Emo Heart Wings Emojis & Text

⣿⣿⣿⣿⣿⣿⣿⣿⡟⢣⡜⣻⣿⣿⡿⢿⣿⣿⣿⣿⡿⢻⣼⡟⠂⡈⣘⣿⣿⡿⠛⠁⣀⠀⠀⠀⠐⣿⠀⠐⠀⠈⠉⠤⠿⣿⡟⠠⠘⣻⣿⣿⣿⣿⡽⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⠿⠿⠀⡜⠻⠿⠿⠿⠀⠈⠻⠷⠆⠀⠿⠾⠟⣠⣤⡿⡿⢷⣉⠀⠁⣿⠀⠀⠀⠀⠀⠀⡄⠙⠻⠉⠀⠀⢿⣿⣿⢿⡣⡟⣿⣿⣻⣿⣽⣯⣝⣿⣿ ⣿⣿⣿⣿⣿⣿⣶⣿⡟⠛⢻⣿⠀⢄⠀⠈⢢⠀⢀⠠⠀⠀⠋⢠⡆⠠⠀⠀⢀⠙⡟⠅⠃⠈⢻⡀⠀⢻⣤⣦⣀⣅⢆⣞⠂⠀⠂⠀⢉⣤⡘⠛⡋⠌⠕⠳⣿⣿⣿⣿⣿⢿⣿⣿⠿ ⣍⢿⣧⣼⣿⣿⣿⣿⠰⠿⢃⣿⣤⡄⠢⡀⠈⠂⢀⠑⢆⢀⠀⠈⠁⠀⠀⢻⣌⡰⠠⢀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣀⡠⠈⠙⣫⠐⠈⠀⠚⢿⣿⣿⣿⣿⣿⢠⣾⡟⣡⣾ ⣿⣶⣜⠻⢿⣿⣿⣿⣶⣦⣾⣿⣿⠿⠠⡘⠢⡀⠑⠑⣄⠹⢆⣢⠨⢦⣠⣼⣿⣄⠈⣴⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠜⢹⣿⠀⠀⣶⣿⣮⣀⢺⠿⠿⠿⢙⡥⣞⣽⡿ ⡙⢿⣮⣗⢮⣙⠿⢿⣿⣿⣿⡟⠀⠀⠒⠈⠀⡈⠢⡀⠈⢿⣷⣽⣷⣟⠸⢿⣿⣿⣷⣿⣿⡿⠟⠋⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣥⡀⠀⣿⡇⠀⢩⣿⣿⡿⢞⣢⠴⣚⣵⣾⣿⡇⣶ ⣧⣇⣿⣿⣧⣼⣧⣄⡸⢿⠿⢿⣤⠿⠀⣿⣧⠘⢄⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⡟⢸⢿⠃⢀⣀⣻⣿⣟⣿⣿⡿⢿⣻⣿⠟⣸⣿ ⣿⣿⡜⢿⣿⣟⡻⠷⢯⣽⣶⣦⣭⣀⡟⠺⠏⢠⣖⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⢻⣿⣿⣿⣿⣴⣿⣿⣿⣟⣛⣫⣿⣵⣶⣾⣿⡟⣡⣸⣽⣿ ⣿⣿⣿⣧⡌⢿⣿⣿⣶⣾⣿⣭⣝⣻⣿⣿⣷⣶⣿⣿⣭⣿⣿⣿⠿⠿⠿⣿⣿⣿⡿⠁⠀⢀⣀⣀⣠⣾⣿⠁⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣽⣿⣿⠟⢋⣸⣿⣿⣿⣿ ⣿⣿⣷⣼⣿⣶⣙⣻⣿⣶⣿⣿⣭⣿⣽⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠹⣿⡇⠀⠀⠈⠉⣹⣿⠛⠛⠻⠶⠦⠀⠀⢸⣿⣿⣿⣿⣿⣭⣭⣭⣭⣭⣽⡿⣋⣿⠛⢀⣸⣿⣿⣿ ⣿⣿⣿⣿⣿⠿⠟⠢⣙⠿⣿⣿⣭⣭⣭⣾⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠠⠿⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣷⣶⣮⣭⣽⡿⠣⠼⢿⠿⣿⡿⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣥⣤⣿⣿⡧⡹⢿⣯⣽⣷⣷⣿⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣶⣿⣿⠁⠳⡄⠀⣤⣤⣿⣷⣽⡟⠋⠉ ⣿⣿⣿⣿⣿⡏⣿⠛⠛⢏⣀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⢿⡉⠹⠁⣈⠛⡀⠀⠰⠀⡸⠛⣿⣿⣿⡇⣠⣿ ⣿⣿⣿⣿⣿⣿⣿⣾⡇⠘⠟⠀⣀⣖⠐⣿⡿⠟⣿⣿⣿⣿⣿⣷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠛⠿⣿⣿⠀⠑⢄⠘⠧⢀⠉⣶⣇⠀⡀⠶⡋⢹⡿⠿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⣴⣶⣿⣿⡔⠀⠀⠀⢈⢏⣿⢿⢿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⢿⠀⠀⣿⣿⠴⠀⡈⢣⣀⠨⣤⣾⣷⣾⠀⣒⣶⣾⢿⣤⣿⣿ ⣿⣿⣿⣿⣧⣿⣿⣿⠈⠀⣸⣿⣿⣿⡾⠲⠄⠀⡈⠘⢯⡿⢃⢹⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢀⣴⣿⣿⣿⡿⡟⠁⢸⠐⠀⣿⣿⡁⢸⣿⠄⠳⡄⠀⣻⣿⣧⡁⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣏⣻⠏⢀⢻⢿⣿⣿⣷⣶⣿⣁⠨⠀⠿⠃⢠⠡⢷⣸⢿⣿⣿⣿⣿⣿⣿⣿⡄⠀⣠⣿⣿⡿⣿⣿⣿⡇⠀⠘⠀⠀⣙⠿⠁⠀⠀⡄⠀⢈⠫⡀⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠄⠉⣘⣸⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢸⢸⠘⣿⣷⣯⣿⣿⢸⢿⣿⣰⣿⣿⡟⡲⡟⠀⢹⡇⠁⠠⢀⠀⣽⡤⠀⠀⣸⣡⣀⣨⣧⠁⠸⠏⠉⣿⣿⣿⣿⣿⣿⣿ ⣿⣯⣽⣿⣯⡄⠀⣽⣿⣿⣿⣿⣿⣿⢻⣿⣷⡆⠈⢡⠀⢸⠀⢠⡗⣽⡏⣿⣿⢸⢸⣿⡇⢹⣿⡇⠀⡗⢠⣾⣷⠀⠀⠀⣿⣿⣿⠀⣼⣿⣿⣿⣿⣿⣿⡟⠀⡜⠛⣿⡟⢸⣿⣿⣿ ⣿⣿⠿⠿⠻⣿⣾⣿⣿⣿⣿⣿⣿⣥⠘⣍⠉⠳⡿⠳⣠⠒⠀⠃⣇⢣⢘⣹⣿⣼⡜⠿⢁⡙⣿⡇⠀⣥⠀⠺⠟⠀⢐⠀⣿⣴⡿⠶⠻⣯⣻⣯⣉⣿⣏⣁⣀⣁⣀⣿⣿⣿⣿⣿⣿ ⣿⡇⠀⠤⠄⣽⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢸⡓⢜⡻⠈⠀⢸⡏⠈⡿⠹⠿⠾⡇⠀⢘⠀⣿⡇⠁⢏⠀⠀⠃⢠⣧⣤⣿⣿⣧⡌⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣧⣤⣦⣤⣿⣿⣿⣿⣿⣿⣿⠉⢿⣧⣈⣠⣼⠟⡶⡦⠀⠃⠀⡇⠀⡥⠀⣤⠆⠴⠀⢀⠢⣿⡇⠀⣏⠀⠀⠀⣘⣻⡈⣿⣿⣿⡿⠛⣿⡿⣔⣿⣿⣿⣿⣿⣿⣿⣴⣛⣻⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢈⠉⢹⣿⣧⡶⠷⡄⠊⢀⡀⠃⡎⣴⡆⢺⢰⣶⡶⣧⠀⣿⡇⠀⡿⠰⣤⣾⣿⣿⣷⣿⣿⣿⣿⣶⣿⣷⣉⡉⢍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⣴⣾⠛⠃⠀⢢⣿⣶⣾⣿⠀⡇⠻⠀⡄⢸⣿⣿⣿⠀⣿⡇⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⣿⣿⣿⣿⣟⡈⡀⣐⡇⠁⣸⣿⣟⣿⠀⠙⠁⠀⡄⠀⣿⢿⡿⣿⢿⣿⣿⣿⣧⡼⣿⢿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣷⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣼⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠟⣛⠼⠓⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠞⠧⣜⠻⣅⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⡷⠋⢀⣤⢄⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⡠⣤⡄⠑⢾⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⠟⠀⡄⡻⠇⠀⢡⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡀⠀⠺⢿⢢⡀⠻⡻⡄⠀⠀⠀⠀ ⠀⠀⠀⣠⢋⠎⠀⡼⠀⡇⠀⠂⡀⠁⡀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢀⠌⢀⠑⠦⢸⠀⣧⠀⠱⡜⢆⠀⠀⠀ ⠀⠀⡰⠁⡞⠀⣼⡃⠀⣧⡄⠚⢷⡄⠈⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠗⠁⢰⣾⠟⢀⣼⡀⢸⣷⠀⢱⠈⢧⠀⠀ ⠀⡸⠁⣸⠁⢠⠇⡅⢰⣿⢡⡇⠀⠻⣿⣦⡰⢌⡑⠢⢤⣤⡀⠀⠀⠀⠀⢀⣤⣤⠴⢊⡡⢆⢴⣿⠟⠀⢸⡄⣿⡇⢸⠘⡄⠀⢧⠈⢧⠀ ⢀⣇⠴⡇⠀⢸⠀⡇⢸⢿⣏⣧⡇⠀⠙⠛⠿⢦⣬⡓⢄⣉⠛⣄⠀⠀⣠⠞⢋⡠⢒⣉⣴⡿⠛⠃⠀⢸⣾⣿⡿⡇⢰⠀⢇⠀⠸⠧⣘⡆ ⠘⠁⢸⠀⠀⡇⢴⠁⠈⡆⢻⣿⣦⡀⣷⣰⡤⠈⠛⢻⣴⣿⡿⠛⠃⠘⠛⢿⣷⣶⡿⠛⡁⢴⣶⣿⢀⣾⣿⡟⢀⠃⢸⣄⢸⠀⠀⠇⠈⠃ ⠀⠀⡄⠀⢸⠁⢸⡇⠀⡇⠀⢻⠻⠿⠿⣿⣡⣿⣶⣶⢈⡌⡅⣶⣆⢰⣶⢨⠰⡉⣷⣦⣻⣾⣿⠿⠿⠟⡻⠀⢸⠀⢸⡇⠀⡇⠀⢸⠀⠀ ⠀⠀⡇⢀⠇⠀⠈⣇⠀⢹⠀⠀⣆⠀⡄⠀⣨⠿⠿⢿⣿⣷⣆⣽⠃⠘⣿⣴⣴⣿⡿⠿⠿⢇⠀⢠⢄⣰⠃⠀⡎⠀⣸⠁⠀⠸⡀⢸⠀⠀ ⠀⠀⣇⣼⠀⠀⠀⣿⠀⠈⡄⠀⠸⡄⠃⠰⠁⠀⣴⡾⠘⣿⠛⠟⠀⠀⠻⠿⣿⡇⢷⣤⣄⠈⢇⢸⢀⠇⠀⢀⠃⠀⣿⠀⠀⠀⣧⣸⡇⠀ ⠀⠀⡿⢹⠀⠀⠀⡿⡇⠀⢡⠀⠀⢹⣗⣿⢠⣿⣿⡇⠀⡇⠀⠀⠀⠀⠀⠀⢸⠁⢸⣿⣼⡄⣺⢾⡟⠀⠀⡜⠀⢰⢿⠀⠀⠀⡟⠻⠇⠀ ⠀⠀⠀⠘⡆⠀⠀⠁⠸⠀⠀⡆⠀⠈⢿⠹⠛⠛⠿⣷⣀⡇⠀⠀⠀⠀⠀⠀⢸⡄⣼⠿⠏⠛⠟⡿⠁⠀⢰⠁⠀⡎⢸⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⢧⠀⠸⡀⠀⠈⢇⠀⠀⠀⠙⣿⡁⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⣰⠃⠀⢀⠏⠀⡸⠀⢸⠀⠀⢸⠁⠀⠀⠀ ⠀⠀⠀⠀⣧⠀⠀⠆⠀⠘⡆⠀⢣⠀⠀⠘⡆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠⠇⠀⠀⡼⠀⢰⠃⠀⢸⠀⠀⣸⠀⠀⠀⠀ ⠀⠀⠀⠀⢹⠀⠀⡇⠀⠀⠸⡄⠈⡆⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢠⠃⢀⠏⠀⠀⢸⠀⠀⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣆⢸⣧⠀⠀⠀⠱⡀⠸⡄⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢀⠇⠀⡞⠀⠀⠀⣼⡇⢰⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣾⠈⢧⠀⠀⠀⢡⠀⠹⣄⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢠⡎⠀⡜⠀⠀⠀⡰⠁⣧⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠀⠈⢣⡀⠀⠀⢇⠀⢻⣦⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⡰⡿⠀⠰⠁⠀⢀⡜⠁⠀⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠸⡄⠈⡆⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢡⠁⢀⠇⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢣⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⡜⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠘⡟⠲⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠗⢺⠃⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀

⠀⠀⠀⠀⠀⢰⣆⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣟⣧⡀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⡟⣝⢾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⡶⣤⣀⡀⠀⠀⠘⢎⠣⣝⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢯⣿⠯⣒⠦⢄⣈⠳⣌⠓⢭⡻⢿⣦⣤⣀⣀⣀⢀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣶⣿⡷⣮⣕⡒⠤⣉⡙⠛⠲⢌⣑⠪⠭⢙⣛⠛⠛⢿⡛⠛⠯⣍⣛⣛⣛⠲⠦⣤⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠛⢿⣒⠬⢍⡓⠲⠭⣕⣒⠀⠬⢍⡓⢲⡬⠒⠒⠚⢻⠦⣄⡘⠷⠀⠀⠉⠂⠀⠉⠛⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠿⣟⡿⣿⡶⠬⣍⣒⡒⠬⠭⠝⣚⣛⠒⠳⢦⣌⠉⠊⠳⣤⡤⢤⠄⠀⠀⠀⠀⠀⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠒⢭⣍⣒⡈⣭⠭⠿⣓⠒⠒⠒⠒⠚⠢⣌⣉⣉⣙⣶⡂⠀⠀⠀⠀⢰⡋⠉⠉⠲⡄⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⢭⣉⣩⠭⣉⣛⣛⣒⣒⣓⣒⣒⡪⠭⠋⣈⣿⡤⠀⢀⣀⠀⠀⣘⣏⣉⠙⠀⠀⢸⡈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⡛⠳⠶⠶⠶⠶⠒⠒⠒⣒⡊⠍⠱⣇⣒⣉⡅⠀⣠⣿⣁⣨⡉⠉⠀⠀⠀⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠯⠽⣭⣥⣴⣿⣭⠭⠤⠔⠚⣉⡡⠀⣸⢶⣚⠓⠚⣧⣤⠄⠀⢰⠃⠀⠙⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠭⣽⣥⣤⣀⣒⣶⣩⣭⣤⢖⡯⠒⣩⠵⢚⡉⢹⣤⠤⠀⠚⡶⠂⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠒⠒⢹⣏⣤⣴⢛⠵⢊⡵⣺⢍⡿⠚⠁⠀⠳⡴⢠⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢻⣥⡴⡣⠚⡡⢚⠗⣶⣽⠏⠀⠓⡏⡰⠀⢠⠀⠈⠙⠲⠦⣄⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡟⢞⣤⠞⡵⢫⠞⣱⣻⡦⢤⣀⡹⢧⣠⣾⡄⢠⠀⠀⠀⠀⠈⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢋⣿⣮⠟⣿⣜⣵⣿⢋⣾⢏⣧⢸⢹⢹⡽⡟⠢⡾⠶⡇⠜⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠛⠋⠸⠿⢻⣼⣼⣿⣾⣶⣾⣇⡿⡴⣧⣸⣶⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠛⠁⠉⠉⠛⠁⠀⠀⠀⠁⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⠋⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠙⢿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣿⠁⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⣿⣆⠀⠀⠀⠀ ⠀⠀⠀⣰⢻⠘⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠁⡟⣆⠀⠀⠀ ⠀⠀⣼⠇⣸⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⣰⡇⠙⣧⠀⠀ ⠀⢰⡏⠀⢹⡍⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠈⢱⡇⠀⢹⠀⠀ ⠀⠀⣷⡄⢸⣧⡀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⣠⣞⠆⡠⣿⠀⠀ ⠀⡆⢻⡀⠀⢟⣏⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⡽⡿⠀⢀⡏⢢⠀ ⢸⠁⠘⣧⡀⠘⣟⣷⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⢀⡾⡿⠁⣠⢞⠃⠈⡇ ⢸⣆⠀⡿⣄⠀⠘⢞⢷⣄⣀⠀⡌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣿⠀⣀⣴⣿⡝⠁⢀⣰⢋⠀⣼⡇ ⡎⣏⠀⠳⡽⣗⠂⢺⣿⣻⣮⣀⣿⣆⠙⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁⣼⣏⣀⣴⣯⣿⠇⢐⣿⣷⠃⠀⣼⢠ ⡀⠙⢧⠀⠙⢿⣷⣤⣙⣿⡟⡉⠛⢿⡇⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠀⠀⣸⡿⠋⡉⣻⣿⠣⣴⣿⡿⠁⠀⠼⠃⢀ ⣧⡀⢰⣦⡀⠀⣿⣿⣦⡛⣿⣿⡀⠀⠙⢦⡄⠀⠀⠀⠙⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⢠⣾⠋⠀⢠⣧⣿⣫⣴⣿⡯⠀⣠⣶⡀⢀⡞ ⠘⣷⠌⢯⡻⣖⡈⣿⣿⢛⠛⢷⣝⠀⠀⢿⣦⣄⡀⣀⣀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⣀⣄⣀⣤⣾⠟⠀⢀⣿⠟⠋⣙⡿⠋⢀⣿⣿⠟⠐⣻⠃ ⠀⢻⢦⣀⠙⢮⣿⣅⡹⣟⣄⠀⠉⠻⡆⠙⠻⢿⣿⠋⠙⠃⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠘⠁⠙⣿⠯⠛⠉⣲⠛⠁⠀⣴⣻⢃⡴⣿⠟⢁⣠⢶⡏⠀ ⠀⠘⡆⠨⣅⡀⠩⣿⣽⣿⣿⣗⡀⠀⢹⣲⣤⣄⣽⡦⣄⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠤⠶⣧⣤⣔⣿⠅⠀⣀⣯⣿⣿⢽⡯⠁⣀⣴⠄⣸⠁⠀ ⠀⠀⠹⣄⠈⢻⣯⣄⡙⣿⡋⠉⠉⠓⣠⡤⢭⣿⡃⠀⠀⠀⠀⠰⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡆⠀⠀⠀⠀⢈⣿⣵⣶⣒⠉⠉⠈⢹⡟⢩⣤⣿⡏⢁⣴⠏⠀⠀ ⠀⠀⠀⢻⣗⠀⠙⠻⢿⣿⣷⣄⡀⠀⠈⠯⠭⠽⣷⣶⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⣶⣿⣿⣿⠖⢀⣀⣀⣴⣾⣿⠿⠛⠁⢀⣽⠟⠀⠀⠀ ⠀⠀⠀⠀⠉⠻⣶⣆⠀⠈⠙⣿⣿⠿⠗⠀⠿⢿⣿⣇⠀⣠⠀⠀⠈⠛⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠋⠁⠀⠀⣄⣀⣼⣿⣿⠿⠀⠛⠿⣿⣿⠉⠀⢀⣰⠾⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢲⡿⠁⠀⠀⢀⣀⣬⣿⣿⣿⡃⠀⣀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⣄⠀⢸⣿⣿⣷⡦⢀⣀⠀⠀⠈⢿⡀⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⡞⠋⠁⠈⢩⣵⣿⣷⣾⡏⠀⠀⠀⠉⢷⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⢹⣿⣿⣿⡾⠁⠀⠀⠉⢳⡠⠤⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢠⡶⠂⠈⠱⣿⣿⣷⡶⡇⢀⠀⠈⠳⣤⠀⠀⢀⣴⠋⢀⣀⡀⣘⢲⣿⣻⡿⠂⠀⠀⢳⣄⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠋⠀⠀⣰⠃⠈⣘⠛⢰⠇⠈⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠁⠀⠘⡆⠛⣅⠀⠘⣆⠀⠀⣉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⣿⣤⣤⣏⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣽⡤⠴⠟⠓⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇

