟⠀⠀⠀⠀⠀⠱⡀⠀⠛⠃⢀⣄⠀⠈⠁⠀⠜⠀⠀⠀⠀⣿⠀⢻⣿⠃⢀⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠘⠦⢄⠠⠔⠁⠈⠢⣄⣀⡠⠞⠁⠀⠀⠀⠀⠀⠑⠹⠶⠤⠔⠋⠈⠓⠲⠶⠟⠀⠀⠀⠀⠀⢻⣦⣀⣀⡴⠏⠙⢦⣀⣀⣀⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣴⠟⠃⠀⠀⠀⠈⠙⢷⡄⠀⠀⠀⠀⠀⢠⠟⠿⣿⣷⣄⡠⠀⡀⢀⣤⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⡿⠷⠀⢶⣶⣆
⠀⠀⢘⠡⠄⠠⢄⡀⠀⢀⠤⠤⠤⡀⠀⠀⠀⠀⠀⠀⢀⡈⣹⡟⠁⠀⢸⣿⣯⠘⠋⠙⡇⠀⠀⠀⠀⠀⡞⠟⠀⠀⠀⠀⠀⠘⢶
⠀⢀⠃⠀⠀⠀⠀⠙⡖⠁⢀⣄⠀⠱⠀⠀⠀⠀⠀⡜⠁⢠⣤⡉⢢⡀⠀⢉⠠⣀⣒⣤⡔⠂⠀⠀⠀⢀⠔⠁⢀⡀⠠⠆
⠀⢸⡇⠀⠀⡿⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⢸⠀⢠⣼⣿⣷⠀⣿⣴⣶⣿⣿⣿⣿⡇⠀⠀⠀⠀⡎⠀⢰⣿⡇⠀⢰⣿
⠀⠈⣷⡀⠀⠀⠀⠀⣀⠀⠉⠁⢀⠄⠀⠀⠀⠀⠀⢇⠈⢿⣿⡟⠀⣸⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⣇⠀⠀⠉⠀⣤⡀⠀⠀⠀⡤
⠀⠀⠙⢿⣦⣤⣤⡞⠉⠓⠀⠘⠁⠀⠀⠀⠀⠀⠀⠈⠣⣄⠀⣀⠔⠁⠈⠛⠿⠿⠛⠁⠀⠀⠀⠀⠀⠸⣦⣤⠴⠊⠀⠈⠢⣤⡴⠁
⠀⠀⠀⠀⠈⠉

⠀⠀⢀⠄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣰⣶⡆⢀⠠⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢄
⠀⢰⣳⣦⠀⠀⠀⠈⢡⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢿⡟⠁⠈⠀⠘⠿⠀⠀⡀⠀⠀⠀⠀⢠⠂⠀⠀⠀⣰⣮⠁⠀⠀⠀⣤⡄
⠀⡿⣿⡿⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣟⠀⠀⠀⠘⣿⡟⠀⠀⠀⠀⠿⠿
⠀⢣⡀⠀⠀⠀⢀⡼⢆⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⢀⡶⢄⠀⠀⠀⠀⡌⠀⠀⠀⠀⢹⡀⠀⠀⠀⢀⡼⢆⠀⠀⠀⠀⡸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⢅⣀⠈⢿⣿⣿⣇⠀⠀⠀⠀⠀⢀⣀⡤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠀⠀⠀⠀⣿⣿⣿⠟⢋⡁⠀⠀⠀⣀⠀⠀⢿⣿⡿⠀⠀⠀⠐⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠸⠛⣀⡇⠙⠻⠀⣿⠀⠉⣣
⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠋⠉⠁⠀⠀⠀⠀⠑⣤⡀⠀⠀⠀⢓⣀⡀⠀⠈⠋⣤⡖⠁⠀⠀⠀⠀⠛⠛⠛⠛⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⢀⣀⣠⣾⣿⣷⣄⠀⢮⣁⣀⡹⠆⣀⣾⣿⣧⣀⡠⠤⢤⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠋⠀⠀⡠⠏⠀⠘⠛⣻⣿⠿⢷⠶⠚⠉⢲⡾⠿⣟⡛⠓⡆⠀⠀⣨⠇⠀⠈⠙⠒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⢀⣨⠉⡠⠖⢇⠀⠀⢀⡎⠀⠀⠀⠀⠙⢧⡠⢄⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠓⢋⠴⠋⠀⠀⠈⡳⠖⠁⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⣀⠔⠋⠀⡠⣄⣶⡒⢤⣤⡤⠴⠃⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⢻⠁⠀⠀⢰⣟⣒⠀⠀⢸⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸⢟⣃⣠⡤⠼⠤⠤⠤⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⣤⡄⠀⠀⠀⣠⣴⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⠿⣿⡟⠀⠀⠀⣽⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⣭⡄⠀⠀⠀⠰⣷⣬⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠒⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡖⢁⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⢳⢀⡲⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⡠⠖⠃⠀⠑⢄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⢤⣀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⡇⡄⠀⠀⠀⠀⠀⠈⠙⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⢀⠴⠋⠙⣄⡇⣇⡜⠉⠳⢄⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢠⠏⠀⡄⠀⢻⣀⣸⠃⢠⡀⠈⢧⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⡏⠰⠊⠀⠀⣼⠀⢸⡄⠀⠑⠆⠈⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢰⠃⢀⡴⠃⠀⡇⠀⠀⡇⠘⢦⡀⠀⢳⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠸⡄⢀⡤⠖⠊⠀⠀⠀⠈⠒⠦⣄⠀⡼⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⣦⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢡⣦⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠚⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠈⠂⠀⠀⠀⠛



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢀⣀⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠂⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⢰⡆⠀⢀⣀⣀⣀⣆⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⣼⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣆⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠻⢿⣿⣿⣿⡇⠀⠹⡆⠀⠀⠀⠀⠀⠀⠈⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠈⠛⠟⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢷⣦⠈⠉⠛⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠻⣷⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⡉⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠙⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣠⣤⣤⣤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⢠⣤⣶⣶⣷⣶⣤⡇
⠀⠀⠀⠀⠀⠀⠀⣀⡄⡀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⣴⣧⣦⠄⠀⠀⠀⠀⠀⠀⣶⣷⣷⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣄⣦⡄
⠀⠀⠀⠀⠀⠀⠰⣿⣿⠇⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢸⣿⠛⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡏⠉⠉⠉⠉⠋⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⣿⣶⣤⣀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣴⣾⣷⣶⣴⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠟⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠈⠈⠘⠀⠀⠀⠐⠀⠂⠘⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠃⠁⠊⠀⠀⠀⠀⠀⠄⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠛⠶⠶⠶⣤⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣿⡀
⠀⠀⠀⠀⣠⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟
⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⡷
⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠁⢠⠄⢀⡤⠀⣠
⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠿⠀⠀⠀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⡀⠀⠀⠀⠀⠒⠒⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠐⢤⡀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⣀⡀⠀⣀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠁⠉⠉⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠶⠦⣤⣤⣤⣤⣤⣀⣀⣤⣤⣤⣤⣤⡴⠶⠶⠟⠃
⣿⣷⠿⠿⠾⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡔⠋⠙⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠀⠀⠈⢉⠙⠒⠦⣄⡀⢠⠖⠛⠲⣄⠀⠀⢀⣠⢤⣀⡞⠁⠈⠙⢧⡀⠀⠀⠈⠳⣄
