⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣻⣾⠁⠀⠀⠀⢀⣶⣺⢿⣖⣢⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣿⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢖⣾⣽⣾⣾⣿⣿⢾⡀⠀⠀⠀⠘⣿⣻⠻⠿⣶⣬⣽⣲⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⣷⣾⣌⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⢳⣵⣿⣿⣿⣿⣿⣿⣿⣯⣷⠀⠀⠀⠀⠘⣯⣷⣿⣶⢹⡝⢻⣯⣿⣷⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣿⣿⣿⣿⣿⣷⡍⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⣛⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡸⡆⠀⠀⠀⠀⠀⠁⠙⢯⣳⣭⣗⣮⢿⡌⠉⠛⠇⠀⠀⠀⠀⠀⠀⠀⡼⣽⣿⣿⣿⣿⣿⣿⣿⣧⣋⡕⣢⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⣯⣷⣿⣿⣿⢿⣯⣟⡾⣿⣿⣿⣿⣿⡇⣹⡀⠀⠀⠀⠀⠀⠀⠈⠙⣷⡻⢿⠟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣱⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣯⣛⣧⠀⠀⠀⠀ ⠀⠀⠀⣴⢋⣾⣿⣿⣿⣻⣽⣻⢾⣽⣻⣿⣿⣿⣿⣿⣿⢐⠳⡤⣀⠀⠀⠀⠀⠀⠀⢹⡙⢫⠰⢽⡀⠀⠀⠀⠀⠀⠀⠀⣠⣧⣿⣿⣿⣿⣿⣿⣯⢿⣽⣻⢿⣿⣿⣿⣞⣧⠀⠀⠀ ⠀⠀⢰⢧⣿⣿⣿⣟⣷⣻⢾⣽⣻⢾⣽⣿⣿⣿⣿⣿⣿⣿⣷⣮⣖⡹⠦⣄⠀⠀⠀⢸⡇⣍⠚⡤⣷⠀⠀⠀⠀⣀⢴⡺⢏⣥⣿⣿⣿⣿⣿⣿⣞⡿⣾⣽⣻⢾⣽⣿⣿⣎⣧⠀⠀ ⠀⢠⣿⣿⣿⣿⣳⣟⡾⣽⣻⢾⣽⣻⢾⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⣿⣷⣜⡳⢤⣄⢸⡇⢆⡹⠤⣹⡀⣠⠶⢊⣵⣾⣿⣿⣿⣿⡿⣽⣿⣿⡷⣯⣟⡷⣯⣽⣻⢾⣽⣻⣿⣮⢇⠀ ⠀⣾⣾⣿⣟⣾⣳⢯⣿⠷⠿⠛⢾⣽⣻⣿⣿⣿⣳⢯⣟⡾⣽⢿⣿⣿⣿⣿⣿⢶⣬⢟⡱⢪⠶⠷⢞⠻⣧⣬⣿⣿⣿⣿⣿⢿⣯⢿⣽⣿⣿⣽⣳⡯⢿⣷⣯⣟⡿⣾⡽⣿⣿⡞⡄ ⢠⣿⣿⡿⣾⠷⠋⠁⠀⠀⠀⠀⠀⢻⣟⣿⣿⣳⢯⡿⣽⣻⡿⢛⠛⡛⢛⠻⣇⢎⣉⠲⣐⠣⣊⠵⢊⠵⢡⢲⡌⡹⢛⡛⣛⢛⠾⣟⣾⣿⣷⣻⠋⠀⠀⢀⣿⠻⢽⣷⣻⢿⣿⣷⢱ ⠸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣹⡿⠉⠉⡿⣀⠇⣾⣷⣿⣶⣿⣶⡎⢱⡈⠷⣀⠾⡈⠶⣁⠎⣿⣷⣷⣾⣶⡉⢱⣎⢿⣿⡾⠁⠀⠀⠀⢹⣿⣾⡀⠉⢿⣿⣿⣿⢰ ⡜⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠁⢀⣠⠞⡱⢨⣽⣿⠟⠉⢿⡏⡍⢆⠣⣜⡶⠓⠋⠉⠛⠲⣼⡸⡿⠉⠙⢿⣿⢦⣌⡙⡚⠶⣤⡀⠀⠀⢿⣿⠝⣤⠀⠀⢹⣿⣿⠘ ⢻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣉⠦⠱⢡⣿⠛⠁⠀⢀⡟⡰⢩⢌⡷⠋⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⠋⠀⢻⡰⣡⣳⣶⣽⡦⢰⣿⠏⠀⡿⠀⠀⠀⣿⡇⠇ ⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣸⠗⣷⣿⠀⠀⠀⡾⡰⢅⢣⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠸⢿⣇⣿⡿⠉⠁⣽⡿⣆⠀⢱⣷⡄⠀⢸⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠿⠶⣟⣁⣀⣠⠞⣽⠰⣉⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⣨⠟⠃⠀⠸⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⠷⣼⣷⣶⡶⣶⠞⠁⣴⢃⠣⡌⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣾⠹⣌⠑⢤⡀⠀⠀⠀⠀⠀⠀⠉⢻⣦⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⡍⢆⢣⠒⡤⢒⣴⢏⡴⣋⠆⢎⡱⣬⣿⡟⠀⠀⠀⠀⢀⠠⠴⠂⠁⠀⣰⡿⣧⡚⡳⣄⠙⣄⠀⠀⠀⣀⡤⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⡴⠑⠎⠦⣙⢰⣥⡟⢫⠔⣡⢚⣴⣾⢻⣼⠃⠀⠀⠀⠁⠀⠀⠀⠀⣠⣼⢏⡷⣱⢟⣶⣉⠳⣼⣶⣭⣿⢶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣿⣼⣧⣼⠿⠿⣟⢄⣼⣤⢿⠧⣜⡿⠣⢤⣀⣀⢀⣀⣀⣀⣤⠟⠻⣧⣟⡸⣇⢿⡸⣧⢣⣼⢟⣻⠤⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢭⣁⡀⠀⣀⣰⣿⣫⣷⣙⢮⡿⠯⠤⠖⠒⠚⠋⠉⠉⠀⠉⠉⠓⠒⢒⣿⡟⣾⣣⣝⣾⡛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⣿⢴⣯⣿⣽⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣼⣣⡟⣏⣴⣩⢷⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢚⣇⠜⠛⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⣽⣗⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