⠀⠀⠀⠀⠀⡤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⠀⠀⠀⠀⠀ ⠀⠀⢠⠻⣼⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣧⠿⡄⠀⠀ ⠀⣀⢸⠀⢹⠁⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠈⠇⠀⡇⣀⠀ ⠀⣏⠛⡇⠀⡄⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⢰⢀⢸⠛⣹⠀ ⠀⢹⡀⢡⠀⢁⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠈⡈⠀⡌⢀⡏⡀ ⢹⡉⢣⠀⢂⠈⣆⢃⠙⢦⣀⠀⠀⠀⠀⠀⠀⣀⡴⠋⡘⣰⠁⡐⠀⡜⢉⡇ ⠀⠱⣄⠱⡃⠑⢏⠙⠂⠄⠈⠙⡆⠀⠀⢰⠋⠁⠠⠐⠃⡹⠊⢈⠌⣠⠎⠀ ⠈⠯⣍⠑⠄⡑⢟⠓⠤⠀⠂⠂⡇⠀⠀⢸⠐⠐⠀⠤⠚⡻⢊⠠⠊⣩⠽⠁ ⠀⠸⣏⠑⠢⢄⣩⠢⠤⠄⠀⠀⡇⠀⠀⢸⠀⠀⠠⠤⠔⣍⡠⠔⠊⣹⠇⠀ ⠀⠀⠈⢛⣦⡄⠈⠢⢤⡤⠂⢀⣷⠀⠀⣾⡀⠐⢤⡤⠔⠁⢠⣴⡛⠁⠀⠀ ⠀⠀⠀⠈⠛⠲⠤⢤⣴⠏⣉⡴⠃⠀⠀⠘⢦⣉⠹⣦⡤⠤⠖⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠤⠠⠤⠤⠠⠤⠤⠠⠤⠄⠀⠤⠤⠤⠄⠤⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀ ⠀⠀⠀⣰⡏⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢹⣇⠀⠀⠀ ⠀⣠⡀⣿⠑⡘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⡄⣿⣀⣄⠀ ⠀⡟⢳⣿⡀⢣⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡸⢀⣿⡟⢻⠀ ⠀⡧⠀⢻⣧⠈⢆⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢠⠃⣸⡟⢠⢸⠀ ⠀⣷⠘⠀⢻⡆⠘⢆⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣰⠃⢠⡿⠀⠇⣼⠀ ⠀⢹⣇⠀⡈⢻⣆⠈⠳⣜⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢋⠞⠁⣰⡟⢁⠄⣴⡟⠀ ⢻⡶⣿⣆⠈⢢⡙⠳⣦⡈⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⢁⣤⠾⢋⡴⠃⣰⣿⢿⡟ ⠀⢻⡄⠙⢷⣄⠙⠦⣈⠙⢶⣜⣿⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⣿⣃⡶⠋⢁⡴⠋⣠⣾⠟⢁⡞⠀ ⢀⠀⢳⡀⠀⠙⠳⣦⣈⠳⢦⣹⣿⣧⡰⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢇⣼⣿⣏⡤⠞⣁⣴⠞⠋⠀⢀⡞⠀⠀ ⠸⣿⢦⣿⣄⠀⠀⣀⠙⠳⣤⣙⣏⢙⣻⣿⡏⠛⠷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⢹⣿⣿⡋⣹⣏⣠⠞⠋⣁⠄⠀⣠⣾⡵⢻⠇ ⣄⡹⣆⣬⡙⢷⣄⡈⠙⠲⢬⣿⡿⣦⣹⣿⣷⣄⣙⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⣋⣠⣾⣿⣏⣴⢿⣿⡥⠖⠊⢁⣠⡼⠋⣡⣠⢏⣠ ⢻⡟⠻⢿⣟⡀⠉⠛⠶⣦⣤⣽⣷⡈⢭⣻⣿⡈⠭⣻⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⠉⢁⣿⣟⡭⢁⣼⣯⣤⣴⠶⠟⠋⠀⣪⡾⠟⢫⡟ ⠀⢻⣆⡀⠉⠻⠦⣄⡒⠦⣽⣷⡈⢿⣾⣿⣿⡟⠻⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⢻⣿⣿⣿⡿⢁⣾⣫⠤⢒⣠⡴⠟⠉⠀⣠⡟⠀ ⠀⠀⠙⣷⣄⠑⠦⣄⠉⠛⠲⢿⣿⠿⠛⢻⣿⣿⣼⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢧⣾⣿⡟⠛⠷⢿⡿⠖⠛⠉⣀⠴⠊⣀⣾⠋⠀⠀ ⠀⠀⠀⢻⣿⠷⢦⣄⣉⠓⠲⠦⣽⣷⣶⣾⣿⠃⠈⣹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣟⠀⠘⣿⣷⣶⣶⣯⠴⠖⠚⣋⣡⡴⠾⣿⡗⠀⠀⠀ ⠀⠀⠀⠀⣙⣶⣄⠀⠉⠹⣻⣶⣿⣏⣀⠙⢿⣿⡿⠛⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠛⢿⣿⡿⠟⣀⣹⣿⣶⣞⠉⠉⠀⣀⣶⣋⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣟⠛⢶⡦⢤⣶⣾⡿⣿⣿⠛⠿⢿⣿⣿⠋⢻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡏⠙⣿⣿⣿⠿⠛⣿⣿⢿⣗⡲⠦⢴⣶⠞⣫⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣙⣷⠦⠤⠤⠤⠴⣖⣯⣿⣿⣷⣾⠟⣿⣶⣿⡇⣹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⠘⣿⣶⣿⠻⣿⣶⣿⣿⣿⣗⡦⠤⠤⠤⠤⣾⣋⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠳⢤⣄⣀⣀⣀⡥⢞⡿⣿⣿⣧⣬⣿⡟⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢻⣿⣥⣼⣿⣿⢿⣳⢤⣅⣀⣀⣠⡤⠞⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠲⢿⣋⣛⣁⣀⣴⠾⠋⠐⣻⣿⣿⣶⣿⣿⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⣿⣿⣶⢿⡿⣿⡃⠙⠳⣦⣄⣘⣛⣙⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⣁⣄⣤⡾⣫⢏⡴⢛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⢧⡙⣜⢿⣦⣤⣈⣿⡯⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⠶⢿⣿⠷⢿⣥⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢯⣿⢾⣿⣷⡶⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢘⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⡚⠕⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠮⠪⢑⢆⠀⠀⠀⠀ ⠀⠀⠀⣾⠋⢰⠇⢂⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠐⠸⡦⠙⣷⠀⠀⠀ ⠀⢀⢎⠃⡜⠀⢀⣄⠠⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠔⢡⡀⠀⢣⠘⡕⡀⠀ ⢀⠂⡆⠸⡆⣼⣰⠙⢶⣄⢕⠠⣀⡀⠀⠀⢀⣄⠤⡪⣡⡶⢉⣆⣷⢸⠃⠰⠘⡀ ⠸⢺⠀⡆⠇⠟⣿⣇⢨⣙⠳⣮⣲⡭⠆⠠⣫⣐⣽⠞⣋⡅⣼⣾⠻⢸⢰⠀⡗⠅ ⠀⡄⢰⠀⡆⢀⠘⡛⠟⠯⣞⣾⣩⡕⣦⢴⢨⢉⣷⣷⠿⠻⢛⠃⠀⢸⠀⡆⢰⠀ ⠀⡇⡆⠀⣷⠘⡀⢱⠀⡐⠉⣭⢻⡷⠇⠸⢾⡟⣍⡉⢂⠈⡎⠀⠃⣾⠀⢰⣸⠀ ⠀⠋⡇⠀⠉⡄⢁⠀⢧⢧⣿⣇⢸⠀⠀⠀⠀⡇⣸⡿⣼⡿⠀⡘⢀⢹⠀⢸⠙⠀ ⠀⠀⠀⠀⠀⢡⠈⡄⠈⠄⠀⠘⣏⠀⠀⠀⠀⢱⠋⠀⢠⠃⢠⠁⡌⢸⠀⠘⠀⠀ ⠀⠀⢸⠀⡀⠀⢂⠰⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠄⠰⠀⢸⠀⡆⠀⠀ ⠀⠀⠀⠆⢧⠀⠈⠄⢃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡐⠠⠁⠀⡼⢰⠁⠀⠀ ⠀⠀⠀⠘⠀⠣⡀⠘⡀⠧⣰⠀⠀⠀⠀⠀⠀⠀⠀⡄⠼⠁⠂⠀⠜⠐⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠑⡀⢡⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⡈⢀⠎⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡌⡖⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⢲⢣⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣄⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣄⡀⠀⠈⢯⠻⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⣿⣕⡠⠀⠱⢄⡋⠟⣶⠦⢤⣤⣤⣤⠤⢤⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢙⣯⣋⠕⣊⠤⢂⣉⣔⢞⠒⣘⣢⠬⠢⠈⠁⠈⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠛⠽⣋⡵⠒⢋⣁⣤⡌⠵⣀⡈⣣⠬⠀⠀⢠⠒⠠⠈⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⣣⣿⣉⣩⣥⣭⣍⡙⠣⢼⠂⠤⠀⡤⢯⠭⠀⠈⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠒⢶⣶⣶⣶⠂⠬⢑⠊⣈⢷⣚⢻⠩⠀⡐⠀⠋⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠛⠻⠓⠶⣟⣡⠖⣭⢢⡷⠆⠹⣥⡀⠙⢄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢵⡞⣡⡠⡻⡳⣁⠉⣧⢀⡀⠈⠁⠲⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⡯⢻⣽⣾⣳⣏⣀⣿⣷⢂⠓⢆⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠘⠛⠟⠛⠛⠉⠛⠋⠀