⠀⠀⢀⡠⠖⠁⠀⠀⠀⠀⣀⣀⣤⡤⠤⠤⢤⣄⣀⣘⠀⠀⠀⢠⠉⠻⡀⠀⠀⠈⠑⢤⡏⠀⠀⠈⠳⣄⠀⠀⠀⠁⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠉⠀⠀⢀⡠⠔⠚⢉⣁⣠⣤⣤⡤⣤⣤⣤⣄⣈⡉⠓⠦⣄⡀⠀⠈⠲⣄⠀⠀⠀⠙⢦⡀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⣠⠞⢉⡠⠔⠊⣩⣟⡽⠛⠀⢉⣀⠀⠰⠹⣽⣯⡑⠢⢄⡉⠳⢄⡀⠈⠳⢄⠀⠀⠀⠈⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⣠⠊⢀⠴⠋⠀⠀⢰⣿⡟⠂⠀⢻⣿⣿⣿⣦⡀⠹⢟⣧⠀⠀⠉⠲⣄⠙⢦⡀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠚⠁⠀⠀⠀⠀⠀⠀⢺⣟⡄⠐⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⠀⠀⠀⠀⠈⠀⠀⠙⠂⢦⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⢄⡀⠤⠤⠄⠀⠸⣿⣦⠀⠻⣿⣿⣿⣿⡿⠁⢀⣾⡿⠀⠀⠀⠀⠀⢠⠆⠐⠦⠚⠀⠀⠀⣈⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠈⠳⣔⢦⡀⠀⠀⠹⣿⣆⡀⡀⠉⠉⠁⢀⣠⣾⡞⠁⠈⠚⡤⣀⡴⠁⢀⡴⠚⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠈⠳⢍⡒⠀⢀⢈⠛⠿⢿⣿⣿⣾⠿⠞⠉⠀⠀⠀⣨⠔⠉⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⡤⠤⠤⠤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣵⣄⡀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠈⠙⠋⠉⠉⠉⠉⠉
⠀⠀⠀⠐⠲⢄⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⣄⣀⡀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠄⠠⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⡀⠀⢀⠀⢀⠀⢀⡀⢀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢰⠆⠈⣇⠔⠹⠆⠈⠆⠁⠗⠉⢷⠈⢧⠤⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠃⠠⠈⠀⠀⠀⠢⠤⠀⠀⠀⢸⡠⠃⡮⣄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠐⠁⠀⠀⠀⠀⣠⣊⠤⢀⠀⠈⠁⠀⠁⠇⡸⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠂⣵⠶⢦⠀⢀⣴⠟⠒⠉⠉⠀⠀⠀⠀⠀⠖⠃⠀⣂⡀⠊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠐⠇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠤⣄⠁⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡇⠀⠀⠈⠉⠙⠫⡉⠉⠢⡄⠀⠀⠀⠀⢀⡠⠛⠂⠐⠳⡦⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢶⡚⠟⠋⠻⣄⡀⠀⠀⠀⠖⠛⠀⠁⠉⠀⣀⣤⠰⠋⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠸⡀⠀⣌⠀⠀⠀⠘⣭⡓⣤⣬⡤⠤⠤⢴⣂⡉⠔⡁⠷⣄⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠳⣤⠀⠀⠛⢄⣹⠀⠀⠀⠀⠀⠉⠛⠻⢄⣀⠀⠀⠀⡠⠊⠀⠀⠈⢳⡀⢀⡜⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⢤⠀⡠⠝⠁⠀⠀⢀⣀⠑⠲⠤⢤⣀⡀⠀⠀⠀⠀⠉⠑⠊⠀⠀⠀⢀⡴⠋⠉⠉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢄⡁⠀⢛⡃⠀⠀⠀⠀⠉⢳⠢⢄⣀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠵⠦⠀⠀⠀⠓⠂⠊⠀⠀⠀⠀⠀⠀⠘⡖⠲⠼⠙⠒⠒⠙⠉⠀⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠶⣤⣀⠀⠀⠈⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⠳⣄⠀⠀⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠘⣧⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠸⠇⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⣀⡀⠀⠀⠀⠀⢀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠟⠉⠀⠀⠀⠀⠈⠛⠶⠾⠂⠀⣿⣰⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣠⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⣴⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣼⠇⣠⡿⠻⠶⣶⡌⠙⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⢀⣴⠏⠀⢀⡾⢋⡿⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⣿⠟⠀⠀⠀⠀⠀⠲⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠙⠷⣾⡳⣦⣴⠏⠀⣸⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⡋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣤⣀⠀⠀⠀⠀⠀⠀⢸⣯⠙⠷⣤⡈⣻⡾⠁⠀⣰⡟⠉⠀⠙⣿⣷
⠀⠀⠀⠀⣠⣾⡿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠹⣞⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⠛⠶⠶⠶⠶⠛⠙⠳⣤⣈⠛⠛⠛⠛⢻⡟⣠⡴⠶⠶⠘⣿
⠀⠀⢀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣮⡻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡄⠀⠀⢸⣵⠏⣠⣤⡄⠀⣿
⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⣙⠶⣦⣄⣀⣀⣀⣤⡴⢟⣽⠷⢦⣤⣤⣤⣄⣀⠀⠀⠀⠀⠈⣧⠀⠀⠘⣿⣴⠏⠀⠀⣸⣿
⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⣭⣭⣭⠴⠾⠋⠁⠀⠀⠀⠀⠀⠈⠉⠛⢶⣄⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⢠⣿⡟
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠈⣷⠀⠀⠀⠀⠀⢸⣿⡁
⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢹⡆⠀⠀⠀⠀⢸⣿⠁
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣾⣷⣶⣶⣶⣶⣾⣿⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⠶⠿⠿⠶⠶⣤⣄⡀
⠀⠀⠀⣠⠴⠚⠉⠁⣀⣀⣀⣀⣀⡉⠛⠿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠟⢋⣁⣠⣤⣤⣤⣤⣄⣀⠈⠉⠓⠦⡀
⠀⠀⠊⠀⠀⠐⠚⠉⠉⠉⠉⠛⠿⣿⣿⣷⣦⣝⠻⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠿⣫⣷⣿⣿⣿⣟⢛⣉⣁⣀⡀⠈⠉⠀⠀⠀⠈⠂
⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡙⢿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⡿⠋⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠰⣿⡿⠿⠛⢋⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣉⠛⠛⠿⣿⡇
⠀⢀⣰⣚⣉⣠⣴⣾⡿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣵⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⡍⠛⠿⣿⣶⣤⣈⣙⣦⡀
⠀⠀⠉⠙⠛⣯⡉⠀⠀⢀⣿⣿⣤⣾⣿⣿⣿⣿⣿⠛⢿⣿⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢻⣿⠟⢹⣿⣿⣶⣾⣿⣿⣿⣿⣿⠀⠀⠀⣀⡽⠋⠉⠁
⠀⠀⠀⠀⠀⠈⠻⣦⡀⠈⣿⣿⣿⣿⣿⣿⡿⢫⡿⠀⠀⠙⢣⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⠋⠁⠀⠸⣷⠹⣿⣿⣿⣿⣿⣿⡿⠀⣠⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⣈⠿⣿⣿⣿⣭⣴⠟⢁⣠⣴⣶⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣤⣄⡙⠳⣦⣭⣿⣿⡿⢟⣡⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣿⣿⣷⣶⣿⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣶⣶⣿⣶⣾⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠂⠉⠉⠉⠉⠉⠉⠐⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠛⠒⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢀⡤⠒⠋⠉⠉⠑⠒⠂⠐⠲⡒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠘⣄⣠⠞⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠙⢦⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⣶⠟⠋⠉⠀⠀⠹⡄⠀⠀⡴⢋⣉⡙⡀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡶⣤⣄⠀⠘⠛⠁⠀⣀⡄⠀⠀⠀⠈⠢⠚⠁⣯⠀⠁⡇⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣀⡼⣆⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⢠⡇⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠴⠋⠘⣤⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⢘⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠹⣄⡠⠴⠊⠀⠉⢲⡀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡎⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⢠⣞⣷⡶⢤⡄⠀⠀⠀⠀⠀⠀⠀⡸⢀⠞⠀⠀⠀⠀⠀⢱⢄⡀
⣀⣀⣀⣀⡀⠠⠤⠤⠤⠤⠄⠒⠒⠒⠒⢂⠈⠢⡈⠑⡇⢁⣾⠃⠀⠀⠀⠀⠀⢀⡴⣡⠋⠀⠀⠀⠀⠀⠀⡆⠀⠉⠓⠦⣀
⠀⠀⠀⠀⢀⡠⠔⠒⠒⠤⣀⠀⠀⠐⠉⠁⠀⣠⠈⠲⣍⠋⠁⠀⠀⠀⠀⢀⡰⢋⡜⠁⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠙⠲⣄
