⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡜⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠀⠨⢿⡟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⢀⣄⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀⣹⣷⣄⠠⣿⣿⡿⣿⣦⣶⠒⢶⣄⣀⣴⣆⠀⠀⠹⣿⡆⠀⠀⣾⡟⡁⣤⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⣀⡀⠀⠀⣘⣿⣿⠻⣋⣿⣷⣽⣿⣠⣿⣿⠃⠀⣻⣿⣧⡈⢿⣤⡀⠀⣸⣿⣦⣤⣿⣳⡿⠿⠂⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⢻⡧⣮⡿⡧⠀⠘⢻⣷⣿⣿⣿⣿⡝⢿⣭⣽⣾⣿⣶⡿⠋⣿⣿⣟⣾⣿⣧⣴⣿⣿⣿⢿⣼⣿⠇⠀⠀⠀⠀⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀
⠁⢠⢀⣀⠀⠀⠈⢹⣿⣤⣴⣷⣶⣼⣷⣿⣿⣿⣀⣸⡧⣿⢿⣿⢿⣿⣿⣿⣿⠿⣿⠿⣟⣧⢿⣿⣿⣿⣿⣿⣟⢿⣿⣾⣿⢿⠏⢀⣄⣿⣆⠀⠀⠸⣿⣄⠀⠀⠀⠀
⠀⣾⣾⣿⠀⠀⠀⠀⢿⣫⣻⣿⣿⣿⣼⣿⠉⣻⣿⣟⢩⣿⣈⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⡾⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣇⠈⢻⣾⠛⣿⢶⠀⡿⣿⡀⢀⣤
⠀⠉⢿⣿⣾⢿⡀⠀⠀⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⡻⣷⣿⣿⣿⣿⣶⡿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣱⣿⣾⡟⣿⣯⠀⢻⣳⣿⣿⣷⢛⣿⣿⣿⣷⣏
⠀⠀⠀⠙⠻⣿⣷⣶⣿⣾⣿⣿⡜⢧⣩⣿⣿⣻⣻⣯⣶⣾⣯⣿⣿⡿⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡉⡯⡿⣿⣿⣿⣟⡻⣶⣸⣿⣢⠘⣿⣿⣾⣧⣿⣿⡿⢣⣾⡿
⠀⠀⠀⠀⠀⠋⢛⣿⠟⠛⣷⣿⣗⣿⣏⢹⣿⡿⠿⢿⣿⢿⣿⣿⣿⣿⣿⡿⢿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣧⢈⣹⣿⣿⣬⣯⣵⣿⣰⣾
⠀⠀⠀⠈⢿⣶⣾⣇⡰⡉⠉⠛⢿⣏⣟⣿⣷⣿⡟⢿⣿⣰⣽⡿⢷⣿⣽⣾⣿⣿⣿⣿⣿⠟⣿⣿⣾⣿⣿⢿⡿⣯⣟⣽⣽⣺⢿⣽⣿⣻⣿⣿⡿⣽⣿⡿⠁⠀⢰
⠀⠀⠰⣶⠀⢴⣿⢿⣿⢾⣿⣦⡀⠀⣾⣿⣿⣿⣷⡴⣯⣿⣿⢿⣿⣿⣿⣿⣶⣿⣿⣿⢿⣿⣵⣿⣷⣗⣶⣿⢿⣶⡟⢿⣽⣿⣿⣾⣿⣿⣿⣷⣛⣾⣿⣿⣤⣤⣾⣿
⠀⠀⠀⢹⣽⣼⣿⡀⣹⡿⣿⣿⣷⣤⣼⣿⣯⣿⣅⣹⣿⣿⣁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣯⣼⣽⣵⣿⣟⡩⣿⣿⣿⡿⢺⣿⣿⣿⣽⣿⠟⠛⠛⠁
⠀⠀⠿⣿⣟⣻⠿⡷⣿⣿⡀⢙⣿⣏⡻⡿⣿⡿⢿⠿⢿⣿⣯⣭⣿⢿⣿⣿⢿⣼⣿⣿⣽⣯⣾⣥⣻⣿⣿⣿⣿⣿⣿⣿⠳⣿⣾⣿⣿⠟⠋⠉⠀⠀⠀⠀
⠀⠀⠀⠈⠉⠙⠛⠷⣿⠏⢿⣻⣿⣿⣿⣿⡿⣳⣶⣴⣿⣿⣿⡿⠛⣟⣿⣿⣾⣿⣷⣿⣿⣾⣯⣿⡷⣛⣿⣿⣿⣾⣏⣾⠿⠟⣿⣛⡿⠿⣥⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠙⠛⠚⠯⢽⣿⣿⢿⣏⣉⣻⣷⣿⣿⡿⢿⣿⣿⣯⣼⣿⣵⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⠓⢯⠿⠁⣰⣿⣿⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⣿⣭⣿⣿⡿⡝⣿⠿⠟⠛⣿⡗⢻⣿⣬⣿⣋⣹⣿⣿⠛⢿⣿⣿⣷⠿⢏⣭⣴⣶⣾⠟⠛⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢿⡁⣿⠀⢀⡶⢻⣿⡿⢫⣿⣿⣽⣿⣿⣿⣶⣿⠿⢿⣷⣾⣾⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣾⣶⣿⣷⠟⠁⠉⠛⠛⠷⠟⠋⠉⠙⠛⠛⠺⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