⠸⣿⣧⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⢛⡿⠟⠓⠒⠶⠶⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣸⣿⠏⠀⠀⠀⠀
⠀⠀⠀⠀⠹⣿⣧⠀⠀⢀⣀⡤⠴⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠲⠦⢤⣄⣀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢹⣿⡶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢰⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⢶⣿⡟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⡤⠤⠤⠤⠶⠶⠶⠿⠶⠶⠶⠮⠭⠥⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⢿⣷⠀⠀⢀⣠⣴⠶⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠲⠶⠤⣤⣀⡀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⣼⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣷⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠀⠀⠀
⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣾⣿⡿⠿⠻⠛⢛⣛⣋⣉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣛⣛⠛⠻⠿⠿⠿⣿⣿⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠻⣿⣦⠀⠀⠀
⢀⣾⡿⠋⠀⠀⣀⣠⣤⣶⣾⣿⣿⠿⣟⣛⣯⣭⣵⣶⡶⠿⢿⣿⣿⣿⠟⠛⠋⠉⠉⠉⠉⠉⠉⣹⡟⠛⣻⣿⠟⠻⣿⢷⣶⣶⣦⣭⣽⣛⡿⢿⣿⣿⣶⣦⣄⡀⠀⠀⠘⢿⣷⡀⠀
⣿⠟⣀⣤⣶⣿⣿⠿⣟⣿⣽⣷⡾⢿⡟⠛⠉⠉⠀⣠⣴⣶⣿⣿⣽⣏⠀⠀⠀⠀⣀⣀⣠⣴⡾⣛⣴⡿⣋⣥⣤⣴⣿⣄⣀⣤⠟⢙⣿⡿⠻⢿⣷⣾⣭⣛⠻⢿⣷⣦⣄⡀⠻⣿⣆
⣿⣾⣿⣟⣿⣽⡾⠿⠛⠋⠉⠀⢠⡟⠀⠀⣀⣴⣿⣿⣿⠟⢛⣿⠿⣿⣷⣤⣶⣿⢿⣟⣯⣷⡿⠛⠉⠸⠿⠿⢛⣿⠟⠛⠋⢁⣤⣿⠟⠀⠀⠈⣿⡌⠉⠛⠻⢷⣮⣽⣻⣿⣶⣜⣿
⡟⢹⣿⣿⠋⠁⠀⠀⠀⠀⠀⢠⡿⠀⣠⡾⢟⣵⡿⠛⠁⠀⣾⣧⣾⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣶⣿⡿⠿⠛⠁⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠈⢩⡻⣿⣏⣿⣿
⣷⣸⣿⣿⣧⠠⣄⠀⠀⠀⠀⣾⢣⣾⣯⣾⠿⠋⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⢀⣾⢰⣿⣿⣿⣿
⠙⠿⣿⣿⣿⣷⡙⢷⣤⣀⢠⣿⣽⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⣠⣿⣱⣿⣿⣿⠋⠁
⢀⣾⡿⠟⠻⢿⣿⡀⣸⠏⢻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣴⡟⣽⣿⡿⠛⠻⣿⣆
⣼⣏⣤⣄⡀⠈⣿⣿⡏⠀⣾⡇⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⣿⡆⣿⢿⢿⡏⠀⣠⡴⣌⣿
⣿⣿⠁⠈⢳⣄⣿⣿⠀⠀⣿⡷⣦⣤⣀⣠⣾⣿⣿⣿⡿⠿⠿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣀⣤⣴⣿⡇⢿⣸⣸⣇⣰⠋⠀⢸⣿
⢻⣯⠀⠀⠀⢻⣿⠃⠀⠀⣿⡇⠹⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠈⠻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠁⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⡿⠃⣿⡇⢸⣿⡟⣿⡇⠀⠀⢀⣿
⠘⣿⣆⠀⠀⣼⡿⠀⠀⠀⢿⡇⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠁⠀⣿⡇⠈⣿⣧⣿⡇⠀⠀⣾⡟
⠀⠘⢿⣦⡀⣿⡇⢰⡀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡃⠀⢹⣽⢸⣧⢀⣾⠟⠀
⠀⠀⠈⠛⢿⣿⠃⠸⡇⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⠀⠸⣿⣟⣿⡿⠋⠀⠀
⠀⠀⠀⠀⣿⣿⠀⠀⢷⡀⠰⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⢿⣷⣿⣇⠀⠀⠀
⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⢀⣴⣾⢿⣦⠀⣼⡟⣀⣤⣤⡀⠸⣿⢹⣿⠀⠀⠀
⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⢹⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠀⠀⠀⠀⢀⣿⠏⠀⠈⣿⣿⡿⣾⡿⠋⠹⣿⡆⢿⣿⣿⠀⠀⠀
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⡎⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢶⣶⣦⣶⣶⠾⠿⠛⠉⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡟⣸⡿⠀⠀⢀⣿⡇⢸⣿⣿⠀⠀⠀
⠀⠀⠀⢸⣿⡶⠀⠀⠀⠀⣀⠈⣯⢿⢸⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⢸⣷⣿⠃⠀⠀⣸⣿⠃⠀⣿⣿⡇⠀⠀
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢹⡄⣿⢸⡆⣿⣿⡏⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣆⠀⠀⠀⢿⡟⣀⣀⣠⣿⡇⠀⡅⣿⣿⠁⠀⠀
⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠸⣷⠛⠀⣧⣿⣿⣧⡈⢿⣭⡛⠿⢷⣶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⣶⠿⠟⠛⣩⣾⣿⡶⢶⣦⣴⣿⠋⠉⠉⠻⣷⣄⢣⣿⡟⠀⠀⠀
⠀⠀⠀⠀⠙⣿⣇⠀⠀⠀⠀⣿⠀⠀⣿⣿⣷⡿⠿⠦⢉⠛⠿⢶⣤⣽⣿⣄⣙⣋⣉⣉⣉⠉⢉⣭⣤⣀⣸⣿⣁⣀⡀⠀⣼⣿⠋⠁⠀⠀⠈⠻⣿⡓⣤⣤⠶⢿⣿⣾⡟⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠙⣿⣆⠀⠀⠀⢻⡆⠀⡟⣿⠿⣧⣀⠙⢿⡿⠿⠛⠛⠋⠉⠉⢯⡉⠉⢹⣿⠀⢸⡟⠉⢩⡟⠛⠛⠻⠿⢿⣿⣿⠀⠀⠀⣀⡤⠞⢻⡟⢻⡀⠀⠀⢻⡟⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⣾⡿⢿⣷⡄⠀⠀⢻⣶⢰⣿⠀⠉⠛⠿⢿⣷⡀⠀⠀⠀⠀⠀⠈⣧⠀⠀⣿⠀⣿⡇⠀⡞⠀⠀⠀⠀⠀⢠⣿⣿⣧⡈⠧⣇⡀⠀⣸⣇⡀⢳⣠⣤⣿⡇⠀⠀⠀⠀⠀
⠀⠀⠀⣰⣿⠏⠀⠀⠙⠻⣷⣤⣀⢻⣼⡟⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠘⡆⠀⣿⠀⣿⠀⠸⠁⠀⠀⠀⠀⠀⣾⡿⣿⣟⣿⣶⣬⣽⣿⣍⣭⣿⣯⣿⣿⣿⠃⠀⠀⠀⠀⠀

⠸⣿⣧⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⢛⡿⠟⠓⠒⠶⠶⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣸⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣿⣧⠀⠀⢀⣀⡤⠴⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠲⠦⢤⣄⣀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣿⡶⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢰⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⢶⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⡤⠤⠤⠤⠶⠶⠶⠿⠶⠶⠶⠮⠭⠥⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣷⠀⠀⢀⣠⣴⠶⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠲⠶⠤⣤⣀⡀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⣼⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀⠀⠀⠀⠀ ⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣾⣿⡿⠿⠻⠛⢛⣛⣋⣉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣛⣛⠛⠻⠿⠿⠿⣿⣿⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠻⣿⣦⠀⠀⠀ ⢀⣾⡿⠋⠀⠀⣀⣠⣤⣶⣾⣿⣿⠿⣟⣛⣯⣭⣵⣶⡶⠿⢿⣿⣿⣿⠟⠛⠋⠉⠉⠉⠉⠉⠉⣹⡟⠛⣻⣿⠟⠻⣿⢷⣶⣶⣦⣭⣽⣛⡿⢿⣿⣿⣶⣦⣄⡀⠀⠀⠘⢿⣷⡀⠀ ⣿⠟⣀⣤⣶⣿⣿⠿⣟⣿⣽⣷⡾⢿⡟⠛⠉⠉⠀⣠⣴⣶⣿⣿⣽⣏⠀⠀⠀⠀⣀⣀⣠⣴⡾⣛⣴⡿⣋⣥⣤⣴⣿⣄⣀⣤⠟⢙⣿⡿⠻⢿⣷⣾⣭⣛⠻⢿⣷⣦⣄⡀⠻⣿⣆ ⣿⣾⣿⣟⣿⣽⡾⠿⠛⠋⠉⠀⢠⡟⠀⠀⣀⣴⣿⣿⣿⠟⢛⣿⠿⣿⣷⣤⣶⣿⢿⣟⣯⣷⡿⠛⠉⠸⠿⠿⢛⣿⠟⠛⠋⢁⣤⣿⠟⠀⠀⠈⣿⡌⠉⠛⠻⢷⣮⣽⣻⣿⣶⣜⣿ ⡟⢹⣿⣿⠋⠁⠀⠀⠀⠀⠀⢠⡿⠀⣠⡾⢟⣵⡿⠛⠁⠀⣾⣧⣾⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⢸⣿⣶⣿⡿⠿⠛⠁⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠈⢩⡻⣿⣏⣿⣿ ⣷⣸⣿⣿⣧⠠⣄⠀⠀⠀⠀⣾⢣⣾⣯⣾⠿⠋⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⢀⣾⢰⣿⣿⣿⣿ ⠙⠿⣿⣿⣿⣷⡙⢷⣤⣀⢠⣿⣽⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⣠⣿⣱⣿⣿⣿⠋⠁ ⢀⣾⡿⠟⠻⢿⣿⡀⣸⠏⢻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣴⡟⣽⣿⡿⠛⠻⣿⣆ ⣼⣏⣤⣄⡀⠈⣿⣿⡏⠀⣾⡇⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⣿⡆⣿⢿⢿⡏⠀⣠⡴⣌⣿ ⣿⣿⠁⠈⢳⣄⣿⣿⠀⠀⣿⡷⣦⣤⣀⣠⣾⣿⣿⣿⡿⠿⠿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⣀⣤⣴⣿⡇⢿⣸⣸⣇⣰⠋⠀⢸⣿ ⢻⣯⠀⠀⠀⢻⣿⠃⠀⠀⣿⡇⠹⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠈⠻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠁⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⡿⠃⣿⡇⢸⣿⡟⣿⡇⠀⠀⢀⣿ ⠘⣿⣆⠀⠀⣼⡿⠀⠀⠀⢿⡇⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠁⠀⣿⡇⠈⣿⣧⣿⡇⠀⠀⣾⡟ ⠀⠘⢿⣦⡀⣿⡇⢰⡀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡃⠀⢹⣽⢸⣧⢀⣾⠟⠀ ⠀⠀⠈⠛⢿⣿⠃⠸⡇⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⠀⠸⣿⣟⣿⡿⠋⠀⠀ ⠀⠀⠀⠀⣿⣿⠀⠀⢷⡀⠰⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⢿⣷⣿⣇⠀⠀⠀ ⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⢀⣴⣾⢿⣦⠀⣼⡟⣀⣤⣤⡀⠸⣿⢹⣿⠀⠀⠀ ⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⢹⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠀⠀⠀⠀⢀⣿⠏⠀⠈⣿⣿⡿⣾⡿⠋⠹⣿⡆⢿⣿⣿⠀⠀⠀ ⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⡎⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢶⣶⣦⣶⣶⠾⠿⠛⠉⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡟⣸⡿⠀⠀⢀⣿⡇⢸⣿⣿⠀⠀⠀ ⠀⠀⠀⢸⣿⡶⠀⠀⠀⠀⣀⠈⣯⢿⢸⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⢸⣷⣿⠃⠀⠀⣸⣿⠃⠀⣿⣿⡇⠀⠀ ⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢹⡄⣿⢸⡆⣿⣿⡏⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣆⠀⠀⠀⢿⡟⣀⣀⣠⣿⡇⠀⡅⣿⣿⠁⠀⠀ ⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠸⣷⠛⠀⣧⣿⣿⣧⡈⢿⣭⡛⠿⢷⣶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⣶⠿⠟⠛⣩⣾⣿⡶⢶⣦⣴⣿⠋⠉⠉⠻⣷⣄⢣⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠙⣿⣇⠀⠀⠀⠀⣿⠀⠀⣿⣿⣷⡿⠿⠦⢉⠛⠿⢶⣤⣽⣿⣄⣙⣋⣉⣉⣉⠉⢉⣭⣤⣀⣸⣿⣁⣀⡀⠀⣼⣿⠋⠁⠀⠀⠈⠻⣿⡓⣤⣤⠶⢿⣿⣾⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⣿⣆⠀⠀⠀⢻⡆⠀⡟⣿⠿⣧⣀⠙⢿⡿⠿⠛⠛⠋⠉⠉⢯⡉⠉⢹⣿⠀⢸⡟⠉⢩⡟⠛⠛⠻⠿⢿⣿⣿⠀⠀⠀⣀⡤⠞⢻⡟⢻⡀⠀⠀⢻⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⡿⢿⣷⡄⠀⠀⢻⣶⢰⣿⠀⠉⠛⠿⢿⣷⡀⠀⠀⠀⠀⠀⠈⣧⠀⠀⣿⠀⣿⡇⠀⡞⠀⠀⠀⠀⠀⢠⣿⣿⣧⡈⠧⣇⡀⠀⣸⣇⡀⢳⣠⣤⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⠏⠀⠀⠙⠻⣷⣤⣀⢻⣼⡟⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠘⡆⠀⣿⠀⣿⠀⠸⠁⠀⠀⠀⠀⠀⣾⡿⣿⣟⣿⣶⣬⣽⣿⣍⣭⣿⣯⣿⣿⣿⠃⠀⠀⠀⠀⠀