⠀⠀⣠⠔⠉⠀⠦⣌⡙⠲⣄⠙⢆⠀⠀⠀⡰⠃⠀⣀⡤⡷⠦⣄⣀⣀⠴⠊⡴⠋⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⡾⠁⠀⠒⠦⢄⡀⠙⢦⠘⡇⢀⠀⢀⠞⠁⡠⠞⠁⢰⠁⠀⠀⠉⡟⣄⡞⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⡇⠀⠀⠠⣄⠀⢹⠀⢸⠀⣅⡈⢠⠏⢠⠞⠀⠀⠀⡏⠀⣀⠤⢄⣡⣹⠤⠒⠒⠢⢄⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⢣⠀⠀⠀⠸⣧⢸⣤⠼⠒⢻⠀⠁⢠⠃⠀⠀⠀⠀⣧⠎⠀⠀⠀⠙⢇⠀⠀⠀⠀⠀⠳⡀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠈⢆⠀⠀⠀⡇⠀⠀⠀⣴⠃⠀⢀⡎⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⢱⠇
⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⢹⠀⠀⡜⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢣⠀⠀⠀⠀⢀⡰⢆⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢠⡇⠀⢀⡠⠊⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⢠⡏⣡⡴⠋⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⢸
⠀⠀⠀⢘⡋⠁⠀⠀⠀⣠⠔⠋⠘⣆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣨⡇⠀⢸
⠀⠀⠀⠘⣇⣀⣠⠴⠊⠁⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⢸
⠀⠀⠀⠀⠈⢩⠁⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇⠀⠀⠀⠀⢸⠃⠀⡀
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⣇⠀⠀⠀⠀⣸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠳⣄⡤⠚⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣓⣤⣴⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠒⠈⠉⠉⠉⠉⠉⠉⠁⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠷⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠁⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⢀⡴⠊⠉⠀⠀⠀⠈⠉⠉⠀⠉⢻⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣄⢠⠜⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠋⠁⠀⠀⠱⡄⠀⠀⢀⡖⢉⡉⠱⡀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⣤⣀⠀⠀⠀⠿⠞⠁⠀⠀⡀⠀⠀⠀⠙⠦⡠⠞⠠⡋⠉⠁⡇⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡍⠉⢳⡀⠀⠀⠀⠶⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣣⠀⢀⡇⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠊⠁⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡁⣀⡼⢣⡀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢻⣯⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣼⠀⠀⠀⢀⡴⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡇⠀⠈⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠘⠦⠴⠖⡋⠀⠀⠀⠹⠄⠀⠀⠀⠀⠀⠀⠀⣸⠀⢀⠟⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⢰⣮⢭⣿⠖⢶⡄⠀⠀⠀⠀⠀⠀⠀⢀⡟⢠⠟⠀⠀⠀⠀⠀⠀⡿⢤⣀
⣀⣀⣀⣀⣀⠠⠤⠤⠤⠶⠤⠶⠒⠒⠒⠒⠒⢂⠈⠳⣄⠉⢻⠈⣠⡿⠁⠀⠀⠀⠀⠀⠀⣠⠞⣰⠃⠀⠀⠀⠀⠀⠀⢰⠇⠀⠈⠙⠲⢄⡀
⠀⠀⠀⠀⠀⢀⣤⠴⠶⠶⣤⣀⠀⠀⠀⠖⠉⠁⠀⢀⠈⠳⣌⡛⠋⠀⠀⠀⠀⠀⠀⢀⡼⢁⠞⠁⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀
⠀⠀⠀⣠⠖⠉⠠⣄⡈⠒⠤⣌⠙⢦⠀⠀⠀⠀⣠⠏⠀⠀⣀⣹⡦⣀⡀⠀⠀⣠⠔⢋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⣠⠞⠁⠠⢄⣀⠀⠉⠳⣄⠈⣧⠠⠁⠀⠀⡴⠃⢀⡤⠞⠉⡜⠀⠈⠉⠛⡿⡁⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⣿⠀⠀⠀⠀⠀⠙⢦⠀⢨⠄⠱⠀⡇⢀⡞⠀⣴⠋⠀⠀⢰⠃⠀⠀⠀⠀⢇⢻⡎⢀⣠⣄⣀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⢿⠀⠀⠀⠙⣷⡀⢸⠀⢸⣀⣸⡖⠡⠋⠀⡞⠁⠀⠀⠀⢸⢀⡴⠊⠉⠓⢾⣾⠉⠁⠀⠀⠉⠳⣄⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠈⡆⠀⠀⠀⢸⡗⠘⠓⠋⠉⣸⠇⠀⠀⡼⠀⠀⠀⠀⠀⢸⡎⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠈⣆⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠸⣄⠀⠀⠸⠇⠀⠀⠀⢰⠁⠀⠀⣰⠃⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠸⡄⠀⢠⠇⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⡰⢷⣀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣸⠀⠀⠀⣠⠞⠁⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⣴⠛⣀⡤⠞⠁⠀⠀⠀⢙⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠿⠚⠋⠀⠀⠀⠀⣠⠴⠋⢧⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠉⠉⠉⠉⠉⣿⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⣀⡴⠛⠁⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠉⠉⠉⣿⠀⠀⣿
⠀⠀⠀⠀⠘⠶⡶⠊⠁⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⠀⠀⡏
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⢧⡀⠀⠀⠀⣴⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠙⢦⠴⠋⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⣀⡖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠿⠿⠛⠉⠉⠛⠉⠉⠉⠉⠙⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠉
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉
⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⣀⣠⣤⠴⠶⠶⠶⠶⠶⠶⠶⣦⣤⣀⡀
⠀⠀⠀⢠⣿⣿⢿⣿⠿⠛⠁⠀⠀⢀⣤⠶⠛⠉⠀⡀⠀⠀⢠⠀⠀⠀⡀⠀⠀⠀⠉⠙⠻⢦⣀
⠀⠀⠀⣼⠏⠓⠉⠀⠀⠀⠀⣠⠞⠉⠀⠀⢆⣀⣠⣵⣶⣶⣿⣶⣷⣶⣷⣤⣤⣄⠀⠀⡀⠀⠈⠑⢤⡀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⣢⡴⢚⣿⠟⠋⠙⠓⠀⠈⠀⠈⠉⠛⢿⣿⣻⣿⣤⡀⠀⠀⠀⠈⠲⣄
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠠⣰⣾⣭⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡕⠻⠿⣦⡀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢠⣿⠁⠀⠀⠀⠀⣤⣶⣶⣦⡀⠀⠀⠀⠀⠘⣿⠀⠐⢜⣷⣤⠤⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⢸⡏⠀⠀⠀⠀⠸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⢻⡆⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠁⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⣸⡏⠀⠀⢀⣴⣫⡟
⠀⠁⠀⠀⠀⠀⠻⣤⣤⣤⣤⣄⣀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢋⣠⠴⢞⡭⠾⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣶⣤⠽⣿⣶⣤⣤⣄⣤⣤⠤⠶⠟⠛⢯⣭⠐⠚⠛⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⡩⠛⠉⢱⠛⣰⠀⠀⢢⠀⡆⢹⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣅⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⢀⣠⣴⣶⣿⣷⡆
⠀⠀⣾⣿⣿⣿⣿⡿⣟⣵⣿⡄
⠀⠀⠹⣿⣿⢟⣽⣾⣿⣿⣿⣿⡄
⠀⠀⢀⣩⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣀⣀⡀⠀⠀⠀⠀⢀⣀⡀⠐⠶⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣀⠐⢶⣄⠀⠈⢿⣶⡄⠈⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠋⢀⡼⠟⠀⢀⣼⡿⠃⢀⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠛⠉⠁⠀⠀⠀⠀⠘⠛⠋⠠⣴⣾⠟⠉

⠀⠀⠀⠀⠀⢀⣠⠀⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛⠋⠉⠀⠈⠁
⠀⠀⢠⡀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢸⣿⣾⣿⣿⣿⣿⣛⠛⠛⠶⠶⢦⣤⣀⡀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⠀⣀⣠⣤⣤⡤⡤⢤⣴⣾⣧⣧⣾⡇
⠀⠀⠈⢻⣿⣿⣟⠛⠿⠿⢷⣦⣤⣀⠀⠐⣯⢝⡳⢦⣀⠙⢷⣦⣤⣆⠜⠀⠀⠀⠰⡀⣄⣀⣴⡾⠋⣀⡴⢞⣛⠍⠉⠀⣀⣤⣶⣿⡿⢿⣿⣿⡿⠃
⠀⠀⠀⠀⠈⢿⣿⣄⠀⠀⢸⣿⣏⣹⣿⣶⣤⣄⣈⣁⠉⠳⢦⣌⡉⠁⠀⠀⠀⠀⠀⠉⠛⠛⣉⡴⠞⠋⠚⢋⣁⣤⣶⠛⢿⣿⠀⠀⠀⣼⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠈⠻⣿⣽⣿⣿⣿⣿⣿⠟⠛⠛⠛⠛⣿⡿⠋⠀⠀⠀⠀⣶⣶⣿⣿⠶⠶⢾⣿⣿⣿⣿⣿⣳⣿⡟⠀⢀⣾⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⡈⠛⠿⠿⠿⠛⠁⠀⠀⣀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠙⢿⣿⣿⡿⠟⠋⣀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⠤⠶⠶⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⣤⣀⣀⣤⡤⠶⠞⠋⠁





⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠞⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠳⠶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠫⠋⠀⠀⠀⠀⡠⠖⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠋⠘⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠤⠐⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⣠⡿⠅⠀⠀⠀⠀⡄⠀⠀⠈⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠱⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⢠⡟⠀⠂⠀⠀⠀⠀⠀⡆⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠎⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⡿⠀⢀⠤⠐⠒⠂⠄⣀⠃⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⣠⠃⢀⠊⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⢸⡇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠠⠤⠤⠄⠂⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣸⢃⠄⠊⠁⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣿⠂⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠈⠲⠀⠀⠒⠒⠒⡀⠀⢀⣀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠨⢀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢷⡒⠀⠚⠁⠀⠀⠀⠀⠀⠀⢀⠃⠈⠂⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠈⠀⠀⠀⠀⡆⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠈⠐⠠⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣀⠀⠐⠒⠊⠅⠀⠀⠀⠀⠀⠀⠈⠁⠂⠒⠈⠰⡀⠀⠀⠒⠄⠀⠀⠀⠀⢀⣴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⡀⠈⠢⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠈⠢⠀⠀⠀⠀⣀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⣤⣀⣈⠂⠐⠒⠁⠀⠀⡀⢀⣀⣀⣤⡴⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠉⠉⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣶⣦⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠛⠛⠛⠉⠁⠀⠀⢀⣀⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⠀⠠⡤⠄⢰⣀⡀⠠⠤⠤⠤⠶⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣧⠀⣠⠔⠋⣱⡀⠄⠀⠀⠒⠐⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢠⠴⢦⡀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣏⣠⣒⠁⠈⢆⣀⠤⠒⢉⡠⠒⣽⣿⣿⣿⣿⣿⣿⡿⠛⠛⠻⢤⡀
⠀⠀⠀⠀⡠⠛⠀⠀⠹⣤⡤⠀⠀⢿⣿⣿⣿⣿⣿⠟⡥⠞⢻⣿⠉⠉⠹⢤⠖⢁⡠⣾⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠳⣀⡀⠀⢀⡇⠀⠀⠀⠈⠻⣿⣿⣿⣿⡄⠀⠊⠡⠽⡗⠒⠒⢞⠉⠉⠙⠟⠛⠛⠋⢩⠟⠁⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠙⠒⠚⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⢦⡀⠀⢸⠁⠀⠀⠘⣆⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡖⠉⠓⠦⣾⠁⠀⠀⠀⠀⠀⠀⢸⠁⠀⢸⠀⠀⠀⠀⠈⢳⣿⣿⡿⢏⡀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠈⣳⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⢀⣼⠀⠀⣸⣷⠀⠀⠀⠀⠀⡏⠉⠉⠁⠈⢦⣀⡀⠀⣀⣀⣸⣄⣀⣀⡀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⣀⡤⠤⠴⠁⠀⠀⠀⠀⡿⠻⠴⠚⠁⢻⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠣⠤⠤⠤⠴⠦⠤⣄⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠦⠤⠤⣤⣤⣤⡤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⢀⡴⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠈⠉⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣽⣻⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠼⣀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⣾⣿⣿⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⠈⠐⠠⢄⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢷⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠸⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⣾⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠇⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢳⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢸⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡆⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢹⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⢸⠁⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⡞⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣿⣿⡿⢹⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⡠⢄⠀⠒⠒⠁⢄⣠⠃⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣶⣶⣶⣿⣶⣶⣯⢿⠁⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠒⠒⠀⠉⠉⠉⠉⠑⢆⠈
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⢃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⠄⠀⠐⠂⠐⠂⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠉⠉⠉⠉⠙⠓⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠠⠤⠤⠀⢀⣀⣀⠀⠀⠀⠀⠀⠸⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⣀⣠⡄⠀⠒⠚⠃⠀⠁⠀⢀⠀⠀⠸⣅⣀⣀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠀⠀⠀⠀⠉⠉⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼

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

⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⠤⠄⣀
⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠧⠤⣄⣀⣀⡀⠀⠀⠑⢄⡀
⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠉⠢⣀
⠀⠀⠀⢀⠞⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣶⡆⠀⠀⠀⠑⢄⠀⠀⠀⠀⠑⢄
⠀⠀⡠⠋⠀⢀⠀⠉⠒⠢⠤⣀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠢⡀
⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⢸⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠘⢿⠙⣿⣿⠀⠀⠀⢀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⢰⠺⣿⣿⣧⣶⣿⡿⠂⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠈⠄⠿⠛⠋⠉⠁⠈⠐⠒⠂⠠⠤⠄⠐⠂⠤⠤⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠔⠒⠒⠒⠒⠒⠉
⣶⣶⠶⠶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠸⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⢱⠀⠀⢀⣀
⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣧⣤⣇⡀⠀⠀⠀⠀⠀⠀⢀⣀⣿⡿⣎⠀⣿⠏⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⠤⠤⠶⠖⠚⠛⠛⠉⠉⠉⠀⣃⣀⣠⣤⡴⠶⠞⠛⠋⠉⢱⣿⣿⡆⠃
⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣀⡤⣤⠴⠒⠒⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠘⠀⠘⢧
⠶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠒⠚⠛⠛⠛⠛⠁⣠⡶⠛⠁⠀⣿⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⣤⡀
⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣠⣴⣿⢏⣠⡴⢶⣿⣿⣯⡉⠉⠉⠉⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣸⣿⣷
⡝⠀⠀⠀⠀⠀⠀⣙⠂⠀⢀⣠⣴⣿⣿⣿⡿⠋⠁⠀⣾⣿⣿⣟⣇⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⣿⣿⣇
⠃⠀⣀⣀⣀⡀⠀⠈⣛⣻⣽⣿⣿⣿⡿⠋⠀⠀⠀⠀⠘⢿⣿⠿⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⣿⣿⣿
⣿⡟⠋⠉⠉⠙⣻⣿⣿⣿⣿⣿⣿⣿⣷⣶⠶⠶⠦⠤⠤⢤⣤⡄⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⢀⣿⣿⣿
⣯⡅⠀⠀⠀⠀⠀⠈⣽⣿⣿⣿⣿⣿⣝⡛⠛⠶⠄⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⣾⣿⣿⠃
⣿⡄⠀⠀⠀⠀⠀⠸⠛⠉⠉⠁⠀⠀⠉⠙⠓⠦⠄⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⣿⠃
⣿⣿⢹⣿⣿⢰⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⢀
⣿⣿⢸⣿⣿⢸⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣴⣿
⣿⣟⣸⣿⣏⣸⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⢸⡇⠀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣄⡀⠀⠀⢀⣀⣤⣴⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠻⢿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠉⠻⠿⢿⡿⠿⠟⠛⠉⠀⠀⢀⣠⣴⣶⠀⠀⠀⢠⣾⣿⣿⣶⣬⣿⣿⣿⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠘⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣿⣿⣿⣿⣦⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣷⣤⣤⣼⣿⣿⣿⣿⣿⠀⠀⢀⣾⣧⡀⠀⠀⢿⣿⣿⣿⣿⣿⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠻⠿⢿⠿⠟⠁⠉⣿⣿⡄⠀⣾⣿⣿⣿⣶⣶⣦⣽⣿⣿⡟⠛⠻⠿⠿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣤⣤⣤⠄⠀⢀⣿⣿⣿⣶⣼⣿⣿⣿⢿⣿⡿⠿⠟⠉⠀⠀⠀⠀⢤⡀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠃⢀⣴⣿⣿⣿⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⠀⠀⠀⠹⣿⣿⣉⠹⣿⣿⢟⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⡏⣴⣿⣿⣿⡿⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⣴⠞⠛⠋⠀⠀⠀⠀⢿⣿⡟⠀⣿⣿⢣⢫⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⡀⢀⣀⠀⢀⣿⣿⣿⣿⣿⢿⡄⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢻⠀⠀⢰⢃⠞⡵⠋⠀⠀⠀⠀⠀⠀⣿⠏⢀⣴⣿⡟⣴⣙⣭⣿⢿⣷
⠀⠀⠀⠀⠀⠔⠂⠁⠀⠁⣸⣿⣿⣿⣿⣏⠺⣧⠀⠀⢀⣀⡀⠀⠈⡀⠀⠀⠀⠀⡠⢋⠂⠈⠀⠀⠀⠐⠢⡀⠀⠈⠁⠀⢸⣿⣿⣳⡎⡏⠀⠀⠀⠻⣇
⠀⠀⠀⠀⠀⠁⠀⠀⠙⠲⢿⣿⣗⡭⡭⠿⠏⣿⠀⠀⠤⠌⠙⠲⡞⠉⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⢀⣼⠟⣥⣻⡵⠶⠛⠀⠀⠈⢹⡀
⠀⠀⠀⠀⠀⢧⡀⢘⡟⢳⣶⣤⣀⠻⠥⠭⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⣴⢟⡡⣟⣀⣤⡴⢾⢿⡃⢀⣸⣿⡇
⠀⠀⠀⠀⠀⠈⠉⠉⠀⢸⣿⣿⣮⡷⠶⠟⠛⠛⠒⠶⠦⢤⣤⣀⠀⢻⣤⣴⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣾⣫⡥⢮⣭⣴⣻⢶⢷⡍⢺⡽⠛⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣟⠉⠈⠀⠼⠁⠀⠀⢀⣠⡴⠛⠉⠟⠁⠀⠀⠀⠀⠉⠛⢿⡌⡳⢻⡆⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠓⠒⠒⠶⠾⣿⡏⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣽⢵⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡳⣤⣀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢸⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡀⣽⢳⣦⣬⣉⡙⢻⠋⠉⠙⢿⣦⣀⡀⠀⠀⣸⠀⢸⠀⡾⠏⠀⠀⠀⠘⡀⠀⠀⢀⣠⡾⠛⠉⠁⠀⠈⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣜⢸⣿⠿⠛⠛⠟⠀⣆⠀⠀⠘⢻⣄⣀⣠⣟⣠⠿⠚⠁⠀⠀⠀⠀⠀⢡⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣧⡙⡶⣴⡾⠶⣛⢻⡆⠀⠀⠀⠀⢉⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠫⠄⠓⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣼⣾⣒⢻⣏⡾⢿⡄⠀⢠⠖⢻⡲⠤⠌⠳⠦⢄⣀⠀⡠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣾⣟⡻⢾⢸⡇⢰⠃⠀⣠⡤⠆⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣷⣾⣁⠘⢆⡼⠁⠙⠂⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣇⠀⠀⣰⠁⠐⠀⣠⡆⠀⠀⢠⡦⠄⠠⠤⠆⠒⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⣇⠀⠀⣠⡟⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠁⣄⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣀⢀⣀⡀⢀⡀⢀⣀⡀⣀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⠴⢾⣿⠻⣛⡿⠿⠿⢿⡿⠿⠿⢿⣛⠟⣿⡷⠦⣤⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣯⣭⣭⣙⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣏⣭⣭⣽⣦⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡈⠁⣙⣿⣿⣿⣿⠿⠿⠛⠋⢀⣸⡇⠀⠙⠛⠻⠿⣿⣿⣿⣿⡏⠈⢀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⢸⠄⠀⢺⡗⠀⠠⡗⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⣿⣿⡿⠟⣯⣿⣿⠟⠋⠁⠀⠀⠈⢹⡆⠀⢨⡅⠀⢰⡏⠁⠀⠀⠈⠙⠻⣿⣿⣿⠻⢿⣿⣿⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣕⣼⣷⣿⣰⣾⣿⣿⣿⣇⠀⠀⠀⠀⠀⢹⣧⠀⣽⣯⠀⣸⡏⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⣆⣿⣾⣧⣮⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣤⣀⢀⣹⣦⣀⣁⣴⣟⣀⣀⣤⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⡈⠙⣿⣿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⡋⢁⣿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣽⣧⠸⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⠇⣼⣯⣇
⠀⠀⠀⠀⠀⠀⠀⠘⡟⣿⣿⡇⣻⣧⠿⣿⣿⣿⠿⢿⣿⣿⡿⢟⣿⡟⢁⠘⠃⡈⢻⣯⡻⢿⣿⣿⡿⠿⣿⣿⣿⢻⣼⣟⢸⣿⣿⢻⠃
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠉⣿⣿⢻⣿⣼⣿⣾⣟⣤⡬⠛⣉⣴⣿⢿⣶⣍⣀⣀⣩⣶⡿⣿⣦⣈⠛⢥⣤⣻⣷⣿⣧⣿⡟⣿⣿⠙⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠋⣿⣾⠹⣿⣼⣿⣿⣿⡿⣿⣿⣷⣿⣿⣯⢼⣿⣿⣿⣿⣿⣿⣿⣾⡷⣽⣿⣿⣾⣿⣿⢿⣿⣿⣿⣧⣿⠏⣷⣿⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⢩⣿⡟⣿⡟⢿⡿⢻⣿⢻⣿⡍⢿⣾⣿⡻⣻⣿⣿⣿⣿⣿⣿⣀⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢻⣿⣿⣿⣿⡝⣿⣿⢻⣿⣇⣼⣿⣧⣿⣷⣾⣷⣾⣿⣼⣿⣧⣸⣿⡟⣿⣿⢫⣿⣿⣿⣿⡟⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⣼⡟⣿⣿⣿⣷⡈⠇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣧⠸⢁⣾⣿⣿⣿⢻⣧⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⠃⣿⠈⢿⣿⣿⣸⠉⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠉⣇⣿⣿⡟⠡⣿⠈⣿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⣿⠀⢺⡿⣿⣿⣿⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⢿⡗⠀⣹⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⣿⡄⢼⣿⠸⣿⣿⣿⣿⣥⣿⣏⡿⣏⣿⣿⣸⡿⣹⣿⣬⣿⣿⣿⣿⠇⣿⡧⢠⣿⣰⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣸⣿⡄⢽⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡯⢠⣿⣇⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠙⢿⡷⡟⣿⡝⠊⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠑⢫⣿⢻⢾⡿⠋⣽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠘⢿⣿⣷⣜⣷⣦⣸⣿⣿⣿⣿⣏⣴⣾⣣⣾⣿⡿⠃⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⢿⣿⡿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠘⠃⠙⠋⠸⠃⠸⠋

⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠐⠒⠂⠤⢄⡀
⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠱⠦⠤⡄⣀⣀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣀⣀⠀⡇⠀⠈⠢⡀⠀⠀⠈⠒⢄⡀
⠀⠀⠀⠀⠀⢀⡞⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⡇⠀⠀⠀⠈⠢⠀⠀⠀⠀⠈⢆
⠀⠀⠀⢀⡰⠋⠀⠀⡀⠀⠉⠒⠢⠤⣀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠁⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⢸⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡊⠀⠀⠀⠀⠀⠸⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⣀⣀⡻⠁⠿⣿⡇⢀⣀⠀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⠘⢿⣿⣷⣾⣿⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠣⠞⠋⠁⠈⠀⠀⠉⠉⠐⠒⠒⠒⠂⠑⠒⠂⠤⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⠿⠟⠛⠛⠛⠛⠻⠿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⣾⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⢨⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣠⣶⣿⠟⠋⠉⠉⠙⠻⢿⣶⣄⡀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣠⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣦⣄⣸⣿⠀⠀⣀⣤⣴⣶⣾⡿⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⣿⡇⠀⢾⣶⣴⣾⠆⠀⠀⠰⣷⣦⣶⡷⠀⢸⣿⠛⣿⣿⠀⢸⣿⢻⣿⡃⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣿⡇⠀⠀⠈⠉⠀⣠⣤⣤⣄⠀⠉⠁⠀⠀⢸⣿⣶⡿⠃⠀⠘⠿⣿⣿⣦⣤⣤⣤⣤⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⠀⠀⠀⠀⣾⡿⠋⠙⢿⣷⠀⠀⠀⠀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⢿⣷⣶⣶⣾⡿⠀⠀⢀⣼⡿⠁⠀⠀⢀⡀⠿⣷⣦⣄⣀⣀⣤⣴⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣦⣄⡀⠈⠉⠉⠁⢀⣠⣴⡿⠟⠀⠀⠀⠀⠹⣿⣦⡈⠉⠛⣿⣿⠋⠉⠉⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡿⠿⠿⣿⣿⠿⠿⢿⣏⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⠀⠻⠇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⡿⠁⠀⠀⠀⠀⠀⠀⠈⢿⣷⣤⣄⣀⠀⠀⠀⠀⠠⣿⡇⠀⠀⠀⢠⣶⡄⠀⠙⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⣿⣿⡉⠙⠿⣷⣶⣤⣤⣤⣤⣶⣾⠿⠋⢉⣿⣿⢿⣶⣤⡀⠀⢻⣷⣄⣀⣠⣾⡿⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⣠⣾⠿⠋⠁⠀⠈⠻⢿⣶⣤⣀⡈⢉⣩⣽⣿⣿⣶⣦⣶⣿⠟⠁⠀⠈⠛⢿⣷⣄⠉⠛⠛⠛⠻⢿⣶⣾⠿⠋
⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⣀⣈⣽⣿⣿⠿⠛⠉⠀⠀⠀⠉⠛⣿⡆⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⣼⣿⣁⣠⣤⣤⣶⣶⣾⠿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧
⠀⠀⣼⡿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⣾⡷⠀⠀⠀⠀⠸⣿⡄
⠀⠘⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣷⣤⣤⣤⣤⣴⣿⠃
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠉⠀⠀⠀⠈⠉⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⢀⡄⠀⢀⡄⢀⢴⠀⡠⣦⢀⣤⡀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⣗⡰⠉⣇⠔⠁⠷⠁⠘⠊⠀⠛⠋⠘⢻⠀⢳⡤⠒⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠎⠘⠀⡄⠉⠀⠀⠀⠸⢤⡤⠄⠀⠀⠀⢸⣠⠞⢰⣡⡄⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢠⠴⠁⠀⠀⠀⠀⠀⢀⠔⢀⡀⠀⠀⠘⠃⠀⠋⢰⠁⢸⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠰⣤⣀⣀⠀⠀⠀⣰⣟⡮⠥⠖⠒⠀⠀⠀⠀⠀⢈⣱⣃⣀⡀⠤⢔⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠘⠋⢉⡝⠀⠀⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠶⠦⠥⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⢀⣈⣓⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠒⠶⣇⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡄⠀⠀⠀⠉⠀⠈⠳⣄⠀⠉⠳⣄⠀⠀⠀⠀⠀⢀⡠⠛⠉⠉⠉⠻⣿⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡒⠿⠓⠉⠻⣄⠀⠀⠂⡩⠀⠴⠚⠒⠚⠋⠉⠀⠀⣀⡤⢲⠋⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣉⠂⠀⠀⠀⠙⣟⡶⢤⣠⣒⣀⣀⣀⣀⣤⠴⠒⣉⠜⢐⣧⡀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⢀⠔⠒⣆⡀⠀⠀⢘⣦⠀⢹⡀⠀⠀⠀⠀⠉⠳⠶⣿⣿⠉⠉⠀⠀⠉⠉⠉⣡⠔⠉⠀⠙⢦⠀⠀⠀⣠⡇
⠀⠀⠀⡰⠛⠀⠀⠐⣿⡁⠀⠀⠈⠓⠚⢧⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠤⣄⣀⣀⠞⠁⠀⠀⠀⠀⣠⠷⡄⠔⠁⡇
⠀⠀⠀⠓⠖⢇⣀⠴⠚⠀⠀⢀⡠⠤⣤⣀⠉⠉⠛⠒⠦⢤⣀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣥⠄⠀⢛⡩⠂⠀⠀⠀⠀⠀⠈⡙⠲⢤⣀⡀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣸
⠀⠀⢀⡴⠁⠈⠷⣦⡀⠀⠀⠘⠒⠦⠜⠁⠀⠀⠀⠀⠀⠀⠀⠓⡖⠲⠬⡏⠓⠒⠒⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠸⣀⡄⠀⠉⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠑⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠋⣉⠉⠉⠀⢄⣀⠉⠉⠉⠉⠉⠛⠛⠻⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠘⠦⣀⣙⠲⠬⠟⣉⣷⣦⣤⣤⣀⣀⠀⠀⠙⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⣀⡴⠋⣽⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣉⣳⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢲⡀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠓⠒⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢸⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠈⠳⢤⠌⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⠿⠛⠻⣴⠚⠉⠉⠒⠚⠁⠈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⣀⡀⠀⠀⠀⠀⢏⡀⠀⠀⠈⠙⠉⠉⢉⣠⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⠶⢶⣦⣧⣤⣴⠶⠶⠾⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣶⣤⣀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⡿⠟⠋⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣽⣷⡀⠀⠀⣠⡄⠀⠀⠀⠀⢹⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠉⠉⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⠿⠿⠃⠀⠀⠀⠸⠟⠀⠻⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠠⣶⠀⢰⣶⠀⢶⡆⠀⠀⣀⣤⣀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣤⣤⣤⡄⠀⠀⠀⢠⣄⠀⣠⡄⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣿⡇⠀⠀⠀⠈⠉⠀⠉⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠻⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃
⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢸⣿⣿⡿
⣿⣿⣿⣿⡏⣾⣿⣿⣿⢻⠁⠈⠂⠄⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⢴⠁⠀⠀⠀⣤⣿⣿⣿⣿⠇
⣿⣿⣿⣿⣿⣼⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠣⠀⠀⠀⠈⠉⠉⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⡤⠖⠋⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⣦⠴⠋⠀⠉⠁⠀⠀⠀⠸⠧⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠀⠀⣠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠏⠀⠀⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠀⠀⠀⠈⠀⠧⢤⠀⠀⢀⡤⣄⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠸⡄⠀⠀⠀⠀⠀⠘⢦⠠⡏⣖⡀⣧⠀⠀⠀⠀⠻⡀
⠀⠀⠀⢤⣀⠀⠀⠈⠳⡀⠀⢳⢠⡧⠄⠀⠀⠀⠘⠶⠇⠇⣠⡏⠀⠀⠀⠀⠀⡧
⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⣸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⡄⠀⠀⠀⣰⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣤⡀⢀⣀⡀⠀⠀⠀⠀⢠⠏⠀⢧⠴⣲⠾⢋⣩⠦⢤⡀
⠀⠀⠀⠙⠒⠦⣄⠀⠀⠀⢀⣤⡀⠛⣫⠞⠁⠀⠀⠀⣰⠋⠀⢀⡴⠚⣡⠔⠋⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠙⣧⠛⠳⣌⠙⡆⠀⠀⣠⣧⡴⠚⢁⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡙⢾⣧⡖⠀⢸⡆⠓⠶⠚⠁⢸⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠙⠲⣿⠀⠀⢸⡇⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡞⠉⢳⠀⣸⢹⡄⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡦⠤⠞⠁⢀⣧⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢰⠀⢀⡄⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠃⠀⢰⠀⠀⢰⡏⡾⢠⣿⡱⡻⠃⢀⡄⢀⢀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠘⡆⢰⠀⣟⣣⢆⡞⣸⣧⣯⡿⡾⣡⣾⣿⡟⣡⣾⢟⠁⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⡧⠠⣛⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣏⣻⠟⣱⠋⣠⡿⠁⢀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢳⣌⣂⣿⣾⣿⣿⣿⣿⠿⢿⣿⣏⠙⠛⢻⣿⣿⣿⣿⣿⣾⣥⣯⡷⣱⡾⣡⣾⣢⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠙⣳⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⡆⠀⣾⡋⠈⣻⣿⣿⡿⣿⣿⣮⣿⣾⣿⢟⡵⣫⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⣿⣾⣿⣿⣿⣤⣿⠟⠻⣿⣿⣵⣯⡖⣡⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠁⠸⣿⣿⣧⣀⣼⣿⣿⣿⣿⣿⡿⠀⠀⠀⠙⢿⣿⣿⣿⡿⠋⠀⠀⠘⢿⣿⣿⡾⢟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⢻⣧⡀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠻⣧⣞⠅
⠀⠀⠀⠀⠀⠀⠀⢾⣁⣀⠀⠘⡈⠳⣄⠀⠀⠀⠉⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⢀⣠⣤⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⣹⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⡄⠱⡀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⢿⣿⣷⡄⠀⠀⢀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠑⡄⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⣿⣿⣿⣷⣴⣿⣿⣿⣤⠖⣩⣾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡈⠂⠀⠀⠈⠙⠶⣄⣀⠀⠀⠀⢰⣿⣏⠀⣨⣿⣿⣿⣿⡿⠟⣋⠥⠊⣼⡯⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢡⠻⣄⠀⠀⠀⠀⠀⠀⠉⠛⠲⠶⠬⠿⠿⠿⠿⠿⠛⠋⠉⠔⠊⠁⢀⣼⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⡼⢷⡄⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠝⢦⣀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠂⠀⠀⠀⡀⢴⡿⠫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⡽⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢐⣩⡾⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⡟⢲⣦⣤⣤⣤⣤⢶⠾⠋⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠇⠸⠸⠈⠀⠂

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠉⠹⡉⠩⡅⢩⠉⠛⠉⠉⠋⢹⠋⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣧⣴⣤⣤⣤⣧⣼⣦⣷⣤⣴⣦⣤⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻

⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠤⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢂⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠘⠜⠀⠑⠀⠀⠀⠀⠀⠀⠀⠠⠘⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠈⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠒⠒⠢⡀
⠀⠀⠀⠀⠀⠀⡄⣈⢈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠰⣀⠍⠸⢄⡰⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⢀⠲


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠁⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⢀⠔⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⣩⣤⣴⡆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠟⢛⣩⣴⣶⣿⡇⢻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠹⠿⢛⣩⣤⣶⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⢻⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣽⡿⣫⣾⣴⣶⣶⣦⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⣈⣭⣤⣞⣹⣿⣿⣿⣿⣯⣀⣺⣿⡷⣾⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢛⠛⠛⣻⣏⠻⠟⠛⠛⣿⠛⠛⠃⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢘⡛⠛⠛⠻⠿⠿⠿⠿⠿⠿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠈⠙⠛⠸⠿⠿⢿⣿⣿⣿⣿⣿⣿⣶⡌⠁

⠀⠀⠀⠉⠁⠈⠙⠓⠶⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠒⠀⠒
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉
⣸⣷⣷⣾⣶⣶⡶⠶⠶⠶⣤⣤⣀⠀⠙⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⣀⣀⣤⣤⣤⣤⣤⣦⣴⣴
⠈⢻⣿⣿⠛⠿⠿⢷⣦⣄⡀⠙⢿⣿⣳⣤⣈⠻⢶⣤⣖⡼⠀⠀⠀⢦⣠⣀⣠⡾⠋⣠⣴⣾⡿⠏⠉⣀⣤⣶⣿⠿⣿⣿⣿
⠀⠀⠙⣿⣧⡀⠀⢸⣿⣍⣽⣷⣶⣤⣬⣉⣉⡳⣦⣌⡁⠀⠀⠀⠀⠀⠉⠋⣉⡴⠞⠛⣉⣉⣥⣶⡟⢻⣿⠀⠀⢠⣿⡿⠁
⠀⠀⠀⠀⠙⢷⣄⠀⠻⣿⣿⣿⣿⣿⡿⠋⠉⠙⢛⣿⡿⠋⠀⠀⠀⠘⢶⣿⠿⠖⠛⠻⣿⣿⣿⣿⣿⣿⠏⠀⣴⡟⠉
⠀⠀⠀⠀⠀⠀⠙⠻⢦⣤⣉⡙⠋⠉⠀⣀⣠⠶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀⠀⠉⠛⠿⠛⠋⣁⣴⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢖⠀⠀⠀⠀⠒⠂⠤⠄⡀⢋⠒⢄⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠀⠒⠒⠒⠓⠂⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠑⠊⢁⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠲⡰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠈⢆⠑⡀
⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠗⠀⠀⠀⠈⡆⢁
⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⣀⠖⠉⠁⠢⡀⠀⠀⠀⠀⠈⢢⠀⠀⠀⡇⠸
⢀⠀⡜⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⢋⡠⠊⠁⠸⡔⠁⠀⠀⠀⠀⠈⢂⣠⠀⠀⠀⠀⢡⠀⠀⠁
⡆⢰⠀⠀⢈⡴⠀⠀⠀⠀⠀⠀⠀⡄⢲⡠⠊⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠁⠰⠀⠀⠠⡤⠆⠀⠀⠀⠀⡀⢀⠀⣀⢀
⡇⠸⠀⠀⠈⡄⠀⠀⠀⠀⢀⠻⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠀⠀⠀⢓⠀⠀⢠⠀⠀⠀⠀⠰⠀⠈⠁⠀⠀⡁
⢡⠀⢣⠀⠀⠁⠀⠀⠀⠀⡌⠀⠀⠀⠀⠠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠷⠂⢤⠀⠀⠀⣠⢂⡁⢀⠀⠀⠀⠉⣄
⠀⢢⡀⠁⢠⠀⢀⢤⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⡃⠀⠈⠁⠀⠀⠈⣄⢀⠖⠐⠁
⠀⠀⠁⠀⠘⠀⠁⠀⠠⠀⠁⠀⠀⠀⠀⠀⠁⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⢳⡀⠶⠀⠀⠀⠀⠀⠀⣀⣀⣈⣀⡀
⠀⠀⠀⠀⠀⠲⣦⡀⠀⢶⠀⠀⠀⠤⠠⡄⠀⠀⠀⠀⠀⠀⠀⢠⠶⠄⠀⠈⠲⡄⠀⠀⠀⠀⠓⠤⡎⢰⠞⠒⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠠⠄⠉⠉⢆⠀⠈⢄⣀⠄⠀⠀⠀⠀⠀⠀⠀⣠⠤⠠⠤⠄⠤⣸⠀⠀⠀⠠⠔⠈⠁⠙⢤⡀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⣄⠧⡈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⠐⠠⠔⠁⠀⠀⠀⡃⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠉⠉⠁⠐⠒⠂⠤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠓⢤⡀⠠⠀⠀⠉⠐⠒⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⢄⠀⣀⠀⠀⠀⠀⣀⠀⠀⠤⠐⢲⠋⠀⠀⠀⠈⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⠁⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠈⠡⣀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠉⢣⡄⠄⠗⠀⠀⠀⠸⠀⠀⠰⡦⣄⠀⢀⢀⠀⠀⠉⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠉⠀⢀⠋⠀⠀⠀⠀⠀⠘⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢈⠄⠁⠁⠀⢥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠃⡰⠁⣀⠀⢀⠀⠀⠀⡇⠀⠀⢠⠁⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⢇⠀⡀⠀⢀⠀⡨
