⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢠⡤⡀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣯⠤⢿⣶⣟⣳⣾⣶⠯⠬⣿⣛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣷⡾⠟⣻⢿⠛⣿⡟⢻⡿⡟⢷⣾⣽⣲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⡍⠱⣟⠀⣿⣯⣿⠀⣭⡅⢸⡿⠀⡺⣾⡝⠛⠻⣶⣗⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣄⠀⢀⣾⣿⢿⣽⡄⠨⣙⠂⠙⣦⣌⣩⣽⣤⣿⣧⣼⣧⣘⢻⡿⣧⠘⣷⣿⡙⢿⣮⡢⡀⠀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⡰⢿⣾⣰⣿⣿⠏⠉⠾⣿⡀⢹⣿⣿⣿⣿⠿⠏⠉⠏⠹⠿⠿⣿⣿⣷⣀⣰⣿⠏⢀⣆⣿⣿⣿⣶⢿⡏⢆⠀⠀⠀ ⠀⢰⠊⣠⢟⣾⣿⠟⢽⣧⠐⣠⣤⣽⣿⣿⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣺⣟⢿⣧⣴⣿⠟⢁⣜⢿⣿⣮⠳⣄⠑⡄⠀ ⠀⠈⢉⣷⣿⡿⣽⣆⢀⠙⢧⣽⣿⢿⣿⡶⣶⢶⣶⠶⠳⢶⠷⠳⡶⠞⠶⣶⡶⣿⣷⢟⣿⣆⠰⣦⡿⠋⠹⣷⣝⢾⠋⠁⠀ ⠀⢸⢿⣿⣻⣄⠈⢍⣈⣷⣿⡿⠁⢨⢿⡽⡯⢟⣨⣆⣀⣸⣀⣀⣣⣀⣀⣿⡿⣽⣿⠀⠑⢿⣿⣏⣠⠘⢃⣸⡿⣿⣿⠆⠀ ⠀⠸⣼⣿⣳⣟⣿⣦⣿⣿⠏⠀⠀⢨⣏⣛⣳⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣛⣙⣿⠀⠀⠀⢫⢿⣧⣰⡿⣯⣟⣿⡿⠀⠀ ⠀⠀⠙⢽⣿⢾⣷⡻⠝⠁⠀⠀⠀⠸⡌⠉⠉⠉⠉⠉⣹⡍⢩⣍⠉⠉⡉⡉⠉⠉⢿⠀⠀⠀⠀⠁⠿⣻⣿⣷⣿⠗⠁⠀⠀ ⢀⣴⢮⡛⠛⢿⡦⡀⠀⠀⠀⠀⠀⠸⠄⠀⣀⣼⣶⡀⢻⣽⣯⡟⢹⢘⡇⣿⠀⠀⢾⠀⠀⠀⠀⠀⠀⢀⣼⠯⠙⢻⣴⣄⠀ ⢾⢏⠎⠈⡏⠀⢹⣵⠀⠀⠀⠀⠀⢸⡁⠀⠛⠉⣽⡷⣤⣿⣹⣧⡼⢿⡟⠛⠀⠀⢺⠀⠀⠀⠀⠀⢠⣿⠇⠈⢋⠀⢡⡽⣆ ⣿⣾⠀⠀⡇⠈⣰⡿⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⢸⡇⢹⣿⣽⣻⣟⣻⣿⠀⠀⠀⣹⠀⠀⠀⠀⠀⠘⡾⡄⠑⢺⠀⢀⣾⡇ ⠈⠮⣳⣦⣶⣾⣕⣁⠀⠀⠀⠀⠀⢨⠅⠀⠀⠀⢸⣷⣾⣟⡾⣝⡉⢻⡟⠀⠀⠀⢼⠀⠀⠀⠀⠀⢀⣘⣯⣶⡶⣴⡺⠟⠀ ⠀⠀⠀⢀⣿⣿⣿⢷⣯⣆⠀⠀⠀⢨⠆⠀⠀⠀⠘⠿⣷⣻⠽⣿⣷⢸⡇⠀⠀⠀⢺⠀⠀⠀⢀⣼⣿⣾⣷⣯⣧⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣟⡾⣯⢿⣽⣮⡢⡀⠘⠣⣄⡀⠀⠀⠀⣿⡽⡧⠙⢾⣰⡇⠀⢀⡤⠟⠀⣠⣴⣿⣟⣷⣻⢾⣽⡿⡇⠀⠀⠀ ⠀⠀⠀⠘⣿⣯⢿⣽⣻⢾⣽⣻⣮⣕⢤⡈⠙⠦⣄⡀⠹⣿⣆⠀⠀⢈⡥⠞⠋⣀⣴⣮⣾⣟⣷⣻⢾⣽⣻⣾⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⡿⣿⣾⣹⢿⡾⡏⠈⣿⣿⣿⣷⣆⣀⣿⣾⡿⠏⣀⣾⣉⢰⣶⣿⢿⡿⠏⡁⠹⣾⣏⡿⣾⣹⠿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢪⡻⣽⣯⡟⢀⣾⡟⢀⣿⠙⢿⣿⠷⣿⣿⣿⣿⡶⠿⣿⠛⣉⣿⣆⠘⣿⡇⢸⣯⣿⢟⠝⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠫⣻⢿⣬⣋⣠⣾⡏⢰⡌⠏⢰⣿⠀⣿⣶⡀⢾⣻⣇⠈⣼⣿⣦⣨⣵⡿⡛⠖⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠽⣻⣽⣶⣿⡷⣄⣾⣟⢀⣿⢯⣇⣸⣟⣾⣴⣶⢿⣻⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⣾⠭⢿⣛⣺⣟⣟⣛⣿⣻⡯⠭⣶⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠊⠋⠉⠣⠘⠟⠉⠙⠁⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