⠀⠀⠀⠀⠀⠀⠠⠤⠄⠐⠒⠈⢇⣀⣀⣀⣀⢠⣬⡎⠤⠊⠀⠀⠀⢡⠀⠀⡧⠤⠀⠞⠒⠒⠒⠒⠒⠈⠁⠀⠀⠀⠀⠀⠈⠣⠠⠊⠉
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠘⣀⢀⠠⠒⠁⢇⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠐⠈⠀⠀⠀⠃⠀⢠
⠀⠀⠀⠀⠀⠀⢖⠉⠀⠀⠀⠀⠈⡲⠀⠄⠀⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⡠⠔⢛⠁⠀⠀⠀⣀⣀⠀⠀⢤⡤⠄⠤⠄⠀⣀⣀⡄⠀⢃⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠀⡀⠀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠉⢆⠀⠈⢢⡑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢣⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠘⡄⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡘⠦⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡕⠠⠀⠀⠀⠀⠀⠀⠀⡰⠁⠸⡀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠐⠠⢈⠀⠂⠠⠄⠊⠀⠀⠀⠹⠀⠂⠀⣀⣀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠈⠁⠱⡀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣀⠀⠀⠀⡁⠀⠀⠀⠀⠑⠤⢀⡀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣘⣯⢹⡏⡷⢾⢼⣶⣇⣼⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⣠⡀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣹⡏⣶⡜⡾⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⢞⣁⣤⣟⣺⣺⣤⡈⠓⠦⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠚⠉⠀⠀⡞⠉⠀⠀⠀⢹⠀⠀⠀⠀⠱⡄⠀⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⡇⢰⠀⠀⠀⠘⢄⣀⣀⣦⣀⣇⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠃⠘⠀⠀⠀⠀⠀⠀⠀⠋⠈⠃⠀⠀⠀⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⠛⠦⣿⣿⠀⠀⣠⠀⡀⠀⠀⠀⠀⠀⠀⢠⠯⠭⠭⠽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡝⢀⠰⠒⣿⣿⠒⠦⣄⢫⡅⠀⠀⠀⠀⠀⠀⢸⡤⠤⣍⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠢⣤⡇⣿⣿⢸⣤⠜⣆⠀⠀⠀⠀⠀⠀⠀⢸⠈⠇⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠤⣶⠋⣿⣿⠙⣶⠤⢸⡄⠀⠀⠀⠀⠀⢀⣸⣟⡛⠋⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠉⠇⣿⣿⠸⠍⠃⢸⡇⠀⢀⣠⢠⡴⢯⠀⠀⠳⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣠⡤⠔⠃⠘⠲⢤⣄⣸⠇⠉⠋⠁⠀⢧⡨⣧⡤⠴⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡤⠴⠚⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢲⣀⠴⠋⠈⠋⠁⠀⠀⠀⠀⣧⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠞⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠃⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣠⠞⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠈⠓⢻⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠐⣆⠀⠀⠀⡇⠀⠀⠀⠀⠀⠉⢹⡀⠀⡴⣩⠙⣦⠀⠀⠀⠀⢰⡇
⠀⠀⠀⡀⠀⠀⠀⠈⢧⡀⠀⢹⡄⢠⠆⡀⠀⠀⠀⢹⣸⡇⡟⠂⣼⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠉⠳⢄⡀⠀⠀⠓⠀⠀⡇⠟⠋⠁⠀⠀⠀⠀⠉⠁⠁⢺⢧⡀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠙⠒⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡇⠀⣀⣀⣴⠷⣄
⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠈⠓⢲⣀⡴⢲⠄⠀⠀⠀⠀⡴⠃⠀⠙⢚⡵⠛⣡⠴⠚⠛⠲⣄
⠀⠀⠀⠀⠈⠉⠓⠀⠀⠀⣠⣴⠲⣄⡀⣾⣁⠀⠀⠀⠀⡼⠁⢀⡤⠚⢁⡴⠚⠁⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡅⣸⠋⠀⠙⣄⢸⡄⠀⢀⡜⢷⠞⠁⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⡙⢿⡾⠁⠀⢸⠀⠉⠛⠉⠀⢸⣧⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠙⢻⣧⠀⠀⢸⡄⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡁⠈⠧⢀⡏⢹⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⠴⠋⠀⢸⣵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⣠⠴⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠒⠛⠛⠛⠛⠛⠛⠛⠛⠓⠶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻⠏⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⢀⣴⠛⠀⢀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠐⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠻⡄
⠀⠀⢰⠏⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠅⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⢀⡿⠀⠠⠂⠉⠀⠐⠠⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⡀⠀⠸⠄⠐⠠⠄⠢⠤⠂⠀⠁⠂⠄⢀
⢰⡏⢀⠤⠐⠒⢤⡀⠀⠀⠀⠀⠀⠀⠃⠁⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡀
⢸⡇⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈
⣾⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠁⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⢷⡀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⢤⡀⡀⠤⠤⠀⠀⠀⢀⡾
⠀⠀⠙⢦⣄⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢃⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠈⢿⡁⠈⠁⠀⠀⠀⠀⠀⠀⡐⠀⠈⡀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⡀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠢⠄⠀⣀⣠⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡈⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⢄⠀⠀⠑⠂⠀⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⣤⣑⡀⠀⠄⡀⢠⡔⠀⠀⠀⠀⠀⠁⣀⣠⡤⠖⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣙⣓⣶⣶⣶⣶⣶⣶⣶⣖⣚⣛⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣀⣀⣠⣤⣤⣤⣤⣤⣤⣠⣿⣀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⢸⡇
⠀⠀⠀⠀⠀⢻⣆⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢙⣷⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠙⠻⣿⣿⣿⣿⣿⣿⣦⣀⠀⣸⡆
⠀⠀⠀⠀⢀⣴⣿⡿⠋⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡍⠻⣿⣷⡟⠁
⠀⠀⠀⣠⣿⡿⠋⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣷⠀⠈⠻⣿⣦⡀
⠀⠀⣼⣿⠟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⡀⠀⠀⠙⢿⣷⡄
⠀⣼⣿⠏⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⢿⣿
⣸⣿⡏⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠈⠛
⢿⡿⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣤⡾⠛
⠀⠀⠀⠀⠿⣦⣄⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡟⠁⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣣⣶⠟⠋
⠀⠀⠀⠀⠀⠈⠙⠻⢶⣦⣄⣙⢿⣿⣿⣿⣿⣇⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