⠀⠀⠀⠀⢀⣴⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⢀⡾⠁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠈⢳⡀⠀⠀⠀ ⠀⠀⢠⢺⠃⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠘⡷⡄⠀⠀ ⠀⢠⠏⢸⡄⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣠⡇⠹⡄⠀ ⠀⢸⡀⢸⡄⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⣰⡇⢠⡇⠀ ⢀⡜⡇⠈⣿⡀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⢈⣿⠁⢹⢡⡀ ⢸⠀⢳⠄⠹⣿⡄⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⣠⣿⠃⠰⡋⠀⡇ ⣸⠆⢸⣧⡄⢸⣿⣶⠀⢢⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢋⡇⢐⣾⣿⠇⢠⣾⠄⢘⢇ ⠁⠷⡀⠹⣷⣄⣻⣿⡟⠺⣷⡀⠉⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠁⢀⡿⠛⣻⣿⠋⣴⣿⠋⠀⠞⢈ ⢧⠀⣶⣄⡘⢿⣦⣽⣿⣄⠈⢱⡦⠀⠀⠉⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⢴⡏⠀⣰⣿⣯⣾⡿⢁⣠⣶⢀⡜ ⠘⣇⠈⠻⣷⡜⢻⣧⠉⠻⣄⠨⢿⣶⣴⠶⡄⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠰⠒⣶⣾⡯⢅⡴⠛⠁⣴⡏⣠⣾⠟⢁⡽⠁ ⠀⢻⠉⣄⠈⢿⣿⣿⣷⡀⠀⣶⣤⣈⣷⣀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠤⣾⣁⣴⡞⠀⣀⣾⣿⣿⡟⢁⣨⠁⡇⠀ ⠀⠈⢧⡈⢿⣥⣍⣿⠉⠉⠃⢶⣮⣿⡁⠀⠀⠀⡚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⠀⠀⠀⢀⣿⡶⠶⠈⠁⢈⣿⣡⣴⠏⢁⡜⠀⠀ ⠀⠀⠘⠳⣤⣈⠛⠻⢷⣦⣤⡌⣶⣾⣿⠃⠀⠀⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⡀⠘⣿⣿⡿⠡⣤⣶⡿⠛⠋⢡⡤⠞⠁⠀⠀ ⠀⠀⠀⠀⠈⠉⠒⠒⣾⠋⠁⠀⣈⣽⣿⣷⡎⠀⡀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢠⠁⠀⢀⡀⢹⣾⣿⡯⣀⡀⠀⠙⣇⠒⠈⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⠦⢴⠋⠁⠀⠹⣿⣿⣿⡁⠀⠀⠙⣄⠀⠀⠀⠀⣰⠋⠀⢀⢈⣿⣿⠿⠋⡀⠀⠙⡆⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢤⠴⠋⠀⡀⠛⠿⠟⡇⠠⠤⠬⠷⠀⠀⠺⠤⠔⠂⢢⠹⡟⠋⢤⠀⠙⠦⠤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠴⣇⣠⣏⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⣹⣤⡼⠦⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀ ⢠⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡄ ⠈⣆⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣰⠁ ⠘⣜⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣷⣣⠃ ⠈⢌⢾⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡷⡡⠁ ⠀⠀⢙⢿⣿⣿⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⡿⡋⠀⠀ ⠀⠀⠀⠑⣻⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣟⠊⠀⠀⠀ ⠀⠀⠀⠐⢒⣛⣻⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣟⣛⡒⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠤⠼⢿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠧⠤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⢚⡭⢿⣿⣿⣿⣆⠀⠀⠀⠀⣰⣿⣿⣿⡿⢭⡓⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⠩⠟⠿⣿⣿⠀⠀⠀⠀⣿⣿⠿⠻⠍⠂⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⣦⠀⣼⠇⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⢸⣧⠀⣴⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠛⢿⣧⣿⡇⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⢸⣿⣼⡿⠹⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⠀⠈⠻⣿⠇⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⢸⣿⠟⠀⠀⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠀⠀⣿⠀⠀⠀⢸⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⡇⠀⠀⠀⣿⠀⠀⣀⠀⠀⠀ ⠀⠀⢠⣿⣷⣤⣿⡆⠀⠀⢸⡀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⢀⡇⠀⠀⢰⣿⣤⡾⣿⡄⠀⠀ ⠀⠀⢸⣇⠈⠉⢻⡇⠀⠒⠈⣇⢀⣀⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⣀⠀⣼⠁⠒⠂⢹⡏⠉⠀⣸⡇⠀⠀ ⠀⠀⠈⣿⡄⠀⠈⢇⠀⠉⠀⢻⠀⠼⠿⢿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡿⠲⠯⢀⡟⠈⠉⠀⡼⠁⠀⢀⣿⠁⠀⠀ ⠀⠀⠀⢻⣧⠀⠀⠸⡄⠀⠀⠈⡇⠀⠀⠈⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⣸⠁⠀⠀⢠⠇⠀⠀⣼⡏⠀⠀⠀ ⢰⣷⠶⠾⢿⡗⠀⠀⢻⡀⠀⠀⠹⡄⠀⠀⡏⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⢸⠀⠀⢠⠏⠀⠀⢠⡟⠀⠀⢺⡿⠷⠶⣾⡄ ⠀⢿⣦⠀⠀⢷⡀⠀⠀⢳⡄⠀⠀⢻⡄⠀⣇⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⣸⠀⢠⡟⠀⠀⢠⡞⠀⠀⢀⡾⠀⠀⣼⡟⠀ ⠀⠈⢿⣆⠀⠀⠳⡄⢀⡄⠙⢤⠀⢸⠿⣄⠹⣆⠀⠀⠈⠛⠻⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⠟⠛⠁⠀⠀⣰⠇⣠⠿⡇⠀⡤⠋⢠⡀⢠⠞⠀⠀⣰⡿⠁⠀ ⠀⠀⠀⠻⣷⣄⠀⠘⢮⡚⠀⠀⠑⢾⡆⠀⠉⠛⠶⠦⢤⠀⠀⠀⠉⠙⢿⡆⠀⠀⠀⠀⠀⢰⡟⠋⠉⠀⠀⢀⡤⠴⠾⠛⠉⠀⢸⡷⠊⠀⠀⢃⡴⠃⠀⣠⣾⠟⠀⠀⠀ ⠀⢠⣤⣤⣼⣿⢷⣄⠀⠙⠦⣄⠀⣄⡻⣄⡀⠀⠀⠀⠀⠀⢀⢠⡀⠀⣸⡇⠀⠀⠀⠀⠀⢸⡇⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⣠⠏⣀⠀⣀⠴⠋⠀⣠⡾⢿⣥⣤⣬⡄⠀ ⠀⠈⠻⣷⣤⡀⠀⠈⠳⢤⡀⠈⠙⢾⡝⠚⠷⠦⣤⣤⠀⠀⢹⡇⠛⠀⣿⡆⠀⠀⠀⠀⠀⢸⡧⠀⠛⢱⡇⠀⠀⣤⣤⡴⠾⠓⢻⡷⠋⠁⢀⣤⠞⠁⠀⢀⣤⣾⠟⠁⠀ ⠀⠀⠀⣈⣙⣿⣶⣄⠀⠀⠉⠓⠶⢤⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡤⠴⠚⠉⠀⠀⣠⣶⣿⣋⣁⠀⠀⠀ ⠀⠀⠀⠻⣿⣍⠉⠉⠓⠦⣤⣀⠀⠀⣀⡙⠦⣄⣀⣀⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀⣀⣀⣠⠴⢋⣀⠀⠀⣀⣤⠴⠚⠉⠉⢩⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣶⣄⣀⢠⡄⠈⠙⠺⢿⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⣿⠷⠋⠉⢠⠄⣀⣠⣴⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⢿⣦⣄⣀⠀⠀⠀⠳⢄⣀⣀⣀⣠⣤⡤⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢠⣤⣄⣀⣀⣀⡠⠞⠁⠀⠀⣀⣠⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣤⣽⣿⠟⠉⠛⠒⠒⠋⠉⠉⢿⣏⡁⣀⣀⣤⠴⣾⣿⠀⠀⠀⠀⠀⣿⣗⠦⣤⣀⣀⣈⣹⡿⠋⠉⠉⠒⠒⠚⠉⠻⢿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣶⣶⣤⣤⣀⣀⣠⣤⣶⡾⠋⠉⠀⣠⣾⡿⠃⠀⠀⠀⠀⠀⠘⢿⣷⣄⠀⠈⠙⢿⣶⣤⣄⣀⣀⣠⣤⣶⣶⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⣿⣿⡿⣋⣀⣠⣤⡾⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢷⣤⣄⣈⡛⢿⣿⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣀⣠⣀⣀⣀⡀⢀⣀⡀⣀⢀⠀⢀⢀⣀⣀⣀⠀⠀⠀⡀⢤⢀⡀⣠⠀⡄⢀⢀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠒⠛⠚⠛⠂⠂⠂⢘⠓⠛⠒⠙⠀⠓⠛⠊⠛⠙⠀⠀⠘⠚⠚⠛⠊⢙⠑⠊⠙⠐⠚⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠸⡄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⡇⢳⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣦⠀⠣⢸⢳⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡏⢰⠃⠘⠀⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢧⢁⠃⢠⠃⠘⢐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⢀⠌⢀⠂⠀⠀⡼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⢃⠂⠠⠃⠀⠀⡐⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⣾⢁⠔⠁⠀⢀⠜⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣣⢾⡾⠁⠀⢀⠔⠁⠀⠀⡁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠔⢁⡼⠋⡀⠔⠁⠀⠀⠀⢀⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⣁⢴⢻⠀⢹⠟⠉⠀⠀⠀⢀⠤⠒⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠐⢁⡠⠖⠉⠀⣼⢊⣴⣯⠤⠤⠀⠒⠉⠀⠀⣠⠃⠀ ⠀⠀⠀⠀⠀⡠⠊⣠⠖⠉⠀⠀⣠⠞⠁⢀⣿⠉⠛⠲⠤⣤⣀⣤⣖⠁⠀⠀ ⠀⠀⠀⢠⠞⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⡔⠁⠑⠂⠄⣀⠀⢀⡤⠋⠀⠀⠀ ⠀⢀⡔⠁⠀⡾⠀⠀⠀⠀⠀⢀⣠⠶⢇⡀⠀⠀⠀⠀⢀⡀⠝⠀⠀⠀⠀⠀ ⢠⠎⠀⠀⢀⣇⣀⠀⠀⢴⠺⠉⠳⣄⠀⠈⠐⠠⠄⡀⠔⠁⠀⠀⠀⠀⠀⠀ ⠘⣄⣀⣀⠜⠁⠀⠈⠉⠛⠅⡀⠀⠸⣙⠲⡤⠖⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀ ⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⢀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡀ ⠘⡀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⢀⠇ ⠀⣧⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⣼⠀ ⠀⢸⣆⠀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⣰⡏⠀ ⢱⡀⢿⣆⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡏⣰⡿⠀⡌ ⠀⢷⡈⢿⣧⣻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣟⣴⡿⢁⡾⠀ ⢀⠈⢷⣌⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⣡⡾⠁⡀ ⠀⠳⡈⢻⣦⡻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣟⣵⡟⢁⠞⠀ ⠀⠀⠙⢦⡹⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⢏⣴⠋⠀⠀ ⠀⠀⠀⡈⠻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠟⢁⠀⠀⠀ ⠀⠀⠀⠈⠢⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣡⠔⠁⠀⠀⠀ ⠀⠀⠀⠀⢀⠈⠛⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠛⠁⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠒⠦⣬⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣥⠴⠒⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠤⢤⣌⣉⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣉⣡⡤⠤⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣉⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣉⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⣉⣭⣽⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣭⣉⣉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠛⠛⠛⠛⢛⣩⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣭⡛⠛⠛⠛⠛⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠾⠟⠛⣫⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣝⠛⠻⠷⠦⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⠛⣫⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣝⠛⠻⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠾⠛⣡⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⢿⣎⠛⠷⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⢀⠿⠋⡿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢿⠙⠿⡄⠙⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢰⣄⡀⢳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡞⢀⣠⡆⠀⠀ ⠰⣦⣄⠻⢿⣦⣝⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣫⣴⡿⠟⣠⣴⠆ ⣀⠙⠿⣿⣦⣝⠿⣷⣝⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣫⣾⠿⣫⣴⣿⠿⠋⣀ ⠙⣿⣶⣬⣙⠿⣷⣯⡛⣿⣿⣷⡀⠀⠀⠀⠀⢀⣾⣿⣿⢛⣽⣾⠿⣋⣥⣶⣿⠋ ⢠⣤⣍⣛⠿⣿⣾⣍⣿⣿⡟⢦⣵⡄⠀⠀⢠⣮⡴⢻⣿⣿⣩⣵⣿⠿⣛⣩⣤⡄ ⠀⠻⢿⣿⣿⣶⣯⣽⣿⠷⣍⣶⣿⠆⠀⠀⠰⣿⣶⣩⠾⣿⣯⣽⣶⣿⣿⡿⠟⠀ ⠀⠀⢰⣦⣬⣭⣛⣋⣿⡿⡏⢹⡏⠀⠀⠀⠀⢹⡏⢹⢿⣿⣙⣛⣭⣥⣴⡆⠀⠀ ⠀⠀⠀⠙⠛⠻⠿⠿⠿⣷⠿⡟⡇⠀⠀⠀⠀⢸⢻⠿⣾⠿⠿⠿⠟⠛⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣿⣿⣿⡿⢷⢬⣿⡀⠀⠀⢀⣿⡥⡾⢻⣿⣿⣿⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣾⡿⡃⠁⠀⠀⠈⢘⢿⣷⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⠔⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⡄⠀⠀ ⠀⢀⡼⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠸⡄⠀ ⠀⡈⢰⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⢸⠀ ⢀⢫⠹⣄⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢀⠇⡙⠆ ⣸⠀⣧⠹⣦⠄⡗⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⡇⣤⡟⣠⠁⣴ ⢇⢣⠘⣧⣿⣯⠛⢄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠚⣁⣟⣴⠏⡴⢁ ⠈⣍⡙⣌⢿⡉⠢⣸⢿⡒⠀⠑⠀⠀⠀⠀⠀⠀⠌⠀⠖⣾⢟⡴⠋⣽⣃⡾⣣⠃ ⠀⠠⡱⣜⢻⡓⠢⣼⣿⠁⠀⡤⠂⠀⠀⠀⠀⠀⠢⠀⠀⢹⣿⠤⠚⣿⣋⠖⡙⠀ ⠀⠀⠑⠌⡙⢿⠷⠘⣿⣇⡄⠑⠀⠀⠀⠀⠀⠠⠊⠀⣨⣿⠀⠲⢿⠏⡡⠔⠁⠀ ⠀⠀⠀⠀⠀⠛⢰⠀⠉⢿⣶⣀⠈⠂⡀⠀⡠⠀⣀⣶⡿⢋⠀⡖⠚⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠹⣤⣎⣹⢩⠉⠉⠁⠈⠉⠉⢋⢫⣸⣤⠝⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣠⡾⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡷⣦⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠏⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠈⢷⡀⠀⠀⠀ ⠀⠀⠀⣰⡟⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠘⣷⡀⠀⠀ ⠀⠀⡼⠉⣇⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣠⡇⠹⡄⠀ ⠀⠀⣇⠀⣧⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢠⡇⢀⡇⠀ ⠀⣰⢯⠀⢻⡇⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⢀⣿⠁⢨⢧⠀ ⠀⡇⠸⡦⠈⢻⣆⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⢠⣾⠃⠠⡞⠀⡇ ⢠⡗⠀⣿⣄⠈⣻⣷⡦⠐⡍⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡇⠀⣶⣿⠃⢀⣼⡅⠐⣇ ⡏⠹⣄⠈⢿⣦⣘⣿⡿⠒⢿⡆⠈⠑⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⢀⣾⠗⠺⣿⢏⣠⣾⠏⢀⡼⠉ ⠹⡄⢹⣧⡀⢻⣷⣍⣷⣷⡀⠙⣢⣄⠀⠈⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠉⠀⢀⣤⡞⠁⣴⣿⣏⣴⡿⠃⣠⣿⠁⡴ ⠀⢻⡈⠻⣿⣤⠛⣯⡉⠙⢧⡀⢹⣿⣿⡶⢦⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢠⠶⣾⣿⣟⠁⣠⠟⠉⣭⡟⢡⣼⡟⠁⣸⠁ ⠀⠈⡟⢶⡊⠙⣷⣿⣿⡄⠀⠘⣷⣮⣽⣅⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣈⣿⣭⣶⡟⠁⢀⣾⣿⣶⡟⠁⣲⠞⡇⠀ ⠀⠀⠱⣄⠹⣧⣌⣻⣏⡉⠑⠲⣬⣽⣯⠀⠀⠀⢰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⠀⠀⠀⢨⣿⣭⡴⠚⠉⣩⣿⣋⣤⡿⢁⡴⠁⠀ ⠀⠀⠀⠻⣤⣈⠙⠻⣿⣿⣶⣤⣶⣶⣿⣟⠁⠀⠘⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠀⠀⢙⣿⣷⣒⣤⣴⣾⣿⡿⠛⣉⣠⠾⠃⠀⠀ ⠀⠀⠀⠀⠀⠉⠐⠲⢬⡿⡉⠀⠀⣉⣿⣿⣶⠁⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢠⠃⠀⢀⠀⢳⣾⣿⣍⡁⠀⠈⠹⣯⠔⠒⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢥⡖⠉⠁⣉⢽⣿⣷⡏⢀⠀⠈⢦⠀⠀⠀⠀⢠⠏⠀⢀⡌⣿⣿⡿⢍⠀⠉⠙⡦⠽⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡔⠁⢀⠞⢿⣿⢿⠤⠤⠄⠱⠆⠀⠾⠡⠤⠤⢼⢿⣟⠟⣆⠀⠱⣶⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣶⣾⣀⣼⠤⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⢹⣄⣼⣶⡶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⠿⣟⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⡏⠀⠀⠀⢣⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣟⠧⠤⠤⠔⠋⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⡀⢀⣶⠤⠒⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠈⢿⣆⣠⣤⣤⣤⣤⣴⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⢿⢿⠀⠀⠀⢀⣀⣀⠘⣿⠋⠁⠀⠙⢇⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⢇⡞⠘⣧⠀⢖⡭⠞⢛⡄⠘⣆⠀⠀⠀⠈⢧⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀ ⠀⠀⣠⣿⣛⣥⠤⠤⢿⡄⠀⠀⠈⠉⠀⠀⠹⡄⠀⠀⠀⠈⢧⠀⠀⠀⠈⠻⣦⠀⠀⠀ ⠀⣼⡟⡱⠛⠙⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠹⣧⡀⠀ ⢸⡏⢠⠃⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠸⣷⡀ ⠸⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⣿⠇ ⠀⣿⡄⢳⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀ ⠀⢹⡇⠘⣇⠀⠀⠀⠀⠀⠀⠰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⡟⠀⠀ ⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢳⣼⠟⠀⠀⠀ ⠀⠸⣧⣀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⣴⡿⠁⠀⠀⠀⠀ ⠀⠀⠈⠙⢷⣄⢳⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⣠⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣷⣦⣄⣀⣀⣠⣤⠾⠷⣦⣤⣤⡶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠷⣦⡀⢀⣀⣤⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⢀⡤⢤⣄⡀⢀⣠⣤⣶⣶⣶⣿⣿⣧⣄⣹⣿⡉⠁⠀⠈⣷⠀⠀⠀⠀⠀ ⠀⢠⠟⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠙⢶⣄⣀⣼⡀⠀⠀⠀⠀ ⠀⢸⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠉⣿⠀⠀⠀⠀ ⠀⢸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣆⠀⠀⠀ ⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠉⠉⠛⠿⣿⣿⣿⣿⡇⠀⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠧⠤⠤ ⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢰⣿⠆⠀⢸⣿⣿⡀⠀⠀ ⠉⠙⣿⣿⣿⣿⣿⣿⣿⠁⠟⠀⠀⣶⣦⠀⠀⠀⠀⠀⠉⠀⠀⢸⣿⡏⠉⠀⠀ ⠀⠰⢻⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣠⠼⠿⣷⡦⠄⠀ ⠀⠀⣸⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡃⠀⠀⠀⠙⣦⠀ ⠀⠀⠈⠋⠀⢀⣿⠿⣟⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⡹⡌⢷⡀⠀⠀⠀⣼⠀ ⠀⠀⠀⣠⡾⣿⣍⣳⣾⣿⣿⣜⣿⣿⣟⣿⣿⣟⣙⢿⣷⡹⡌⢷⡄⣀⡴⠋⠀ ⠀⠀⣼⠉⠀⠈⢹⣿⣿⣿⣿⣿⢡⣤⠀⣤⠀⢿⣿⠀⣸⣷⣹⣌⠟⠋⠀⠀⠀ ⠀⠀⣿⠀⡴⠞⠋⠉⠉⠙⢿⣿⣦⣉⡄⢉⣠⣿⡿⠟⠉⠉⠉⠙⢦⡀⠀⠀⠀ ⠀⠀⠘⣿⠁⠀⠀⠀⠀⠀⠀⠙⣿⣾⣯⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀ ⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀ ⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀ ⠀⠀⠀⠀⠘⠷⣤⣀⠀⠀⠀⣠⠿⠿⠿⠿⠷⣄⡀⠀⠀⣀⣠⡾⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⣄⣤⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⠈⢻⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⡅⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⠂⠀⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣈⣻⣿⣿⡀⠘⠻⢿⣿⣿⣿⣿⣿⠟⠛⠛⠃⠀⠐⠻⢿⣿⣿⣿⣿⣿⠟⠁⢀⣴⣿⣿⣿⣷⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⣿⣶⣤⡄⠈⠻⠟⠉⢀⣠⣴⣶⣶⣶⣶⣄⠀⠈⠙⠿⠟⠁⣀⣴⣿⠟⠀⠛⠿⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠙⠿⠿⠟⠉⠉⣀⠈⠻⣿⡟⠀⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣠⠀⢸⣿⠟⠁⣠⣶⣤⣀⠈⠉⠉⠁⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⣆⣠⣄⣤⣾⣿⣿⣷⡄⠈⠁⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠈⠁⣠⣾⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢀⣰⣿⣿⣿⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⠛⠁⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⠟⠻⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠁⠀⠀⠀⢹⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⢠⣼⣿⣿⣷⣄⠀⠀⣠⣾⣿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⠀⠈⢿⣿⣷⡀⡀⢀⣸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠏⠁⠀⠉⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⠟⠉⠉⣀⣤⡄⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠠⢼⣷⣄⠈⠻⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣤⡀⠀⣠⣼⣿⡿⠟⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⡀⠙⢿⣷⣄⠀⢠⣤⣼⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣿⠋⢁⣀⣠⡄⠀⣿⣿⣿⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣷⣄⠀⠙⢿⣷⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣈⣿⣿⣿⠁⠀⠈⢿⣿⣅⠀⠻⣿⣿⣿⠀⢸⣿⣿⣿⡏⠀⣿⣿⠟⠀⣠⣿⣿⡗⠀⠀⣹⣿⣿⣄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠈⡿⣷⣄⠈⠉⠉⢀⠀⡉⠉⠉⠁⠀⠈⠁⣀⣼⣿⠟⠻⠄⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠈⡅⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⡃⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠐⡄⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠹⠀⠀⠀⡅⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⢰⡟⣿⣿⣿⣿⣿⠏⠁⠀⠀⢘⠀⠀⠀⠅⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠸⠀⠀⠻⣿⡛⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⡻⠆⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

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⠀⠀⢠⢾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⡄⠀⠀ ⠀⢠⠇⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠘⡄⠀ ⠀⡏⡃⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢈⢸⠀ ⡰⢋⠸⡀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⢀⡇⡘⠆ ⢷⢸⣅⣻⣤⢸⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢞⡇⣴⡟⣰⠅⡆ ⡌⢀⠹⣦⣿⣍⠃⡀⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠈⢠⠞⣩⣿⣽⠋⡀⢡ ⠸⢌⣷⣟⣧⠙⢦⠻⡖⠲⠀⠡⠀⠀⠀⠀⠀⠀⠎⠀⠂⠶⠟⡔⢉⣼⣡⠞⠡⠃ ⠀⢢⠲⣝⣟⠒⠠⣿⡋⠁⠀⠔⠀⠀⠀⠀⠀⠀⠒⠀⠈⢹⣯⠐⠚⣿⣫⢞⡜⠀ ⠀⠈⠓⠌⡙⡷⠖⠹⣿⣀⠀⠑⠄⠀⠀⠀⠀⠐⠊⠀⣄⣿⠋⠐⢾⢉⠱⠊⠀⠀ ⠀⠀⠀⠀⠀⠃⠐⠀⠙⢿⣶⣀⠀⢄⠀⢀⠠⠀⢀⣷⡟⠃⠀⠂⠚⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠩⠠⣃⡍⡉⠀⠉⠀⠀⠀⠀⢉⣣⣸⠤⠍⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣠⣤⣴⠿⠿⠻⡶⠄ ⢀⣤⣶⡿⠿⣿⣿⣿⣽⣧⣿⣿⠁⠀⠀⠀⠁⠀ ⠛⠓⠀⠀⠀⠀⢻⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⣀⣤⣤⣄⠀ ⠀⠀⠀⣠⣤⣤⣤⣀⣿⣿⣿⣷⣾⣿⣿⣿⡿⠀ ⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡿⠏⠀⠀ ⠀⠀⠀⠀⠉⠻⠿⣿⣿⣯⠁⢰⣿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⠀⠀⠀ ⠀⠀⣸⢇⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠘⣇⠀⠀ ⢀⡷⣿⠘⡜⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢇⢇⣿⢾⡄ ⢸⡇⠹⡇⠱⡹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⡌⢸⡏⣄⡇ ⠀⣇⠀⢹⣄⠱⡝⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⠞⢠⡟⠐⢸⠃ ⣤⣻⡆⠢⡙⢦⡈⠪⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠵⢃⡴⢋⡔⢱⣟⣤ ⠘⣏⠻⣦⡘⠦⡙⠳⣜⣿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⣣⠖⢋⡴⢋⣴⠟⣱⠃ ⢀⡘⣆⠀⠙⠶⣌⡳⢌⣿⣧⣺⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣗⣴⣿⡧⢞⣡⠴⠋⠁⢠⢃⡀ ⠘⣟⠻⢦⡀⠠⢌⡙⢦⣷⡨⣿⣧⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠉⣸⣿⢇⣼⡴⢋⡡⠔⢀⡴⠟⢫⠇ ⢷⠿⣿⡮⠙⠶⣤⣈⣙⣯⠛⡻⣿⠓⡺⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠖⠚⣿⢟⠛⣹⣛⣁⣤⠶⠋⢁⣿⠯⣾ ⠈⢧⡈⠙⠲⢤⣐⠬⣿⣍⢷⣿⣿⡗⠾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⢺⣿⣿⡾⢫⣟⡥⢀⣠⠖⠋⢁⡴⠃ ⠀⠀⢻⣆⡑⠢⣈⣉⠻⢿⡛⠉⣿⡿⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⢾⣿⠉⢛⡿⠟⣋⣁⠴⢊⣠⡟⠁⠀ ⠀⠀⠘⢿⡙⠓⠦⠬⢍⣻⡿⠻⣿⣤⣤⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣧⣤⣿⡟⢿⣟⡩⠥⠴⠚⢋⡿⠃⠀⠀ ⠀⠀⠀⠲⣿⠲⢤⣭⡭⠭⣿⣶⡶⣿⣧⣶⠟⢿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠻⣶⣼⣿⢶⣶⣿⡭⠭⣥⣤⠔⣻⠖⠀⠀⠀ ⠀⠀⠀⠀⢈⣷⠮⠤⠭⠭⣒⠿⣷⣶⡾⣻⣴⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣅⣿⣦⣟⢿⣶⣾⡿⣖⠬⠥⠤⠵⣾⡁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⢲⣦⣤⠴⠒⢽⣻⢿⣶⣾⡏⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣝⣷⣶⡿⣟⡯⠒⢦⣤⣤⣖⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠲⢶⡶⠋⢀⣴⣿⢏⠿⣿⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⡙⣝⣧⡀⠙⢷⡶⠖⠚⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⢿⠵⣷⡯⢾⡭⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢽⣷⢽⣾⡬⡿⠍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀ ⢰⣾⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠦⣷⡆ ⢸⠘⡄⢝⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠪⢠⠓⡇ ⢮⢇⢙⠦⡙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢃⠴⡣⡸⡵ ⢈⣆⠑⢕⡪⣻⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣯⣟⢅⡪⠊⣠⣁ ⣼⣽⠦⣄⡘⣿⠾⣷⣭⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠯⣾⠷⣿⢃⣠⠔⣫⢧ ⠘⢌⢑⠠⢞⣿⣶⣿⣳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣖⣿⣟⣽⡳⠄⡊⣡⠃ ⠀⠘⡓⠭⢐⣺⡶⣿⣽⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣎⣻⣶⣗⡂⠭⢒⠃⠀ ⠀⠀⠛⣲⠂⠻⣿⣞⣳⣾⡽⢷⠀⠀⠀⠀⠀⠀⣾⣯⣳⣾⣓⣿⠟⠁⣖⠟⠀⠀ ⠀⠀⠀⠡⣦⠀⣘⠟⢷⣾⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⣷⣾⠻⣃⢦⣴⠌⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠓⢖⢽⡮⡿⠁⠀⠀⠀⠀⠀⠀⠀⣿⢵⡯⡲⠚⠂⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣤⡤⣤⠤⣾⣿⣽⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⣠⣤⣤⣀⠀⣀⣼⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠆ ⣼⣿⣿⣿⣿⣧⣤⣿⠿⠉⠿⠿⠿⠛⠛⠛⠛⠛⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⠿⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡌⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢀ ⣿⣌⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⣱⣿ ⢹⣿⣧⡈⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠟⣡⣾⣿⠇ ⢰⡙⢿⣿⣷⣌⠛⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⢋⣡⣾⣿⡿⣫⡆ ⠈⢿⣦⣝⠻⣿⣿⣦⣉⠻⢿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⡿⠛⣡⣴⣿⣿⠟⣩⣾⡿⠁ ⠀⠈⠻⣿⣷⣮⡙⢿⣿⣷⣤⡉⠻⢿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⡿⠟⢉⣴⣾⣿⠿⣋⣵⣾⣿⠟⠁⠀ ⠀⠀⠰⣌⠻⣿⣿⣷⣬⡛⢿⣿⣷⣤⡉⠻⢿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⡿⠛⣉⣤⣾⣿⡿⢛⣥⣾⣿⣿⢟⣡⠆⠀⠀ ⠀⠀⠀⠹⣿⣮⣙⢿⣿⣿⣷⣭⡻⣿⣿⣷⣦⣉⠻⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠟⣁⣴⣾⣿⡿⣟⣽⣾⣿⣿⠿⣋⣴⣿⠏⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⣷⣬⣛⢿⣿⣿⣷⣿⣿⣿⣿⡇⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⢸⣿⣿⣿⣿⣾⣿⣿⡿⣛⣵⣾⡿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⣮⣟⢿⣿⣿⣿⣿⡇⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⢸⣿⣿⣿⣿⡿⣻⣵⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣇⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⣼⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⠘⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢁⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡏⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡶⠀⠀⠀ ⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀ ⢀⠀⢱⡘⣿⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣫⣿⡏⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⢃⡜⠀⣀ ⠈⢷⣷⣽⣿⣿⣿⣷⣤⣀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠻⣟⣿⠷⠖⠚⠓⠒⠲⠶⣤⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣠⣴⣿⣿⣿⣿⣮⡾⠁ ⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣯⡛⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⡀⠀⠀⠀⠀⢛⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀ ⠀⠀⠐⠬⢽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⠆⠀⢠⣿⠀⢰⡀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠈⣷⠀⠰⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣯⠥⠄⠀⠀ ⠀⠀⠀⠒⢒⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣿⡇⠀⣾⣿⡄⠀⠀⠀⠀⢠⣿⣧⠀⠀⢸⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠒⠂⠀⠀⠀ ⠒⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⢻⡏⠁⠠⠀⠀⠀⠘⣻⠟⢀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠔ ⠀⠀⠈⢹⠉⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣔⢃⢠⠁⠂⠀⠀⠀⠉⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣉⠉⠉⠉⠀⠀ ⠀⠀⠀⠀⠘⢫⠿⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⣝⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⠉⣹⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⠋⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡾⢿⣿⠟⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢭⡳⡽⠻⠩⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠻⣿⡿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⢿⣿⡏⠝⢿⣿⣿⣿⣏⠳⡆⠀⠀⠀⠀⢸⣿⣿⣿⡿⠯⢻⣿⡿⠙⠁⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠈⠀⠀⢿⣿⣿⣯⠻⡆⠀⡄⠀⠀⢸⣿⣿⡿⠀⠀⠁⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠃⣿⣷⡄⣸⡇⠄⠀⢸⡟⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⡐⠄⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⣏⣷⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛⬛🏻🏻🏻🏻🏻🏻🏻🏻⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬛⬛🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻⬛⬛⬜⬜⬜ ⬜⬜⬛⬛🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻⬛⬛⬜⬜ ⬜⬛⬛🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻⬛⬜⬜ ⬜⬛🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻⬛⬜⬜ ⬜⬛🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻⬛⬜⬜ ⬜⬛🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻⬛⬜⬜ ⬜⬛🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻⬛⬜⬜ ⬜⬛🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻⬛⬜⬜ ⬜⬛🏻🏻🏻🏻⬛⬛⬛⬛⬛⬛🏻🏻🏻⬛⬛⬛⬛⬜ ⬛⬛⬛⬛⬛⬛🏻🏻🏻🏻🏻🏻⬛⬛⬛🏻🏻⬛⬜⬛ ⬛🏻🏻🏻🏻⬛🏻🏻⬜⬛🏻🏻⬛🏻⬛⬛🏻⬛⬜⬛ ⬛🏻🏻🏻🏻⬛🏻🏻⬛⬛🏻⬛🏻🏻⬛⬛🏻⬛⬜⬛ ⬛🏻🏻🏻🏻⬛🏻🏻🏻🏻⬛🏻🏻🏻⬛⬛🏻⬛⬜⬛ ⬛⬛🏻🏻🏻🏻⬛⬛⬛⬛🏻⬛🏻🏻⬛🏻⬛⬛⬛⬜ ⬜⬛⬛🏻🏻🏻🏻🏻🏻🏻🏻⬛⬛⬛⬛🏻🏻⬛⬜⬜ ⬜⬜⬛🏻🏻🏻🏻🏻🏻🏻🏻🟫🟫🟫🟫🏻🏻⬛⬜⬜ ⬜⬜⬛🏻🏻🏻🏻🏻🏻🟫🟫🟫🟫🟫🟫🟫🏻⬛⬜⬜ ⬜⬜⬛⬛🏻🏻🏻🏻🏻🟫⬛⬛⬛⬛⬛🟫🏻⬛⬜⬜ ⬜⬜⬜⬛⬛🏻🏻🏻🏻🟫🏻🟫🟫🟫🏻🟫🏻⬛⬜⬜ ⬜⬜⬜⬜⬛⬛🏻🏻🏻🟫🏻🏻🟫🏻🏻🟫🏻⬛⬜⬜ ⬜⬜⬜⬜⬛⬛⬛🏻🏻🟫🟫🟫🟫🟫🟫🟫⬛⬜⬜⬜ ⬜⬜⬜⬛⬛🟨⬛⬛🏻🟫🟫🟫🟫🟫🟫⬛⬛⬜⬜⬜ ⬜⬜⬜⬛🟨🟨🟨⬛⬛⬛⬛⬛⬛⬛⬛🟨⬛⬜⬜⬜ ⬜⬜⬜⬛⬛⬛🟨🟨🟨⬛🏻🏻🏻⬛⬛🟨⬛⬜⬜⬜ ⬜⬜⬜⬜⬛🟨🟨🟨🟨⬛⬛🏻⬛⬛🟨⬛⬛⬜⬜⬜ ⬜⬜⬜⬛🟨🟨🟨🟨🟨🟨⬛⬛⬛🟨🟨🟨⬛⬜⬜⬜ ⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜

⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬛⬛⬛⬛⬛⬛⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜ ⬛⬛🟥🟥⬛⬛⬛⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬛⬛🟥⬛⬛⬛⬛⬛🟥🟥⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛🟫🟫🟫⬛🟫⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬛⬜🟫🟫🟫🟫🟫🟫⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬛🟫⬛🟫🟫🟫⬜🟫🟫🟫⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬛🟫🟫🟫🟫🟫⬛🟫🟫🟫⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬛⬛🟫🟫⬛🟫🟫🟫🟫🟫🟫⬛⬜⬜⬛⬛⬛⬛⬜ ⬜⬛🟫⬛🟫🟫🟫🟫🟫🟫🟫🟫⬛⬜⬛⬛⬛🟫🟫⬛ ⬜⬛🟫⬛⬜⬜⬜🟫🟫⬛🟫🟫⬛⬛⬛⬛⬛⬛🟫⬛ ⬜⬛⬛⬜🟫🟫⬜🟫⬛🟫🟫🟫⬛⬛🟫🟫⬛⬛⬛⬛ ⬜⬜⬛⬜🟫🟫⬜🟫⬛🟫🟫⬛⬛⬛⬛🟫🟫⬛⬛⬛ ⬜⬜⬛⬛⬜⬜⬜🟫⬛⬛⬛⬛🟫⬛⬛🟫🟫⬛⬛⬜ ⬜⬛🟫🟫⬛🟫🟫🟫🟫🟫🟫⬛🟫⬛⬛🟫⬛⬛⬜⬜ ⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛🟫🟫⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜

⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛⬛⬛🟨🟨⬛⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬛⬛🟨🟨🟥🟥🟨🟨⬛⬛⬜⬜⬜ ⬜⬜⬛⬛🟨🟨🟥🟥🟥🟥🟨🟨⬛⬜⬜⬜ ⬜⬜⬛⬛⬛🟨🟨🟥🟥🟨🟨⬛⬛⬜⬜⬜ ⬜⬛⬛⬛⬛🏻🏻🟨🟨🏻🏻⬛⬛⬜⬜⬜ ⬛⬛⬛⬛⬛🏻⬛🏻🏻⬛🏻⬛⬛⬜⬜⬜ ⬛⬛⬛⬛⬛🏻⬛🏻🏻⬛🏻⬛⬛⬜⬜⬜ ⬛⬛⬛🏻🏻⬛🏻🏻🏻🏻⬛🏻🏻⬛⬜⬜ ⬛⬛🏻🏻🏻🏻⬛⬛⬛⬛🏻🏻🏻🏻⬛⬜ ⬛⬛⬜⬜⬛🏻🟨🏻🏻🟨🏻⬛⬜⬜⬛⬜ ⬜⬛🏻🏻⬛🟨🟨🟥🟥🟨🟨⬛🏻🏻⬛⬜ 🟨🟨⬛⬛⬛🟥🟥🟨🟨🟥🟥⬛⬛⬛⬜🟨 🟨⬜⬜⬜⬛🟦🟨⬜⬜🟨🟦⬛⬜⬜🟨🟨 🟨🟨⬜⬜⬛🏻🟦⬛⬛🟦🏻⬛⬜⬜🟨⬜ ⬜🟨🟨⬜⬛🏻🏻⬛⬛🟥⬜⬛⬜🟨🟨⬜ ⬜⬜🟨🟨⬛⬜🟥⬛⬛⬜🟥⬛⬜🟨⬜⬜ ⬜⬜⬜⬜⬛🟥⬜⬛⬛⬛⬛🟨🟨⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠩⠠⠀⣠⣾⣿⣿⣿⣿⣟⠛⠉⠉⢻⣿⣧⡀⠀⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣿⣿⣿⣾⣿⣿⡟⣻⣿⣿⣟⣿⠛⢿⡶⠶⠶⢿⠿⠿⠟⠋⠉⠀⠘⢧⡴⠂⠄⢻⣿⣷⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠏⣸⣿⣿⣿⣿⡟⣽⠛⣿⢏⣿⡿⠁⣴⠀⠀⠀⠀⠈⠀⠀⣠⠀⠀⢀⣄⠈⢿⣿⣿⣿⣿⣿⣿⡉⣟⠙⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡜⠀⣿⣿⣿⢿⣿⣵⣯⠀⠛⢸⡿⠁⣼⡇⠀⠀⡄⠀⢰⡇⠀⢿⡀⠀⠀⣿⡀⠘⣿⢿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠁⢰⣿⢻⣿⣸⣿⣿⣿⡄⠀⢸⡇⢰⢿⡧⠴⢾⣿⡞⢿⢿⣦⢼⣷⣶⣶⣿⣷⡆⢹⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⣿⣿⣿⣿⣿⠂⣿⣇⡿⢸⡇⣆⣾⢿⡇⢸⠈⣿⢸⣿⣿⣿⣿⣿⣿⣼⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⠇⢸⠋⣇⣿⢸⡇⣾⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠆⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣶⣾⣿⠚⣿⣿⠀⠘⣿⣿⢻⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⠈⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣽⣿⣿⡗⠀⠉⠉⠀⠀⠉⠁⠀⣛⣦⣭⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⡇⠀⣿⣿⡇⢿⣿⣿⣿⣿⣿⣿⣏⠀⢸⡹⣿⣽⠛⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⢻⢽⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢱⡀⢸⣿⣿⠈⣿⠋⠸⣿⣿⣿⣟⠓⠚⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠾⢿⣿⣿⣿⢷⣾⣿⣿⣿⡿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⡈⣿⣿⣇⢸⣧⡔⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⢂⣩⣿⣿⣿⣇⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢉⡟⠛⢿⣮⢿⣝⣿⣿⣿⡟⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣀⣸⣿⣿⣟⣿⣿⣿⣿⣿⢸⣿⡇⠀⠀⠀ ⠀⠀⢰⠋⢹⣄⣀⡶⠛⢲⣀⣀⢻⣿⣿⣿⣿⣿⣷⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⡇⠀⠀⠀ ⠀⠀⢿⣷⣶⡟⠁⠁⡀⢸⠻⣿⡟⢁⣼⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠘⠻⠯⠭⠭⠽⠆⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡿⢸⣿⣿⡇⠀⠀⠀ ⠀⠀⢸⣿⣿⣶⣦⣤⣷⣾⣷⣾⣿⣿⣿⠘⣿⣿⣿⣿⠻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣷⣿⣿⣿⣿⣿⡟⠃⣿⣿⣿⣧⠀⠀⠀ ⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡇⣿⣿⣿⣿⣆⢹⣿⣿⢿⣶⣤⣀⠀⣀⣠⠶⣾⡏⠁⣿⣿⣿⣿⣽⣿⣿⣿⡿⠁⣸⣿⣿⣿⣧⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣷⢿⣿⣿⣿⣿⠀⣿⣿⠙⣿⡿⠟⠋⠁⠀⠀⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃⢠⣿⡏⣿⣿⣿⡆⠀⠀ ⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣿⣾⡿⣿⣿⣿⠀⣻⡏⢰⠏⠀⠀⠀⠀⣠⠔⠙⣧⣾⡏⢸⣿⣿⣿⣿⣿⡏⠀⣾⡿⡇⣿⣿⣿⠇⠀⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⣇⣿⣿⡿⠀⣿⡷⠏⠀⠀⢀⣠⠞⠁⠀⠀⠙⣿⣿⣨⣿⣿⣿⣿⣿⠁⣼⡿⢹⠁⢹⣿⣿⡀⠀⠀ ⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠹⣿⣿⣿⡇⢸⣿⣷⣦⣤⣤⣈⣀⣠⣤⣴⣶⣾⣿⢻⣿⣿⣿⣿⡍⠀⣸⣿⠇⢸⠀⢸⣿⣿⣇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⣿⡿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣰⣿⣿⣄⣰⠞⢸⣿⣿⣿⡗⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣾⣟⠃⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢘⣿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⠛⠉⠉⠀⣀⣀⣀⣀⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠟⠋⠁⢀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄ ⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⠿⠿⠟⠻⣿⡟⠋ ⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠉⠉⠉⠀⣀⣠⣤⣼⣿⠀⠀⠀⣼⣿⠇⠀ ⠀⣼⣿⣿⣿⣿⣿⡿⣿⣿⠉⢽⣿⠿⣦⠀⢰⡿⢿⣿⠉⢹⣿⠀⠀⠀⠙⣿⣧⠀ ⣸⣿⣿⣿⠿⠋⠁⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⣿⠀ ⢿⡿⣿⣷⡀⠀⠀⠀⣿⣿⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⣸⣿⠀⠀⠀⣰⣿⡏⠀ ⠀⠀⠘⠿⣿⣶⠀⠀⠸⣿⣦⡀⠀⠙⠿⠿⠿⠛⠁⢀⣴⣿⡟⠀⠰⣿⡿⠋⠀⠀ ⠀⠀⠀⠀⢿⣿⡄⠀⠀⠈⠻⣿⣷⣦⣄⣀⣀⣤⣾⣿⠟⠋⠀⠀⢠⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣦⣤⣤⣴⣿⡿⠛⠻⠿⠟⠛⢿⣷⣤⣤⣤⣴⣿⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠀⢀⡤⣖⡫⠭⠭⠭⠭⣍⣑⣒⣒⣒⣻⠭⢝⠲⣄⡀⠀⠀⠀ ⠀⠀⠀⢀⡾⠁⠠⢖⡽⣪⡑⠬⡭⠭⢙⡄⠀⠀⠀⢐⠒⠒⠒⢤⠀⠀⠹⡄⠀⠀ ⠀⠀⣠⡞⠁⠀⠀⢈⡜⠁⠁⣠⣭⣄⠐⢈⢦⠀⠀⢠⠒⠈⠉⣩⠉⠲⢄⢷⡀⠀ ⠀⡴⡻⢛⣩⠥⣄⡙⢆⢀⠄⠛⠿⠋⠀⠅⡼⠁⠲⣇⠁⠀⠺⣿⠗⠀⢄⡧⡹⡆ ⢸⢱⢀⡏⠀⣰⣄⡉⠀⠉⠒⠛⠓⠚⣚⡉⠀⠀⠀⢯⣐⠠⠴⠤⠄⡒⠛⢸⢰⡇ ⢸⡄⡈⡇⠉⢻⡀⠙⢳⣦⣄⡉⠉⠁⣏⠤⠦⠄⠀⠀⡽⠇⠄⡀⢀⣿⡄⡊⢲⠇ ⠀⠻⣌⠒⠀⠈⣿⣶⣬⣧⣀⠉⠙⡷⠶⠤⢤⣄⣘⣛⣁⣠⣤⠖⡏⢻⡇⢠⡏⠀ ⠀⠀⠘⢧⠀⠀⣿⣿⣿⣿⣿⣿⣶⣧⣤⣀⣸⣇⣀⣸⣀⣀⣼⣤⣿⣾⣷⠘⡇⠀ ⠀⠀⠀⠘⢧⡀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀ ⠀⠀⠀⠀⠈⠻⣆⠹⣌⢻⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠈⢳⡈⠻⣀⠀⠈⡟⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⠓⢾⣇⡀⠀⢸⡇⠀⢸⠏⠉⡏⢹⣃⣷⠃⢠⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣌⣉⠙⠛⠓⠒⠚⠓⠚⠋⠉⠉⣀⣠⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀

⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀ ⠸⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⡏ ⠀⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⠁ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠀⢀⣴⡟⠀⠀⠀⠀⢠⣟⠛⠛⠛⠛⠛⠛⣣⡀⠀⠀⠀⠀⠹⣷⡀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀ ⠀⠀⠉⠛⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣰⣿⣿⣦⠀⠀⠀⠀⣰⣿⣿⣄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠛⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⠿⣿⣿⡀⠀⠀⣴⣿⣿⣿⣿⣷⡀⠀⣼⣿⣿⣿⣿⣦⠀⠀⠀⣿⣿⡿⠿⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣤⣶⣿⣿⡇⠀⠼⠿⠿⠿⠿⠿⠿⠷⠾⠿⠿⠿⠿⠿⠿⠷⠀⢰⣿⣿⣷⣦⣤⣤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢁⣹⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⢠⣆⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⡀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⠿⠟⠛⠉⠁⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢀⣾⣿⣆⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠉⠛⠻⠿⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⡿⠋⣸⣿⣿⣿⣿⡿⠃⢀⣾⣿⣿⣿⡄⠀⠿⣿⣿⣿⣿⣯⠈⢿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⠋⠀⢠⣿⣿⣿⡏⠀⠀⢀⣼⣿⣿⣿⣿⣷⡀⠀⠀⠘⣿⣿⣿⡆⠀⠙⢿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⠟⠁⠀⠀⣾⣿⣿⣿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⡿⠂⠀⠀⢿⣿⣿⣿⡀⠀⠀⠙⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⣸⣿⣿⣿⡇⠀⢠⣤⡀⠉⢻⣿⣿⣿⠋⠀⣠⣄⠀⠘⣿⣿⣿⣧⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠀⢠⣿⣿⠃⠀⢸⣿⣿⣿⠀⠈⢿⣿⣇⠀⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⢸⣿⣿⣿⠂⠀⠈⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡿⠿⠿⠿⣿⣿⡆⠀⠀⠈⢿⣿⠃⠀⠀⠰⣿⣿⠿⠿⠿⢿⣿⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢧⡀⠀⠀⠘⠉⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠈⠛⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣄⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢷⢽⢦⡀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠳⡙⢦⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⡦⣄⣀⠀⠀⠀⠀⠀⠈⢷⡙⢦⡙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠻⣮⡿⣿⢶⣤⣀⠀⠀⠀⠻⣄⠙⢦⡙⠿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢨⠻⣮⣝⠲⢌⣙⠒⠦⣤⣈⡳⣤⡉⠲⢬⡑⠿⣟⣷⢶⣤⣤⣄⣀⣤⣀⣀⣄⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣿⡷⣿⣿⣶⣬⣙⠲⢤⣀⡉⠙⠛⠳⢤⣈⡑⠲⠬⣍⣉⡒⠛⠛⠛⣿⠛⠛⠻⠭⣍⣉⣉⣛⣛⠻⠷⣶⣤⣄⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣿⣗⠦⣍⡙⠛⠶⢦⣍⡙⠒⠦⢤⣄⣉⠓⠲⢦⢤⣭⡤⠶⠒⠚⢷⣦⣀⠀⠸⣧⡄⠀⠉⠙⠒⠀⠈⠙⠳⡿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣶⣶⣽⣷⣦⣍⣑⠒⠤⢌⣉⣙⠒⠶⠤⢬⣹⣿⣄⢹⣇⡒⠒⠦⠤⡸⣧⡉⠛⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠻⢾⣕⡺⠭⣙⣛⠲⠶⢦⣭⣍⣑⣒⠒⠒⠒⠂⠉⠉⢛⡖⠆⣀⣀⣈⣙⣶⠒⠒⠚⠀⠀⠀⠀⠀⢀⣠⣤⣀⣀⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⢓⣶⣬⣍⣑⣒⣶⠶⠭⠭⠭⠉⠉⠉⠍⠭⠉⠙⠶⣥⣄⣀⣀⣩⣿⡓⠒⠀⠀⠀⠀⠀⢻⣁⣀⠀⠈⠙⢦⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣭⣉⠉⢭⣉⡛⠛⠓⠒⠲⠶⠶⠶⠶⠖⠒⠒⣚⡩⠍⠉⢻⣍⣤⠀⠀⠀⠀⠀⠀⠀⢾⡉⠉⠛⠓⠀⠀⠈⣇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣻⣳⣶⣮⣭⣭⣍⣉⣉⣉⣉⣉⣉⣭⣭⠤⠴⠒⢋⡿⢋⠤⠔⠒⠊⠉⢀⡴⠚⠛⢛⠓⠶⠆⠀⠀⠀⢻⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣍⣧⡤⠭⣍⣉⣉⣉⣉⣀⣠⡤⠤⠴⠒⠊⣉⣨⠿⠒⠒⢶⣛⣀⣠⣞⣛⣶⠖⠲⠶⠀⠀⢀⡄⠀⠸⡦⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⡶⣶⣦⣤⣤⣿⡦⠤⠴⠖⠛⠋⣉⣀⠤⠔⣀⡤⢿⣛⡩⢤⣈⣻⡤⠶⠆⠀⠀⡞⠁⠀⠀⠉⢽⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢯⣭⣓⣀⣤⣒⣒⣒⣾⣉⣉⣁⣤⡴⢚⡥⠖⢋⣥⠶⠚⡉⠉⢧⣤⣤⠀⠸⢿⡶⠃⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣽⣯⣭⡥⠴⢻⡟⠘⣉⣠⡾⢋⡤⠖⣭⡴⢖⠻⣯⡴⠗⠀⠀⣧⣠⡆⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢛⣿⣫⠖⠉⣰⠟⣡⠖⢉⣾⣏⣀⣠⢤⡄⠈⣿⣠⡗⢀⠀⠀⠀⠙⠻⣦⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣁⣱⣶⡞⣡⠞⣁⡴⢋⡴⢋⡿⢶⡟⠀⠀⠈⢻⣀⡿⠀⢀⡇⠀⠀⠀⠈⠙⠓⠶⢤⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢠⡟⡝⣡⣾⢋⡴⠋⣴⠏⣠⠋⣿⠦⣶⠀⢈⠿⣧⢀⣾⣷⡀⢠⡀⠀⠀⠀⠀⠁⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠚⣹⣣⢞⣷⣿⢇⡼⣡⣿⣵⢃⣾⡟⣹⢠⢸⢩⠘⡏⣳⡞⢧⣀⣿⣦⣷⢀⡞ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠷⠛⠁⣿⣿⡾⢛⣿⣡⢾⣹⢡⣿⡏⣾⣼⢠⣿⡇⣷⣀⣽⠀⢨⢉⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠋⠁⢸⣷⠟⣿⣣⠟⣿⡾⣿⣷⡏⠛⠛⠶⠾⠾⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢷⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸⠀⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡰⢸⢰⢸⢆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⠃⣸⠂⡘⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠘⢠⠃⢀⠃⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⠃⠎⢀⠎⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢳⢁⠎⢀⠎⠀⠀⢠⠓ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢃⢃⠂⡠⠃⠀⠀⠠⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢃⠚⣇⠜⠀⠀⢀⠔⠁⢀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡱⠋⡿⠁⠀⢀⠔⠁⠀⠀⠁⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⣡⡞⢠⢮⣊⡠⠀⠁⠀⠀⠀⢀⡴⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠒⣉⡤⢺⢛⠂⢠⠏⠁⠀⠀⠀⣀⠠⠐⠋⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⣠⠴⠊⠁⢀⡮⢊⣴⣯⡤⠄⠒⠀⠉⠀⠀⠀⡼⠀⠀ ⠀⠀⠀⠀⠀⢀⠞⢁⡴⠋⠁⠀⠀⣠⠞⠁⢁⣼⠉⠉⠓⠶⢤⣤⣤⣤⣊⠀⠀⠀ ⠀⠀⠀⢀⠔⠁⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⡔⠃⠁⠂⠤⢀⡀⢀⣀⠴⠃⠀⠀⠀ ⠀⠀⡠⠋⠀⢰⠇⠀⠀⠀⠀⠀⢀⣠⠶⢏⠀⠀⠀⠀⠀⠀⣀⡉⠇⠀⠀⠀⠀⠀ ⢀⡜⠁⠀⠀⣿⠀⠀⠀⠠⡤⠴⠚⢦⡀⠀⠉⠒⠤⣀⣀⣀⠝⠀⠀⠀⠀⠀⠀⠀ ⢸⡀⠀⠀⣠⠟⠉⠉⠙⠒⠟⡀⠀⠀⢉⠓⢦⣄⣠⠤⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠑⠋⠁⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⠏⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⡲⠖⠛⠉⠉⠉⠉⠉⠙⠛⠿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣡⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢡⣶⠏⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣶⣶⣦⣄⣸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⢀⣿⠏⠀⠀⠀⠀⠀⠀⠸⠿⠋⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡼⢿⣦⣄⠠⠤⠐⠒⠒⠒⠢⠤⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠠⠇⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣁⠀⣀⣤⣴⣾⣿⣿⣿⣿⡿⢿⣿⣶⣄⠀⠀⠀⠀⠀⣿⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⡇⠘⠟⣻⣿⣧⠀⠀⠀⠀⢿⣿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠸⣿⠿⠋⠉⠁⠛⠻⠿⢿⣧⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠋⠁⠀⢀⣄⡀⠀⠀⠀⢀⣀⣤⣴⣿⣿⣧⠀⢀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⠏⢀⠀⢀⡴⠿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣇⠀⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣤⣿⣷⡈⠀⠀⠀⠙⠻⣿⣿⣿⣿⠿⠛⠛⣻⣿⣿⡄⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠈⠋⢉⣠⣴⣾⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⢻⡏⢹⠙⡆⠀⠀⠀⠒⠚⢛⣉⣉⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⠁⠉⠀⠁⠀⣄⣀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠛⠋⠉⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣻⠿⠿⢿⣿⠿⠿⠋⠁⠀⠙⣿⡁⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣹⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣄⣀⣀⡄⠀⣀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⢰⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀ ⠀⠀⠀⢀⣤⣤⣤⣶⣿⣿⣿⣿⠿⠿⠟⠋⢹⠇⠀⠀⢀⣼⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢀⡏⠀⠀⢀⣾⠋⣹⣿⣿⣿⡟⠀⠀⣸⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⡼⠀⠀⢀⣾⠏⢀⣿⣿⣿⠋⠀⠀⣰⣿⣧⡀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇

⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢸⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣿⣶⣄⡀⠀⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠀⢀⣠⣶⣿⡿⠀⠀⠀⠀⠀ ⠐⣶⣤⣀⠀⠈⠻⣿⣿⣿⣦⣄⠙⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⠋⣠⣴⣿⣿⣿⠟⠁⠀⣀⣤⣶⠂ ⠀⠹⣿⣿⣿⣶⣄⡈⠛⢿⣿⣿⣷⣤⡙⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⢋⣤⣾⣿⣿⡿⠛⢁⣠⣶⣿⣿⣿⠏⠀ ⠀⠀⠈⠻⣿⣿⣿⣿⣶⣄⡈⠻⣿⣿⣿⣦⡙⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡿⢋⣴⣿⣿⣿⠟⢁⣠⣶⣿⣿⣿⣿⠟⠁⠀⠀ ⢶⣦⣤⣀⠈⠙⠿⣿⣿⣿⣿⣶⣌⡙⢿⣿⣿⣦⡻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⢟⣴⣿⣿⡿⢋⣡⣶⣿⣿⣿⣿⠿⠋⠁⣀⣤⣴⣶ ⠈⢿⣿⣿⣿⣶⣤⣀⠉⠻⢿⣿⣿⣿⣦⣝⠿⠿⢿⣦⣼⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣧⣴⡿⠿⠿⣫⣴⣿⣿⣿⡿⠟⠉⣀⣤⣶⣿⣿⣿⡿⠁ ⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣤⣉⠻⢿⣿⣿⣷⣤⣼⣿⣿⣿⡛⠿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⢛⣿⣿⣿⣧⣤⣾⣿⣿⡿⠟⣉⣤⣾⣿⣿⣿⣿⣿⡿⠋⠀⠀ ⢀⣤⣄⣀⣈⠉⠛⠻⢿⣿⣿⣿⣿⣶⣍⡉⢹⣿⣿⣿⡟⠛⢿⣦⣼⣿⣄⠀⠀⠀⠀⠀⠀⣠⣿⣧⣴⡿⠛⢻⣿⣿⣿⡏⢉⣩⣴⣿⣿⣿⣿⡿⠟⠛⠉⣁⣀⣠⣤⡀ ⠀⠻⣿⣿⣿⣿⣿⣶⣦⣌⣙⠻⢿⣿⡿⣿⣿⣿⣿⠿⢿⣦⣀⠙⠿⠿⠿⠃⠀⠀⠀⠀⠘⠿⠿⠿⠋⣀⣴⡿⠿⣿⣿⣿⣿⢿⣿⡿⠟⣋⣡⣴⣶⣿⣿⣿⣿⣿⠟⠀ ⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣸⣿⣿⡿⢷⣦⣈⣻⣿⣶⣿⡿⠆⠀⠀⠀⠀⠰⢿⣿⣶⣿⣟⣁⣴⡾⢿⣿⣿⣇⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀ ⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⢿⣿⣿⣤⣴⣿⡿⠟⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠻⢿⣿⣦⣤⣿⣿⡿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⣾⣿⣶⣶⣶⣦⣤⣍⣙⣁⠈⣿⣿⡿⢿⣿⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⣿⡿⢿⣿⣿⠁⣈⣋⣩⣤⣴⣶⣶⣶⣿⣷⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣿⣦⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣴⣿⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠿⠿⢿⠟⠹⣿⣿⡿⢿⣿⡘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⣿⡿⢿⣿⣿⠏⠻⡿⠿⠿⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣶⣶⣶⣶⣶⣶⣿⣿⣧⣀⡙⢷⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡾⢋⣀⣼⣿⣿⣶⣶⣶⣶⣶⣶⣶⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⠛⢿⣿⡟⢶⡝⣿⣆⠀⠀⠀⠀⠀⠀⢰⣿⢫⡶⢻⣿⡿⠛⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣿⣷⣾⡿⠈⠻⠆⠀⠀⠀⠀⠰⠟⠁⢿⣷⣾⣿⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⡏⠻⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠟⢹⣿⣿⣿⡿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠟⢡⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠙⢿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⡏⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠈⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⡏⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠁⣿⣄⠀⠀⠀ ⠀⠀⢀⡾⠁⣇⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢠⡇⠹⣆⠀⠀ ⠀⠀⢸⡁⠀⣿⠑⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢩⡇⠀⢹⠀⠀ ⠀⠀⢸⣧⡀⣿⣆⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⢀⣼⠇⢠⣾⠀⠀ ⠀⢠⠾⡇⠁⠘⣿⡉⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⣹⡿⠀⠀⡿⢦⠀ ⠀⡿⠀⢿⣆⠀⠱⣿⡆⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⣾⣿⠁⢀⣼⠃⠘⡆ ⠀⣿⡀⢈⢷⡀⠀⠱⡿⣦⣀⡀⢰⡹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢣⠀⢀⣠⣾⡿⠁⠀⣠⠏⠀⢰⡇ ⣴⢿⡄⠈⢯⢿⡖⠀⣿⢿⢷⣍⣈⣷⡈⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⣰⡟⢀⣹⢿⣿⡇⠐⣺⣯⠇⠀⣸⢧ ⣏⠈⢷⣄⠀⠳⣿⣦⣌⣻⣿⡏⠙⠻⣟⠀⠀⠈⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠁⠀⢸⡿⠛⠉⢿⡿⢋⣠⣾⡿⠋⢀⣴⠏⠈ ⠹⡄⠈⣿⣅⠀⠘⣿⣷⣍⢻⣇⣷⠄⠈⠳⣤⡀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⣀⣴⠋⠀⢠⡇⣾⢋⣤⣿⡿⠁⢀⣽⠋⠀⡴ ⠀⢻⠦⠹⣝⣷⡂⠈⣿⣿⠛⠻⣮⡃⠀⠀⣿⣿⡶⣄⣀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠁⠀⢀⣀⡴⣾⣽⡿⠀⠀⣾⡿⠛⠻⣿⡟⠀⣲⣿⡽⠡⢾⠃ ⠀⠈⣷⣄⠈⠳⣝⣧⡀⢿⣷⣀⠈⠙⠶⣄⡚⠽⣿⣿⡉⠙⠂⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠘⠋⣝⣿⣻⠕⣂⣴⠞⠉⠀⣠⣿⠇⣠⢾⡿⠋⢀⣰⡏⠀ ⠀⠀⢸⠙⢯⣅⠀⢽⡯⣿⢷⣽⣂⠀⠀⣓⡯⣗⣾⣷⣄⡀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣀⣽⣿⣖⡿⣟⡋⠀⢀⣺⣷⢿⣻⣿⠉⢀⣩⠟⢹⠃⠀ ⠀⠀⠈⢧⡀⠙⣿⣇⣉⠻⣿⡋⠉⠓⠶⡤⢭⣽⣿⡅⠀⠀⠀⠀⣴⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⣽⣿⣭⠥⠴⠖⠋⠉⣻⡿⢋⣁⣽⡟⠁⣠⠟⠀⠀ ⠀⠀⠀⠘⣿⡂⠈⠓⢯⣷⣿⣿⣾⠤⠀⠩⠭⢽⣿⣦⡴⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠰⣦⣾⣿⠭⠭⠁⢀⣬⣾⣿⣷⣿⠟⠋⠀⣺⡿⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⢶⣤⠀⠈⠻⣿⣿⣿⠶⠶⠶⣒⣿⣿⡶⠀⡀⠀⠈⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠀⠀⣄⠠⣼⣿⣖⡒⠲⠶⢾⣿⣿⡿⠉⠀⢠⣴⠾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⣼⣟⡁⠀⠀⢀⣀⡭⣟⣿⣾⠁⠀⡀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⣀⢀⢹⣿⣿⣿⣅⣀⠀⠀⠀⠘⣿⡔⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣃⣴⠞⠋⠁⠈⣛⣽⣿⣶⣾⠃⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⡼⠋⠀⢀⢀⢹⣾⣿⣿⢯⡋⠁⠉⠙⢶⣄⣻⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣶⡀⢠⠞⠁⠉⣵⣿⣿⣦⣼⡀⠀⠀⠙⢦⡀⠀⠀⣠⠞⠁⠀⠀⣸⣾⣾⢿⢷⣍⠀⠙⢦⣀⣰⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⢶⡏⠀⠀⡼⠁⢉⡿⠋⡽⠉⠉⠉⠓⠚⠉⠀⠀⠙⠒⠋⠉⠉⠹⡍⠿⣇⠁⠹⡆⠀⣈⢿⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠭⠿⣧⣖⣼⡧⢦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠢⢻⣔⣲⡿⢿⡽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣄⠀⢰⡟⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢻⡆⠀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⢿⣧⣼⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣧⣼⠿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠙⣿⠇⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠸⣿⠋⠀⣿⠀⠀⠀⠀ ⠀⢀⣄⠀⣿⠀⠀⢸⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⡇⠀⠀⣿⠀⣠⡀⠀ ⠀⢸⡟⠳⢿⡆⠠⠘⡄⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⢰⠃⡄⢸⡿⠞⢻⡇⠀ ⠀⠸⣇⠀⠈⡆⠀⠀⢧⠨⠿⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠴⠇⡼⠀⠂⢸⠁⠀⣸⠇⠀ ⠀⠀⣿⣄⠀⠹⡀⠀⠸⡄⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⢠⠇⠀⢀⡇⠀⢠⡿⠀⡀ ⢿⡟⠛⢿⠀⠀⢣⡀⠀⢳⡀⠸⡁⠹⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⢸⠇⢀⡎⠀⢀⡞⠀⠀⡽⠛⢻⡟ ⠘⣷⡀⠈⢣⡀⢀⠱⡀⠀⡷⣀⢧⠀⠈⠙⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⠋⠀⠀⡜⢀⢾⠀⢀⠎⡀⢀⡜⠁⢀⡾⠃ ⠀⠈⢻⣆⠀⠙⢔⠂⠈⠲⣇⠈⠙⠓⠦⠄⠀⠀⠉⠻⡇⠀⠀⠀⠀⢸⠛⠉⠀⠀⠤⠴⠚⠋⠁⣸⠖⠁⠀⡢⠊⠀⣰⡟⠁⠀ ⠀⣶⡶⠿⠛⢄⡈⠑⢤⣰⣼⣦⣀⠀⠀⠀⢠⡄⡄⢰⡇⠀⠀⠀⠀⢸⡀⢠⢤⡄⠀⠀⠀⢀⣴⣣⣄⡤⠊⠀⡠⠟⠿⢶⣶⠂ ⠀⠈⠛⣶⣄⡀⠈⠒⢤⣈⣣⡈⠉⠉⠁⠀⠀⠃⠀⢸⡇⠀⠀⠀⠀⢺⡇⠀⠈⠀⠀⠉⠉⠉⢁⣞⣁⡤⠒⠉⢀⣠⣶⠛⠁⠀ ⠀⠀⢿⣟⠋⠙⠢⢄⡀⠀⢉⠑⢤⣀⣀⡀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⣀⣀⡠⠊⡉⠀⢀⡠⠔⠋⠙⣻⡿⠀⠀ ⠀⠀⠀⠙⢷⣤⡄⠀⠈⠙⠻⡍⠉⠉⠁⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠉⠉⠉⢩⠿⠋⠁⠀⢠⣤⡾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⢉⣻⣶⡤⠤⠤⠬⠶⠦⣴⡶⠛⠀⢀⣠⣿⠀⠀⠀⠀⣿⣄⡀⠀⠛⢶⣦⠤⠶⠥⠤⠤⢴⣶⣟⡉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠻⢿⣤⣄⣀⣀⣀⣀⣬⡿⠚⠉⢉⣼⠏⠀⠀⠀⠀⠹⣧⡉⠉⠛⢿⣥⣀⣀⣀⣀⣠⣤⡿⠟⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⣿⣋⣀⣤⠾⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⣀⣙⣿⣿⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠖⠛⠛⠙⠙⠘⠓⠒⠛⠀⠓⠟⠛⠓⠀⠐⠓⠞⠟⠛⠚⠓⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣖⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣲ ⣹⣦⣝⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⣫⣾⡏ ⠘⢾⣝⢷⣬⡛⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⢛⣵⡾⣫⡿⠃ ⠀⠰⣝⣿⣾⣿⣷⣭⡛⢷⣦⡀⠀⠀⠀⠀⠀⠀⢠⣴⡾⣛⣥⣾⣿⣷⣿⣫⠆⠀ ⠀⠀⠈⠻⢯⣿⣿⣿⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡷⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⡿⠟⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⣿⣧⠀⠀⠀⠀⠀⠀⣼⡿⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣿⣿⣿⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠺⠶⢶⣦⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣴⣶⠶⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠿⠿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠿⠿⠄⠀⠀⠀⠀⠀⠀ ⠀⢴⠶⠶⠾⠟⣧⡴⠶⠖⠚⠛⠉⠉⣉⡉⠉⠉⠛⠒⠶⠶⣦⣼⠻⠷⠶⠶⡦⠀ ⠀⠀⠀⠀⠀⠀⢁⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⡉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀ ⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀ ⠀⢠⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⡄⠀ ⢠⣿⣿⣿⣿⣿⣏⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⣹⣿⣿⣿⣿⣿⡄ ⣸⣿⣿⣿⣿⣿⣿⡄⠀⠈⠻⠿⠿⠇⠀⠀⠸⠿⠿⠟⠁⠀⢠⣿⣿⣿⣿⣿⣿⣇ ⠻⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠟ ⠀⠀⠉⠛⠻⠿⠿⣿⣇⠀⠀⠀⠀⢰⣶⣶⡆⠀⠀⠀⠀⣸⣿⠿⠿⠟⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠙⠋⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⡀⠀⠀⢀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛🏻🏼🏼🏻🏻🏼⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛🏼🏻🏻🏻🏻🏼🏻🏻⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🏼🏻🏼🏼🏻🏼🏼🏻🏼🏼⬛⬜⬜⬜⬜ ⬜⬛⬛⬜⬜⬛🏼🏻🏼🏼🏻🏻🏻🏻🏻🏼⬛⬜⬜⬛⬛ ⬜⬛🟫⬛⬜⬛🏻🏻🏻🏻🏼⬜⬜🏼⬜🏻⬛⬜⬛🟫⬛ ⬜⬜⬛🟫⬛⬛🏻🏼🏻🏼⬜⬛⬛🏻⬛⬜⬛⬛🟫⬛⬜ ⬜⬜⬜⬛🟫⬛🏼🏻🏼🏻⬜⬛⬛🏼⬛⬜⬛🟫⬛⬜⬜ ⬜⬜⬜⬜⬛🟫⬛🏻🏼🏻🏼⬜⬜🏻⬜🏼⬛⬛⬜⬜⬜ ⬜⬜⬜⬜⬛⬛⬛⬛🏻🏼⬛⬛⬛🏼🏻⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬛⬛⬛⬛⬛⬛🏼🏻🏼🏻🏼⬛⬛⬛⬛⬜⬜⬜ ⬜⬜⬛🟥🟥⬛⬛⬛🟥⬛⬛⬛⬛⬛⬛⬛🟥🟥⬛⬜⬜ ⬜⬛🟥🟥🟥⬛⬛⬛⬛🟥🟥🟥⬛⬛⬛⬛🟥🟥🟥⬛⬜ ⬜⬛⬛⬛⬛⬛⬛⬛🟥🟥🟥🟥🟥⬛⬛⬛⬛⬛⬛⬛⬜ ⬜⬛🟥🟥🟥⬛⬛⬛🟥🟥🟥🟥🟥⬛⬛⬛🟥🟥🟥⬛⬜ ⬜⬛🟥🟥🟥⬛⬛⬛🟥🟥🟥🟥🟥⬛⬛⬛🟥🟥🟥⬛⬜ ⬜⬜⬛⬛⬛⬜⬛🟫🟫🟫⬛🟫🟫🟫⬛⬜⬛⬛⬛⬜⬜ ⬜⬜⬜⬜⬜⬛⬛⬛🟥🟥🟥🟥🟥⬛⬛⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛⬛🟥🟥🟥🟥⬛🟥🟥🟥🟥⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬛⬛🟥🟥🟥🟥⬛⬜⬛🟥🟥🟥🟥⬛⬛⬜⬜⬜ ⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜ ⬛⬛⬛🟥🟥🟥🟥🟥⬛⬜⬜⬜⬛🟥🟥🟥🟥🟥⬛⬛⬛ ⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛

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⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬛🟫🟫🟫🟫🟫🟫⬛⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛🟫🟫🟫🟫🟫🟫🟫🟫⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬛🟫🟫🟫🟫🟫🟫⬛⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛🟪🟪🟫🟫🟫🟫🟫🟫🟪🟪⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛🟪⬜⬜🟪🟫🟫🟫🟫🟪⬜⬜🟪⬛⬜⬜⬜⬜ ⬜⬜⬜⬛🟫🟪⬜⬛🟪🟫🟫🟫🟫🟪⬜⬛🟪🟫⬛⬜⬜⬜ ⬜⬜⬜⬛🟫🟫🟪🟪🟫⬛⬛⬛⬛🟫🟪🟪🟫🟫⬛⬜⬜⬜ ⬜⬛⬛🟫🟫🟫🟫🟫⬛🟫🟫🟫🟫⬛🟫🟫🟫🟫🟫⬛⬛⬜ ⬛🟫⬛🟫🟫⬛🟫🟫⬛🟫🟫🟫🟫⬛🟫🟫⬛🟫🟫⬛🟫⬛ ⬛🟫🟫🟫⬛🟫🟫⬜🟫🟫🟫🟫🟫🟫⬜🟫🟫⬛🟫🟫🟫⬛ ⬜⬛⬛🟫🟫🟫🟫🟫⬜⬜⬜⬜⬜⬜🟫🟫🟫🟫🟫⬛⬛⬜ ⬜⬜⬜⬛🟫🟫🟫🟫🟫🟫🟫🟫🟫🟫🟫🟫🟫🟫⬛⬜⬜⬜ ⬜⬜⬜⬜⬛🟫🟫🟫🟫🟫🟫🟫🟫🟫🟫🟫🟫⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬛🟫🟫🟫🟫🟫🟫🟫🟫⬛⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜

⬜⬜🟫🟫🟫🟫🟫🟫🟫🟫🟫⬜⬜ ⬜🟫🟫🟫🟫🟫🟫🟫🟫🟫🟫🟫⬜ 🟫🟫🟫🟫🟫🟫🟫🟫🟫🟫🟫🟫🟫 🟫🏻🟫🟫🟫🏻🟫🏻🟫🏻🟫🟫🟫 🟫🟫🏻🟫🏻🟫🏻🟫🏻🏻🟫🏻🟫 🟫🏻🟫🏻🟫🏻🏻🟫🏻🟫🏻🟫🟫 🟫🏻🏻🏻🟦🏻🏻🏻🟦🏻🏻🏻🟫 🟫🏻🏻🏻🟦🏻🏻🏻🟦🏻🏻🏻🟫 🏻🟫🏻🏻🏻🏻🏻🏻🏻🏻🏻🟫🏻 🏻🟫🏻🏻🏻🏻🏻🏻⬛🏻🏻🟫🏻 ⬜🏻🏻🏻🏻⬛⬛⬛🏻🏻🏻🏻⬜ ⬜🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻🏻⬜ 🏻⬛⬛🏻🏻🏻🏻🏻🏻🏻⬛⬛🏻 🏻⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛🏻 🏻⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛🏻 🏻⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛🏻 🏻⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛🏻 🏻⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛🏻 🏻⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛🏻 🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦 ⬜🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦🟦⬜ ⬜⬜🟦🟦🟦🟦⬛🟦🟦🟦🟦⬜⬜ ⬜⬜⬜🟦🟦🟦⬛🟦🟦🟦⬜⬜⬜

⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜ ⬜⬛⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬛⬜ ⬜⬛⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬛⬜ ⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜ ⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜ ⬛⬜⬜⬛⬛⬛⬛⬜⬜⬜⬛⬛⬛⬛⬜⬜⬛ ⬛⬜⬛⬜⬛⬛⬜⬛⬜⬛⬜⬛⬛⬜⬛⬜⬛ ⬛⬜⬛⬜⬛⬛⬜⬛⬜⬛⬜⬛⬛⬜⬛⬜⬛ ⬛⬜⬜⬛⬛⬛⬛⬜⬜⬜⬛⬛⬛⬛⬜⬜⬛ ⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛ ⬛⬜⬜⬜⬜⬜⬛⬜⬛⬜⬛⬜⬜⬜⬜⬜⬛ ⬜⬛⬜⬜⬜⬜⬜⬛⬜⬛⬜⬜⬜⬜⬜⬛⬜ ⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜ ⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⠿⠿⠆⠀⣼⣿⣿⣿⣿⣿⣿⣧⠀⠰⠿⠿⣿⣿⣿ ⣿⡿⢿⣷⣄⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣾⡿⢿⣿ ⠿⠇⠈⠙⠿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠘⠿⠋⠁⠸⠿ ⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠿⠿⢿⣿⠟⠀⠀⠀⠀⠀⠀⠀ ⣶⡄⠀⣠⣶⡄⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⢠⣶⣄⠀⢠⣶ ⣿⣧⣾⡿⠋⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠙⢿⣷⣼⣿ ⣿⣿⣿⣶⣶⡄⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⢠⣶⣶⣿⣿⣿

⠀⠀⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⠀⠀⠀ ⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀ ⢀⣆⠀⠈⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⢸⣿⣷⣶⣶⣶⠂⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣟⠁⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠸⣿⣿⣿⣿⣿⣶⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠙⢿⣿⣿⣿⣿⣿⡆⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠀⠀⠈⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⠁⠀⠀ ⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢻⣷⣄⣀⣀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣤⣤⣠⣾⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣻⣿⣿⣿⠿⠛⠛⠉⠉⠁⠀⠉⠉⠙⢻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣾⡿⢿⣿⣇⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠿⣿⣿⣦⠀⠀⠀⠀ ⠀⠀⣴⣿⠟⠁⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠈⣿⣿⣷⡄⠀⠀ ⠀⣼⣿⠃⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠃⢻⣿⣿⡄⠀ ⢸⣿⡇⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠃⠀⢻⣿⣿⡀ ⣿⣿⡇⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇ ⢿⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷ ⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇ ⠀⢻⣿⣿⣄⠀⠀⠀⠀⠀⠘⣿⡇⠀⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀ ⠀⠀⠹⣿⣿⣧⡀⠀⠀⠀⠀⢿⣿⡀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠀⠀ ⠀⠀⠀⠈⢿⣿⣿⣦⣀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣤⣾⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠋⠻⢿⣿⣷⣤⣸⣿⣿⣿⣇⣀⣀⣀⣤⣶⣿⣿⣿⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠀⠀⠀⠀⢤⠀⠙⢿⣿⣿⠟⠛⠉⢹⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠘⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀

⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⣠⣶⣶⣄ ⣿⣿⠿⠿⠿⠿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⠿⠿⣿⣿⣿⣿ ⣿⡿⠀⠀⠀⠀⣹⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣏⠀⠀⠈⠙⠋⠁ ⠀⠀⠀⣴⣾⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣷⣦⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⬜⬛⬛⬛⬛⬛⬜⬜⬛⬛⬛⬛⬛⬜ ⬜⬛⬜⬜⬜⬛⬜⬜⬛⬜⬜⬜⬛⬜ ⬜⬛⬜⬛⬜⬛⬜⬜⬛⬜⬛⬜⬛⬜ ⬜⬛⬛⬛⬜⬛⬜⬜⬛⬜⬛⬛⬛⬜ ⬜⬜⬜⬜⬜⬛⬜⬜⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜ ⬜⬜⬛⬛🟨⬛⬛⬛⬛🟨⬛⬛⬜⬜ ⬜⬛⬛🟨🟨🟨⬛⬛🟨🟨🟨⬛⬛⬜ ⬜⬛⬛🟨🟨🟨⬛⬛🟨🟨🟨⬛⬛⬜ ⬜⬛⬛🟨🟨🟨⬛⬛🟨🟨🟨⬛⬛⬜ ⬜⬛⬛🟨🟨🟨⬛⬛🟨🟨🟨⬛⬛⬜ ⬜⬛⬛⬛🟨⬛⬛⬛⬛🟨⬛⬛⬛⬜ ⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜ ⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜ ⬜⬜⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜ ⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜ ⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜ ⬜⬛⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬛⬜ ⬜⬛⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬛⬜ ⬛⬛⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬛⬛ ⬛⬛⬜⬛⬛⬛⬛⬛⬛⬛⬛⬜⬛⬛ ⬛⬛⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬛⬛ ⬛⬛⬜⬜⬛⬛⬛⬛⬛⬛⬜⬜⬛⬛ ⬜⬜⬜⬜⬛⬛⬜⬜⬛⬛⬜⬜⬜⬜ ⬜⬛⬜⬜⬛⬛⬜⬜⬛⬛⬜⬜⬛⬜ ⬜⬛⬛⬛⬛⬛⬜⬜⬛⬛⬛⬛⬛⬜ ⬜⬛⬛⬛⬛⬛⬜⬜⬛⬛⬛⬛⬛⬜

⠀⠀⠀⠀⠀⠀⣠⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⡏⠉⠉⠉⠉⠉⠉⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠀⣾⣦ ⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣀⠀⣾⣿⠀⠘⠋ ⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣀⠀⣾⣿⠀⠟⠉⠀⠀⠀ ⠀⠀⣿⣿⣇⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⠀⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀

⬜⬜⬜⬜⬜⬛⬛⬜⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛🟩⬛⬛🟩🟩⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬛🟩⬛🟩🟩🟩🟩⬛⬛⬛⬛⬜⬜⬜⬛⬛ ⬜⬜⬛⬛🟩⬛🟩🟩🟩⬛🟩🟩🟩⬛⬜⬛⬛🟩⬛ ⬜⬜⬛🟩⬛🟩🟩🟩⬛🟩🟩🟩⬛⬜⬛🟩🟩🏻⬛ ⬜⬜⬛🟩🟩🟩🟩🟩🟩🟩⬛⬛⬛⬛🟩🟩🏻🟧⬛ ⬜⬛🟩🟩🟩🟩🟩🟩🟩⬛🟩🟩🟩⬛🟩🏻🏻⬛⬜ ⬜⬛🟩🟩🟩🟩🟩⬛⬛⬜🟩🟩⬛⬛🟩🏻🟧⬛⬜ ⬜⬜⬛🟩🟩🟩⬛⬜⬛⬜🟩⬛🟩🟩⬛🟧⬛⬜⬜ ⬜⬛⬛🟩🟩🟩🟩🟩⬜⬛⬛🟩🟩⬛⬛⬛⬜⬜⬜ ⬛🟩🏽⬛🟩🟩🟩⬛⬛🟧⬛🟩⬛🟩🟩🟩⬛⬜⬜ ⬛🟩🏽⬛⬛⬛⬛🟩🟩🟩🟩⬛⬛🟩⬜⬜⬛⬜⬜ ⬛🏽🏽⬛⬛🟩🟩⬛⬛🟧🟧⬛🟩⬜⬜⬛⬜⬜⬜ ⬛🏽⬛⬛⬜⬛⬛🟩🟩⬛⬛🟩⬜⬜⬛⬜⬜⬜⬜ ⬛🏽⬛⬜⬛🟩🟩⬛⬛🟩⬛🟩⬜🏽⬛⬛⬜⬜⬜ ⬜⬛⬜⬜⬛🏽🟩🟩⬛⬛⬛⬛⬜⬛🟩⬛⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜⬛⬜⬛🟩🟩⬛⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛🏽🟩🏽⬛⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬜⬜⬜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣷⣆⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠋⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟⠁⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠯⠟⡿⠛⠧⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡿⠛⠋⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡆⣠⣴⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣦⣤⣔⠁⠀⣀⣤⡄ ⠀⠀⢀⣀⣴⣾⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡿⠋⠀ ⢸⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⠛⠉⠀⠀⠀ ⠀⠙⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⣿⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠀⣠⣿⠀⢸⣿⣿⣧⠀⣿⣄⠀⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣴⡞⠁⣰⣿⡿⠀⣿⣿⣿⣿⡄⢸⣿⣆⠈⢳⣦⣀⠀⠀⠀⠀ ⠀⢀⣤⣾⣿⠟⢀⣼⣿⣿⡇⢠⣿⣿⣿⣿⣧⠀⣿⣿⣧⡀⠻⣿⣷⣤⡀⠀ ⢴⣿⣿⣿⠋⢠⣾⣿⣿⣿⠀⣸⣿⣿⣿⣿⣿⠀⢻⣿⣿⣷⡄⠙⣿⣿⣿⡆ ⠀⠉⠉⠁⠰⠿⠿⢿⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇⠘⣿⡿⠿⠿⠆⠈⠉⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⡻⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡿⡘⡀⠀⠀⠀⠰⡀⠀⢦⡌⠉⠁⠒⠢⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⠀⠘⠦⣀⠀⠀⠙⢶⠏⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠒⠢⢄⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⣀⣀⣀⣀⣳⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⢿⣮⣦⣤⣤⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣧⣀⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢿⣿⣿⣿⣶⣾⡿⠁⣠⠁⠇⣀⡤⠤⡞⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⡖⠫⢋⠈⠋⠉⠉⠛⠛⠉⣀⠴⡁⠀⠀⡨⢀⡄⢣⠀ ⠀⠀⠀⠀⠀⢀⡴⢚⠍⠈⢠⠔⠁⠀⠀⠀⠀⠀⡠⢒⠋⠀⠸⠀⣞⠄⠈⠉⠉⠀ ⠀⠀⠀⢀⠔⡡⠊⠀⢀⠔⠀⡰⢳⡀⠀⠀⢠⠎⠀⣼⢇⠀⠀⡠⠁⠀⢀⠔⠛⠀ ⠀⢀⠔⡡⠾⠔⠒⠒⠛⠒⠳⠆⡀⢏⠒⢤⡇⠀⢠⡇⠈⠤⢠⠁⠀⢠⠇⠀⣀⣱ ⠰⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢗⠺⢄⣠⠃⢡⠀⣀⣼⡈⢀⠋⠉⠉⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠤⣇⢀⢿⠋⠀⢸⡰⠎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢠⠃⣼⠀⠀⣼⠞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⡙⡙⠀⠚⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⡝⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢃⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⣶⣶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣦⠀⠀⠀ ⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⡀⠀ ⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⢠⣾⣿⣿⣦⠀⠀⢸⣿⣿⣷⠀ ⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⣿⣿⣿⣿⠃⠀⢸⣿⣿⣿⡄ ⠀⠈⠙⠿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠉⠛⠋⠁⠀⢀⣾⣿⣿⣿⡇ ⠀⣤⡀⠀⠀⠉⢛⡋⠉⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣿⣿⣿⣿⣿⠃ ⠀⢿⣿⣷⣦⡴⣿⣿⣿⣦⡀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀ ⠀⠈⢿⣿⣿⣇⠀⠈⠛⠟⠁⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀ ⠀⠀⠀⠻⣿⣿⣦⣄⣀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠲⣦⠀⠀⠀⠐⡍⠥⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣦⡀⠠⠛⣧⡀⣀⠐⢑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡄⠀⠀⠈⠣⡻⣿⠦⠐⠒⠚⠉⠣⠀⠀⠁⢕⢄⠀⠀⠀⠀⠀⠀⠀ ⠀⡠⡔⠒⠃⢣⢀⣀⠀⢠⢊⠆⠁⠀⠀⠀⢀⠀⠁⠀⠀⠀⠊⡘⠀⠀⠀⠀⠀⠀ ⢆⠠⠤⠀⠠⣦⣿⣿⣿⣾⣾⣁⡀⣀⡠⠀⢈⣈⡉⠃⠀⢠⡢⣚⡮⢖⢄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⡮⠔⣂⠡⣬⣤⣤⣴⣿⣿⣾⠁⠀⠙⢕⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⠓⠀⢊⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠁⠵ ⠀⠀⠀⠀⠀⢆⠀⠀⠀⣰⣿⣿⣿⣿⢤⠀⠸⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢷⣶⣾⣿⣿⣿⣿⠁⠀⣷⣦⣿⣷⣄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⡿⣿⡿⠀⢠⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠞⠇⠐⡊⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣤⣤⣴⣤⣶⣶⣶⣤⣾⣿⣦⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠟⠉⠉⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠛⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠑⠚⠉⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⠀⠀⠉⢦⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠉⠉⠛⠦⡄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡟⠉⠉⢉⠉⠛⠛⠛⠛⡇⠀⠀⠀⠀⠀⣼⠯⠤⠤⠤⠤⠤⣤⣤⣼⣇⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠛⠃⠀⣀⡴⠚⠉⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⡀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢀⡈⠙⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠙⠁⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡼⠋⠉⠛⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⠀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡞⠁⠀⠙⢲⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠁⠀⠀⠀⢀⣴⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡏⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠙⠛⠛⠋⠉⠁⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢯⣀⣀⣀⡀⠀⠀⣀⣀⣠⣴⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⣿⣿⣿⡿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡏⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⡴⠚⠛⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣙⣧⡀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣴⣿⣷⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⡠⠴⠒⠒⠈⠉⢁⣾⢿⡇⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠈⠙⠛⠻⠿⢿⣷⣶⣤⣄⣀⠀ ⠀⠀⠀⠀⠀⠀⣿⡇⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢿⣿ ⠀⠀⠀⠀⠀⠀⣿⠀⠘⢷⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠉⠛⠛⠛⠋⠻⣦⣀⣀⣀⣠⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⢿⣿⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⠻⢿⣿⣮⣻⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡅⠀⣉⣿⡇⣿⣻⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣷⠆⢴⣧⣗⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⡇⢀⣿⣛⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠈⢻⠾⣿⣟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⠋⠀⠀⠀⠀⡀⢱⠘⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⠿⠛⠁⠀⠀⠀⠀⠀⡀⠀⠀⠅⠈⢿⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⡈⠌⢻⣷⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠁⠀⠀⠀⠀⠀⣿⡌⠀⠈⠀ ⠀⠀⠀⠀⠀⣀⡀⠤⠤⠤⠀⠀⠀⢒⣒⠈⠁⠄⠀⠀⠀⠀⠀⠀⠀⣿⡧⡇⠀⠀ ⠀⠀⡠⠒⠉⠀⠀⠀⠀⠄⠂⠉⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⣰⣿⡇⠃⠀⠀ ⣠⠀⠄⠀⠒⠀⠀⠈⠉⠀⠉⠢⠀⠀⠀⠀⡀⠄⠈⠀⠀⠀⢀⣼⣿⡟⡈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠆⡀⠀⠀⠀⠀⢀⣴⣿⡿⢋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠐⠈⠉⠻⠫⠐⠁⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣷⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠟⠋⢉⣉⣁⣈⣉⠉⠛⠻⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣿⡿⠋⣠⣴⣾⣿⣿⣿⣿⣿⣿⣷⣦⡀⠙⢿⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⣿⠋⢠⣾⣿⡿⠛⠉⣁⣀⣀⣈⠉⠻⣿⣿⣦⡀⠻⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⠇⢠⣿⣿⠏⢀⣴⣿⣿⣿⣿⣿⣷⣦⠈⢻⣿⣷⡀⢻⣿⡆⠀⠀⠀ ⠀⠀⠀⣿⡿⠀⣾⣿⡏⢀⣿⣿⠏⠁⠀⠀⠈⠻⣿⣧⠀⢿⣿⣇⠈⣿⣿⠀⠀⠀ ⠀⠀⢸⣿⡇⠀⣿⣿⡇⢸⣿⣿⠀⠀⠀⠀⠀⠀⣉⣉⠀⢈⣉⣁⠀⣿⣿⠀⠀⠀ ⠀⠀⠈⣿⣿⠀⣿⣿⣇⠈⣿⣿⣆⡀⠀⠀⢀⣴⣿⡟⠀⣾⣿⡏⢀⣿⡿⠀⠀⠀ ⠀⠀⠀⢻⣿⡆⠘⣿⣿⣆⠈⠻⣿⣿⣶⣾⣿⡿⠟⢀⣼⣿⡿⠁⣼⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣄⠘⢿⣿⣷⣤⣀⣉⠉⠉⣉⣠⣴⣿⣿⠟⠁⣼⣿⡏⠀⠀⠀⠀ ⠀⢀⣴⣾⡿⣿⣿⣦⣄⠙⠻⢿⣿⣿⣿⣿⣿⣿⡿⠟⠁⣠⣾⣿⡿⢿⣶⣤⡀⠀ ⢺⣿⡟⠁⡶⡌⠻⣿⣿⣷⣦⣤⣀⣉⣉⣉⣉⣀⣤⣶⣿⣿⡿⠋⣠⡆⠈⣻⣿⡗ ⠀⠙⣿⣦⡑⠤⣦⢀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠁⢠⡲⠬⢁⣴⣿⠋⠀ ⠀⠀⠈⠻⣿⣦⣌⠚⠚⡰⣠⢀⢀⣉⡉⢉⣁⡀⢠⠄⡰⠥⠃⣡⣶⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠈⠙⠿⣿⣶⣬⣉⣙⠚⠹⠧⠼⠆⠀⣈⣉⣥⣶⣿⠿⠋⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠐⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⠀ ⠀⠸⡏⠙⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⠖⠋⣸⠃⠀ ⠀⠀⢻⠀⠀⠈⢳⡀⠀⠀⠀⢨⢢⠀⢠⠞⠁⠀⢠⡏⠀⠀ ⠀⠀⠈⣧⠀⠀⠀⢻⡀⡠⠔⠊⠀⢣⡏⠀⠀⠀⡾⠀⠀⠀ ⠀⠀⠀⠈⠓⠦⣴⣼⡏⠀⠀⠀⢠⣾⣤⣤⠶⠛⠁⢀⣿⠀ ⠀⠀⠀⠀⠀⣶⠟⢻⣿⣦⣀⣤⣾⣿⡏⠙⢲⠀⠀⣾⣿⡇ ⠀⠀⠀⠀⣸⠃⠀⢀⠀⢹⣿⣿⠃⢀⡇⠀⠘⣶⣶⣿⣿⠇ ⠀⠀⠀⠀⢰⠀⠀⠈⠻⣿⣯⣿⡿⠟⠁⠀⠀⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠙⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⣄⠀ ⠀⠀⠀⠀⠀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡟⠁⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣦⣴⣴⣤⣶⣤⣾⣿⣿⣿⣿⡁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⣿⠟⠋⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠺⠿⢿⣿⠏⠻⣿⡿⠿⠇⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠛⠉⣀⣀⠉⠻⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣶⣿⠋⢁⣠⣴⣾⠟⠿⣷⣦⣀⠈⠛⣿⣶⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⣀⣴⣾⠟⠋⢀⣿⣶⣿⠟⢋⡄⠀⠀⢨⡙⢻⣿⣶⣟⡈⠙⠻⣷⣤⡀⠀⠀ ⣴⡿⠟⠉⣀⣤⣾⡿⢿⣿⣿⣿⣿⡇⠀⠀⣾⣿⣿⣿⣿⡿⢿⣷⣤⣀⠉⠻⢷⣦ ⣿⡇⢰⣾⠿⠋⠁⢶⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣷⡦⠈⠛⢿⣷⠀⢸⣿ ⣿⡇⢸⣿⠀⠀⠀⠀⠙⠻⣿⣿⣿⠿⠀⠀⢿⣿⣿⣿⠟⠁⠀⠀⠀⢸⣿⠀⢸⣿ ⣿⡇⢸⣿⠀⣿⣶⣤⣀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠉⠀⠀⣀⣤⣶⣿⢸⣿⠀⢸⣿ ⣿⣇⣸⣿⣷⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣾⣿⣄⣸⣿ ⣿⡏⢹⣿⡿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⣿⠉⢹⣿ ⣿⡇⢸⣿⠀⣿⠿⠛⠉⠀⢀⣀⡀⠀⠀⠀⠀⢀⣀⠀⠈⠉⠛⠿⡇⢸⣿⠀⢸⣿ ⣿⡇⢸⣿⠀⠀⠀⠀⣠⣴⣿⣿⣿⣶⠀⠀⣾⣿⣿⣿⣦⡀⠀⠀⠀⢸⣿⠀⢸⣿ ⣿⡇⠸⢿⣦⣄⡀⠾⣿⣿⣿⣿⣿⡿⠀⠀⣿⣿⣿⣿⣿⡿⠗⢀⣠⣾⡿⠀⢸⣿ ⠻⣷⣦⣀⠉⠛⢿⣷⣾⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣷⣾⠿⠛⠁⣠⣴⡾⠟ ⠀⠀⠉⠛⢿⣦⣄⡈⣿⠿⣿⣦⣌⠃⠀⠀⢘⣡⣼⣿⠿⣯⢁⣠⣴⡿⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠿⣿⣄⡀⠙⠻⢿⣦⣶⡿⠟⠉⢀⣤⣿⠿⠋⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣷⣤⣀⠉⠁⣀⣴⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡝⠙⠻⣿⣫⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⡆⣤⡀⠙⢰⣌⠋⠉⠻⣿⣿⣿⣿⣿⣁⣥⣾⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⡿⣿⣷⠈⢣⢿⣿⣷⡈⠇⠃⠹⠁⠈⣭⣶⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣿⡄⣯⣰⡄⣜⣿⣿⠟⠃⠀⠀⢲⠀⢘⢹⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⡟⠿⠜⠑⡛⠈⢚⠛⠀⠀⣤⣄⠡⣿⠀⡇⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⡿⠛⢂⢠⣦⠀⠀⢴⣦⣶⣾⣿⣿⣇⣿⡇⣇⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⣿⢡⣶⣮⡻⡻⣧⣿⣿⠏⠉⠉⠻⣿⣿⣿⠃⢻⣿⣿⣿⣿⣿⣿⡇ ⢸⣿⣿⣿⣿⢡⣿⣿⣿⣯⣧⣿⣿⣿⣆⠀⠀⠀⠈⢿⠇⠀⢸⣿⣿⠟⢽⣿⣿⡇ ⢸⣿⣿⣇⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⡏⠠⢤⣀⠀⠁⢃⠄⠚⠋⣡⣶⡄⢠⣿⡇ ⢸⣿⣿⣿⡄⣾⣿⣿⣿⡿⠿⠿⣿⣿⡿⠂⠀⠈⠛⠂⠁⣰⣶⣶⣿⣿⡃⢿⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⡟⠁⠀⢂⠈⢊⢿⡇⠀⡗⠠⣀⣀⣴⣿⣿⣿⣿⣿⠃⢺⣿⡇ ⢸⣿⣿⣿⣿⣿⣿⣷⠀⠀⢈⠢⠠⠁⠃⠀⢱⣓⡂⠢⠉⠙⢻⣝⠛⣡⣾⣿⣿⡇ ⢸⣿⢿⣿⣿⣿⣿⣿⣧⣰⡅⠀⠁⠀⠀⠀⠀⠉⠛⣋⣀⣷⠞⣁⣾⡹⣿⣿⣿⡇ ⢸⣶⣶⣿⢿⣿⣿⣿⣿⣿⣍⠑⠠⣤⡗⠀⠀⢠⣾⣿⡟⣱⣾⣿⣿⡿⠿⠻⣻⡇ ⢸⣿⣿⣿⣧⣬⣭⣉⣶⣿⣿⣷⣶⣿⣷⣾⣉⣵⣿⣯⣾⣿⣿⣿⣿⣷⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⣿⣿⣿⡿⠛⢿⡿⠛⢻⣿⣿⣿⣿⡀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⢸⣷⣶⣾⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀ ⠀⢀⣤⣀⣾⣿⣿⣿⠟⠛⠛⠛⠛⠻⣿⣿⣿⣷⣀⣤⡀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⢸⣿⡟⢿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⡿⢻⣿⡇⠀ ⠀⢸⣿⡇⠈⠙⠛⢛⣿⣿⣤⣤⣿⣿⡛⠛⠋⠁⢸⣿⡇⠀ ⣤⣼⣿⣧⣤⡀⠀⠙⠛⠛⠛⠛⠛⠛⠋⠀⢀⣤⣼⣿⣧⣤ ⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛

⠀⠀⠀⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠀⠀⠀ ⠀⠀⠀⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠀⠀⠀ ⠀⠀⠀⠻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⠀⠀⠀ ⠀⠀⠀⣀⠈⠻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡟⠁⣀⠀⠀⠀ ⠀⠀⠀⣿⣦⡀⠘⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠋⢀⣴⣿⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣦⡀⠙⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠋⢀⣴⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠙⢿⣿⣿⣿⣦⡀⠙⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠋⢀⣴⣿⣿⣿⡿⠋⠀⠀⠀ ⠀⠀⠀⣤⡀⠹⣿⣿⣿⣿⣦⡀⠙⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠋⢀⣴⣿⣿⣿⣿⠏⢀⣤⠀⠀⠀ ⠀⠀⠀⣿⣿⣦⡈⠻⣿⣿⣿⣿⣦⡀⠙⢿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⠋⢀⣴⣿⣿⣿⣿⠟⢁⣴⣿⣿⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣦⡈⠻⣿⣿⣿⣿⣦⡀⠙⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠋⢀⣴⣿⣿⣿⣿⠟⢁⣴⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠈⠻⣿⣿⣿⣿⣆⠈⠻⣿⣿⣿⣿⣦⠈⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠁⣴⣿⣿⣿⣿⠟⢁⣴⣿⣿⣿⣿⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣄⠈⢿⣿⣿⣿⣧⠈⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠁⣼⣿⣿⣿⡿⠁⣠⣾⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⣤⣀⠙⢿⣿⣿⣿⣷⡀⢻⣿⣿⣿⣧⠈⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠁⣼⣿⣿⣿⡟⢀⣾⣿⣿⣿⡿⠋⣀⣤⣀⡀⠀⠀⠀ ⠀⠀⢠⣿⡟⠛⣿⣧⠀⠙⣿⣿⣿⣿⡄⢻⣿⣿⣿⡆⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⢰⣿⣿⣿⡟⢠⣿⣿⣿⣿⠋⠀⣾⡿⠛⢻⣷⡀⠀⠀ ⠀⠀⠈⢿⣷⣴⣿⠏⠀⠀⠘⣿⣿⣿⣷⠈⣿⣿⣿⣷⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠁⣾⣿⣿⣿⠁⣾⣿⣿⣿⠃⠀⠀⠻⣿⣦⣾⡿⠀⠀⠀ ⠀⣶⣄⣀⣉⣉⣁⣀⣀⠀⠀⢻⣿⣿⣿⡆⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣿⢠⣿⣿⣿⡟⠀⠀⣀⣀⣈⣉⣁⣀⣠⣾⠀ ⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⠀⢸⣿⣿⣿⣇⣿⣿⣿⣿⢠⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡄⣿⣿⣿⣿⣸⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⣿⣿⣿⠟⠀ ⢠⣄⠈⠙⠛⠛⠛⠛⠋⠁⠀⣿⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⡇⠀⣴⣿⠿⣿⣿⣿⡟⠃⠀⢸⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠙⠛⠛⠛⠛⠋⠁⢠⡄ ⠘⣿⣷⣶⣶⣶⣶⣶⣶⣆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠸⠿⣿⣿⣿⣿⣿⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢠⣶⣶⣶⣶⣶⣶⣾⣿⠇ ⠀⠈⠻⠿⠿⠿⠿⠿⠿⠏⠀⣿⣿⣿⣿⣿⣿⠁⠀⠀⠉⠻⠿⠟⠀⠀⠀⣸⣿⣿⣿⣿⣧⠀⠀⠀⠻⠿⠟⠉⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⠘⠿⠿⠿⠿⠿⠿⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠹⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⠏⢀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⠟⠀⠈⠻⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣴⣾⣿⣿⣿⣿⣿⠙⣿⣿⣷⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⠟⠁⠀⠻⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀ ⠀⠀⠴⠿⠿⠿⠟⠛⠉⠁⠀⣰⣶⣦⡀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⢀⣤⣶⣆⠀⠈⠉⠛⠻⠿⠿⠿⠦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠁⢀⣶⣤⡀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣠⣶⣿⣿⣿⡿⠟⠛⠉⢀⣤⣶⡄⠀⠻⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⢸⣿⡿⠃⠀⣶⣶⣤⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⣠⣶⣶⠀⠘⢿⣿⡇⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠻⠟⠋⠀⠀⣿⣿⣿⣿⣿⣿⠋⠙⣿⣿⠀⠀⠘⠻⠟⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠀⠀ ⠀⣼⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣧⠀ ⣸⣿⣿⣿⣿⣿⣿⣷⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⠿⠛⠋⠉⠉⠉⠛⠛⠻⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣿⣿⣿⣿⣿⣿⡆ ⢿⣿⣿⡏⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⢹⣿⣿⡟ ⠀⢩⣿⣿⣷⣦⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⡄⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣴⣾⣿⣿⡁⠀ ⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢠⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡄⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀ ⢰⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠛⠁⢠⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⠈⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⠈⠻⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⡿⠟⠁ ⠀⠀⠀⠈⠉⠉⢉⣿⣿⣿⣿⣿⣷⣦⣄⣉⠛⠛⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣠⣴⣾⣿⣿⣿⣿⣿⠉⠉⠉⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣷⣶⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⣶⣾⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⠀⣼⣿⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⢉⣁⡄⠀⣸⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠁⠀⣿⣿⡏⠀⢸⣿⣿⡇⠀⠉⢿⣿⠉⢹⣿⣿⠉⠉⣉⣉⣀⠀⢸⣿⣿⡆⠀⢿⣿⣿⠉⠘⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣶⣤⣄⣉⠁⠀⣸⣿⣿⠇⠀⣄⠀⠙⠀⢸⣿⣿⣦⣤⣄⣉⡉⠉⢻⣿⣿⡇⠀⠈⢉⣠⣤⣶⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣷⣿⣿⣿⣄⣀⣿⣷⣄⠀⢸⣿⣿⡀⠀⠉⣉⣁⣀⣸⣿⣿⣷⣶⣿⣿⠿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡉⠙⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⢉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣶⣶⣤⣤⣤⣄⣀⣀⣀⣈⣀⣀⣤⣤⣤⣴⣶⣶⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⣿⣿⠿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⢰⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⡚⡶⢾⢇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⣾⠟⢫⠀⠊⠈⢯⠙⣦⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣧⣤⠼⡿⠀⠀⠀⠀⠀⢀⣀⡁⠀⠀⠐⡃⠀⣚⠀⣾⣟⣷⣤ ⠀⠀⠀⣠⠖⢰⠃⠁⠈⡲⢾⣦⡀⠀⠀⠀⠘⠈⠙⢦⣀⣪⠴⠋⢸⠄⠘⢿⣿⠋ ⢀⣴⢿⢿⠀⡧⠀⠰⠄⠁⠀⠙⠈⠀⠀⠈⢀⡀⠀⠈⢾⡁⠀⠀⡘⠀⠀⠀⠀⠀ ⠻⣿⣿⠏⠀⡏⠳⣄⡢⠀⣠⠞⠛⢢⠐⠀⠘⠃⠀⠤⠜⠃⠀⢺⡟⠀⠀⠀⠀⠀ ⠀⠉⠁⠀⠀⢃⠀⠀⠙⣯⠃⠀⠀⠀⠂⠀⠐⠐⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢼⡦⠀⠰⠇⢀⠀⠸⠇⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⣀⠀⠀⠀⠀⣠⣴⡶⠿⠛⠛⠿⢶⣄⠀⠀⢀⣤⣴⡶⠶⠶⠶⣤⣤⡀⠀ ⢠⣾⠟⠛⠻⣷⣤⣾⠋⠁⠀⠀⠀⠀⠀⠀⠙⢷⣴⡿⠋⠀⠀⠀⠀⠀⠀⠙⣿⣆ ⣿⠃⠀⠀⠀⠘⡿⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢠⠀⠀⠀⠀⠀⠀⢸⣿ ⢻⣆⠀⠀⠀⠀⠀⣰⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣧⡀⠀⠀⠀⠀⣸⡟ ⠈⢿⣶⣤⣤⣤⣾⠟⠉⢻⣦⣄⡀⠀⠀⣀⣀⣀⣀⣤⡾⠃⠙⠿⠿⠶⠶⠟⠋⠀ ⠀⠀⠀⢩⣽⠁⠀⠀⠀⠀⠈⠛⠛⠿⠿⠛⠛⠛⠋⠉⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀ ⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⢸⣿⠀⣀⣀⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣀⡀⣿⡇⠀⠀⠀ ⠀⠀⠀⢸⣿⡟⠛⠛⠉⠉⠉⣠⠞⠛⠶⡄⢠⠖⠛⠻⣌⠉⠉⠛⠛⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⡼⠁⠀⣠⡀⢹⡟⢀⣤⠀⠈⢷⠀⠀⠀⣿⣷⠀⠀⠀ ⠀⠀⠀⠰⣿⡇⠀⠀⠀⢸⡇⠀⠀⠛⢁⡿⢷⡈⠛⠀⠀⢸⡇⠀⠀⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⣿⣇⠀⠀⠀⠈⠳⣤⣤⣤⠞⠁⠈⠳⣤⣤⣴⠞⠀⠀⠀⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠱⣶⣀⣀⣤⣴⡲⠛⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣆⠀⠀⠀⣠⣾⣿⠟⠋⠉⠉⠙⠿⣷⣆⠀⠀⠀⣸⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣦⣴⣿⣿⠃⠀⢠⣤⣤⠀⠀⠘⣿⣷⣠⣴⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣦⣤⣠⣿⣿⣤⣴⣶⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡦⠠⠂⠒⠒⠂⢤⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠠⢄⡊⡁⠀⠀⠀⡄⠀⠀⠀⠈⢆⠀⠀ ⣀⣎⠐⢄⠀⠀⠀⠀⠀⠀⠀⣇⡀⠠⠐⠀⠂⣀⡀⠀⢣⡈⠒⠁⠀⠀⠀⢸⠀⠀ ⠤⣈⢱⠐⣢⠀⠀⠀⠀⠀⠀⠂⡀⠐⡀⢀⠔⠒⠢⡀⠉⠀⠀⠀⠠⠀⢀⣘⠀⠀ ⢭⣙⠛⢡⠀⡆⠀⠀⠀⠀⠘⣄⣀⠤⠃⠀⠀⠃⠀⠰⠀⡀⠊⠀⠀⠀⠀⣠⠀⠀ ⠀⠀⢧⡀⠀⢠⠀⠀⠀⠀⠀⡏⠀⠀⣀⢌⠢⡤⠐⠁⠀⠐⣉⢇⡀⠤⠚⠁⠀⠀ ⠀⠀⠀⠙⠶⡀⠑⡤⡀⠀⢸⠀⠀⢰⠀⠀⠢⢀⣀⣀⠀⠀⢣⣉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠓⣤⠃⠈⠢⡘⠤⠤⠚⠀⢢⣖⣺⢿⠋⠀⠄⠘⡈⠓⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⢋⠈⠁⠀⠀⡠⠊⠉⠱⠾⠷⢾⠟⠛⠁⠀⡸⠀⠀⡇⠀⠀⠀⠢⣀⠀ ⠀⠀⠀⠀⠀⠓⢄⠀⠀⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⡠⠁⠀⠀⠀⠀⠀⠑ ⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠒⠣⢀⠀⠀⠀⣀⠤⠎⠉⠉⠁⢀⠀⠀⠀⢄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠉⠉⠁⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠑⢄⡀

⢀⣤⣶⣶⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣶⣶⣤⡀ ⠀⠀⠀⠈⠙⠛⠿⣿⣿⣷⣶⣶⠂⠀⠀⠀⠀⠐⣶⣶⣾⣿⣿⠿⠛⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⢿⡋⠀⠀⠀⠀⠀⠀⢙⡿⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣼⡇⠀⠀⠀⠀⠀⠀⢸⣦⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣹⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣏⣀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠈⡆⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⢹⡄⣼⣿⣸⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣧⡇⣿⢣⣿⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣿⣿⡟⣹⢧⡿⣵⣿⡆⣀⡀⠀⣀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⢏⣿⡟⣡⣿⣎⡼⣫⣟⣼⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⢀⠤⠒⠒⡺⠿⠿⡽⢹⣥⢸⣿⢹⢿⣿⣿⢟⣽⣿⡑⠆⡢⢼⣿⣿⡀⠀⠀⠀ ⢀⢼⠶⣿⡏⢻⣷⡄⠀⠚⠛⠚⠻⠇⠛⠛⠑⠛⠋⠈⢁⡌⠉⠉⠁⢀⣀⠈⢢⠀ ⣇⢿⡇⣿⡇⢀⣿⡇⡇⣀⣀⢀⠀⡀⡠⡀⣀⣄⢀⢤⢸⣇⡤⣄⣠⢈⢻⢀⠧⡀ ⠈⢹⠀⣿⡗⢾⣍⠀⡇⣥⣿⢸⡇⢿⡇⡁⠈⢹⣿⠀⢸⡧⣆⣿⣿⡼⡼⡸⠀⡜ ⠀⢸⠀⢿⡇⣸⣿⡇⣇⣉⡉⠀⠁⠀⠁⣁⣉⣈⣀⣁⣨⣥⣭⣥⣬⣤⢄⡇⠸⠀ ⠀⠸⠤⢼⡧⣤⣤⡥⣇⣶⡎⠿⢩⣏⠁⡀⣨⡆⣿⣿⣷⣽⣿⣿⣿⣿⠤⣃⡆⠀ ⠀⠀⠀⢸⠇⣿⣿⡇⡿⡻⣬⣭⣯⡍⢰⣧⣿⣶⣿⣿⡿⣲⣿⣿⣿⣿⢩⡴⠃⠀ ⠀⠀⠀⠸⠀⣿⣿⣿⢿⣤⣺⡝⢿⣧⣼⣿⣿⣿⣿⡿⣻⣿⡿⣿⣿⣿⠘⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⣿⣸⡿⡋⣾⢸⢹⣿⣿⣿⣿⣷⣝⡪⢉⡷⣿⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⡟⢾⡇⣿⢸⢿⣻⢹⣿⣟⠛⢿⣯⢳⢫⡔⣻⣥⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣿⣿⡸⠳⠿⠬⢾⣟⣾⢟⡅⣿⢸⠐⣭⣟⣛⡅⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣔⣕⣤⡦⣎⢽⢸⡇⣿⢘⣾⣿⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣍⡆⡆⢾⢸⢇⣵⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⣾⣶⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬛⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬛⬜⬜⬜⬛⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬛⬜⬛⬛⬛⬛⬛⬜⬛⬛⬛⬜⬛⬛⬛⬛⬛⬜⬛⬜⬜⬜⬜ ⬜⬜⬜⬛⬜⬛⬛⬛⬜⬛⬛⬛⬜⬜⬜⬛⬛⬛⬜⬛⬛⬛⬜⬛⬜⬜⬜ ⬜⬜⬛⬜⬛⬛⬛⬜⬜⬜⬛⬛⬛⬛⬛⬛⬛⬜⬜⬜⬛⬛⬛⬜⬛⬜⬜ ⬜⬛⬜⬛⬛⬜⬛⬛⬜⬛⬛⬜⬛⬜⬛⬜⬛⬛⬜⬛⬛⬜⬛⬛⬜⬛⬜ ⬛⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬛ ⬛⬜⬛⬜⬛⬛⬜⬛⬛⬜⬛⬜⬛⬜⬛⬛⬛⬜⬛⬛⬜⬛⬛⬜⬛⬜⬛ ⬛⬜⬛⬛⬛⬜⬛⬜⬛⬜⬛⬜⬛⬜⬛⬛⬛⬜⬛⬜⬛⬜⬛⬛⬛⬜⬛ ⬛⬜⬛⬜⬛⬜⬛⬜⬛⬜⬛⬜⬛⬜⬛⬜⬛⬜⬛⬜⬜⬜⬛⬜⬛⬜⬛ ⬛⬜⬛⬛⬛⬛⬜⬛⬛⬛⬜⬛⬛⬜⬛⬛⬜⬛⬛⬜⬛⬜⬛⬛⬛⬜⬛ ⬛⬜⬛⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬛⬜⬛ ⬛⬜⬛⬛⬛⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬛⬛⬛⬜⬛ ⬜⬛⬜⬛⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬛⬜⬛⬜ ⬜⬛⬜⬛⬜⬛⬛⬜⬜⬜⬛⬛⬛⬜⬛⬛⬛⬜⬜⬜⬛⬛⬜⬛⬜⬛⬜ ⬜⬛⬜⬛⬛⬛⬜⬜⬛⬛⬛⬛⬜⬜⬜⬛⬛⬛⬛⬜⬜⬛⬛⬛⬜⬛⬜ ⬜⬜⬛⬜⬛⬛⬜⬛⬛⬛⬜⬛⬛⬜⬛⬛⬜⬛⬛⬛⬜⬛⬛⬜⬛⬜⬜ ⬜⬜⬛⬜⬛⬛⬜⬜⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬜⬜⬛⬛⬜⬛⬜⬜ ⬜⬜⬜⬛⬜⬛⬛⬜⬜⬜⬛⬛⬜⬜⬜⬛⬛⬜⬜⬜⬛⬛⬜⬛⬜⬜⬜ ⬜⬜⬜⬛⬜⬛⬛⬛⬛⬛⬛⬜⬛⬛⬛⬜⬛⬛⬛⬛⬛⬛⬜⬛⬜⬜⬜ ⬜⬜⬜⬜⬛⬜⬛⬜⬛⬛⬜⬛⬜⬜⬜⬛⬜⬛⬛⬜⬛⬜⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬛⬜⬛⬛⬜⬛⬜⬛⬜⬜⬜⬛⬜⬛⬜⬛⬛⬜⬛⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬛⬜⬛⬛⬛⬜⬛⬜⬜⬜⬛⬜⬛⬛⬛⬜⬛⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬛⬜⬛⬛⬛⬜⬛⬛⬛⬜⬛⬛⬛⬜⬛⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬛⬜⬛⬜⬛⬜⬜⬜⬛⬜⬛⬜⬛⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬛⬜⬛⬛⬛⬜⬛⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬛⬛⬜⬛⬛⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬛⬛⬛⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬛⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜ ⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬛⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜⬜

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⣡⣿⣟⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣯⡟⣁⣨⣁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠉⠉⠛⠛⠀⠀⣠⠟⠛⠛⠿⠿⠶⠶⠶⣤⡍⠙⠋⠹⠿⠛⢫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣠⣴⣤⣴⣾⠃⠀⣴⣧⣤⣄⡤⠖⠋⠉⠉⠉⠛⠛⠀⠀⠀⠀⢀⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢠⠎⠉⠋⠁⢾⣷⣀⣀⣈⣡⠟⣻⠟⠻⣦⣴⣶⣶⣶⡄⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⢿⣿⠀⠀⣿⡦⠀⣠⣶⣿⡿⠟⢻⣏⣀⣼⣥⣶⢠⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣷⣾⣧⡞⠉⠟⠉⠀⠀⠘⢛⣿⡿⢁⡟⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣆⠃⠹⡟⠀⣠⠴⠚⠛⠳⣔⢿⣿⢁⡼⣵⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⢀⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠳⣄⢀⡼⠁⠀⣀⣀⠀⡿⠘⣿⣿⣾⠁⢀⡴⠶⢦⡀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣦⡈⠛⢀⣴⣿⣿⣿⢾⣧⠀⣸⠁⢿⠀⠀⢳⣀⠀⠉⠀⣸⡟⢿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣻⠿⠷⠎⠀⠉⠁⢠⣿⡿⠞⠁⢀⣈⣷⣄⡀⠈⠛⠓⣚⡿⠃⠀⠉⠻⢿⣿⣿⣿⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠹⣆⣀⣠⡀⣀⣴⣿⢿⡀⠀⠀⣿⢉⠉⢻⡙⣿⣿⣿⣿⣦⣤⣀⠀⠀⠀⠉⠛⠞⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠟⠁⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣶⣽⡄⠀⢻⡼⣇⣈⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠙⠶⠿⠶⠋⠛⠋⠉⣉⣿⣿⣿⣿⡿⢉⣷⡀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡟⢋⡿⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣋⣠⣾⣿⣿⣆⠈⣧⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⠟⠀⢸⠃⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠐⠛⢿⣆⡴⣄⠀⣤⣄⣾⠋⣻⠋⠀⠀⠉⠻⣿⣿⣿⣿⣿⣷⣸⡇⠀⣠⣄⡉⢻⣿⣿⣿⣿⣿⣿ ⣿⣿⡵⡄⠀⣿⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⡅⠀⠀⠀⠀⠀⠀⠀⠈⠙⢆⠈⠻⡃⠀⠉⠀⢻⡀⢠⡞⠛⢦⡘⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠙⣆⣿⣿⣿⣿⣿⣿ ⣿⡿⠀⡿⠀⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣡⣀⠀⢹⡄⠀⠀⣀⣤⣴⣶⣶⣾⣿⣿⣶⣾⣦⣄⡀⠈⣷⣸⣧⠀⢈⣿⡿⣿⣿⣿⣿⣿⣦⡈⠳⣄⣀⣹⡿⣝⠻⣿⣿⣿ ⣿⣧⣼⣣⣼⡥⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣳⣼⠗⠛⠋⠉⠈⠛⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠛⠛⠛⠋⠰⡜⣿⣿⣿⣿⡿⢿⣿⡟⢻⡍⠳⣌⠙⢾⣿⣿ ⣿⣿⣿⠁⠸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⢀⡤⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠳⡀⠀⢳⡘⢿⣿⣯⣤⣾⣿⣿⡄⠹⣦⣈⠳⢄⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠾⣥⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠙⠆⠀⠁⠈⢻⣿⣿⣿⣿⣿⣿⣆⣹⣿⣷⣾⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣯⣤⣤⣶⣏⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠹⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⣤⣀⣠⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⡏⠁⣾⠁⠀⣭⠀⢘⡏⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠤⠀⠀⠀⢠⠠⠕⠢⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠒⡢⠀⠁⢢⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⡀⠄⠢⠢⣀⠉⡄⠀⡀⠀⠀⠱⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⠀⠀⢷⠀⡈⡏⠉⣑⠂⠀⢡⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠠⠉⣉⡠⠀⡀⠀⠀⠰⠀⠉⠀⠀⠀⡆ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡛⠦⠄⢤⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⣀⡈⣦⣤⡜⠀⠀⠀⠀⠃ ⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠄⠨⠘⡆⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠆⠐⠃⠀⠀⢀⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡠⠓⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢀⡠⠂⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠊⠐⢦⡀⠈⠑⠢⠤⣔⣁⣈⡀⠀⠀⣀⡀⠜⠂⠁⠀⠀⠀⠀ ⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⢀⠜⢅⠀⡀⡀⠀⠀⠀⢠⢤⡤⠀ ⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⢀⣀⣠⠂⠀⠤⠙⠷⡳⠧⡠⠔⠁⠀⠀⠀ ⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠉⢹⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣾⠀⠀ ⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣶⡶⠶⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠶⢤⣤⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⣼⠀⢀⡏⠀⠀ ⠀⠀⠀⠀⣸⣿⣿⠟⠉⠉⠉⠉⢀⣠⣤⣴⠶⠛⠛⠛⠛⠛⠛⠛⠛⠿⠶⣦⣤⣄⣈⠉⠉⠙⠛⢿⣿⣷⡀⠀⠀⠀⡟⠀⢸⠃⠀⠀ ⠀⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠛⠻⠋⣁⣠⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣈⠙⢻⡷⠦⠀⠀⠀⣿⣿⡇⠀⠀⢸⡇⠀⣿⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣶⣅⠀⠀⠀⠀⢸⣿⡇⠀⠀⣼⠀⢠⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠃⠀⠀⣠⣾⣿⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣷⣄⠀⠀⠘⣿⠀⠀⢀⡟⠀⢸⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⣼⣿⣿⠟⠁⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠻⣿⣿⣧⠀⠀⣿⠀⠀⢸⠇⠀⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⢀⣿⣿⠏⠀⢠⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⡄⠀⠹⣿⣿⡇⠀⣿⠀⠀⣾⠀⢰⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠘⣿⣿⠀⠀⠈⢿⣿⣿⣿⠏⠀⣰⣾⣿⣿⣆⠀⠘⣿⣿⣿⡿⠃⠀⠀⣿⣿⡇⠀⣿⠀⢀⡏⠀⣼⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠟⠀⠀⠀⠉⠁⠀⠀⠀⢰⣿⣿⠃⠀⣿⠀⢸⠃⠀⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣿⠀⠀⠸⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠛⠲⠶⠖⠛⠁⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⠀⣿⣀⣾⠀⢸⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⡇⠀⠀⠀⠉⠻⢿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣿⣿⠿⠋⠀⠀⠀⣿⣿⣃⣀⣼⡄⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⣿⣶⣶⣶⣶⣾⣿⡿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀ ⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠉⠀⠀⠀⠙⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⢠⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡆⠈⠛⢿⡿⠟⠁⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡇⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡇⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠛⠛⠻⠿⠿⠿⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⣿⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⡴⠟⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⢶⡀⠀ ⠀⠀⠀⣼⠁⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠈⢷⠀ ⠀⠀⠀⡟⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⣿⠀⠀⠀⠀⠘⡇⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⢰⡇⠀⠀⠀⠀⢸⠇ ⠀⠀⠀⢻⡄⠀⠀⠀⠠⠷⠚⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠺⠧⠀⠀⠀⠀⡿⠀ ⠀⠀⠀⠈⣷⢀⠀⠀⠀⣀⣠⠤⠶⠒⠒⠒⠒⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀ ⠀⠀⠀⠀⣸⣃⡴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⣄⣀⠀⠀⠀⠀⠈⢯⠀⠀ ⠀⠀⠀⡼⠛⠁⠀⢀⠔⠂⢀⠔⠁⠀⢀⡠⠔⠊⠀⠀⠉⠙⠻⢶⣤⡀⠀⠘⣧⠀ ⠀⠀⡜⠁⠀⠀⢠⢋⡤⠺⠥⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠀⢸⡇ ⠀⢸⠃⠀⠀⠀⠘⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠈⣿ ⠀⠘⡇⠀⠀⠀⢀⡇⢰⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⣸⡇⢠⡿ ⠀⠀⢱⠀⠀⠀⢸⡀⠈⠉⠀⠀⠀⠀⢠⡀⠀⡀⠀⠀⠀⠀⠙⠁⠀⣠⡟⠀⣼⠃ ⠀⠀⢸⢀⡀⠀⢸⠿⣦⣄⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⣀⣤⡾⠋⢀⡼⠃⠀ ⠠⠴⠵⢪⠇⠀⢸⣦⣄⡙⠛⠷⢶⣦⣤⣤⣤⣤⣴⡶⠾⠛⠋⣁⣤⠾⠋⠀⠀⠀ ⠀⠀⠀⡞⠀⢀⣿⣶⠋⣹⠛⠳⣶⠦⠤⠤⠤⠤⢤⡶⠖⠚⣏⠻⣦⣄⠀⠀⠀⠀ ⠀⠀⢸⠁⣰⣿⣽⠁⣼⠃⠀⠀⠘⢦⣀⠀⠀⣠⡞⠁⠀⠀⠘⣆⠹⣽⢷⣄⡀⠀ ⠀⠀⣼⡷⠉⠀⢧⣾⠃⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠹⣦⠇⠈⠉⢹⡆ ⠀⠀⠸⡇⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣿⠁ ⠀⠀⠀⠻⢦⣤⣿⠛⠒⠶⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠶⠚⠻⣧⣤⠾⠋⠀ ⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣟⠫⣭⣙⣛⣛⣛⣛⣽⣯⣭⣉⣉⣉⣭⡭⠝⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⣶⣶⣶⡶⠶⠋⠹⠶⣶⣶⣶⡶⠶⠞⠃⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠉⠉⠉⠀⠀⠀⠀⣠⠴⠒⠚⠿⢭⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⢻⣿⣿⣿⣿⣇⠉⠉⠉⠁⣠⠖⠋⠉⠉⠛⠢⣄⠀⠀⠀⠀⢠⣞⣀⣤⣤⣤⣤⣤⣽⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⢹⣾⣿⣿⣿⣿⡿⢤⣀⣀⡾⠗⠒⠒⠒⠒⠒⠒⠛⣆⣠⠤⠤⣾⠀⠀⠀⢀⣤⠀⠀⠀⢸⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣙⣾⣿⣿⣿⣿⡟⠀⠀⠀⢹⡃⠀⠀⠰⡶⠀⠀⠀⠀⢸⠀⠀⠘⠛⠓⠲⠤⣄⠉⠀⠀⠀⣸⠁⠈⠉⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⢸⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡴⠃⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⣀⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⢀⣀⡤⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⢰⡃⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠉⠑⢦⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡟⠀⣴⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠓⠶⠖⠒⠋⠉⠉⠉⠀⠀⠉⠉⠛⠲⠦⢤⣀⡤⠞⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠇⠀⢿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⡤⠚⠙⠢⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠸⣷⣄⠀⠀⠀⠀⣹⣿⠛⠒⠒⠒⣶⡖⠒⠒⠒⠚⣏⠉⠁⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⢿⣿⣿⣷⣦⣴⣿⣿⣶⣤⣄⣰⣿⠃⠀⠀⠀⠀⠸⣄⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣀⣠⡤⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⠈⠙⠻⣿⣿⣿⣿⣿⣿⠿⠷⠖⠒⠒⠒⠒⠲⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠂⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⡀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠲⢤⡀⠀⠀⠀⠀⠀⠀⡼⠀⠈ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⢀⡼⠁⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⠊⠀⠀⠀⢀ ⠀⠀⠀⠀⢀⡟⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡀⠀⠀⠀⠀⠀⠀⡼⠃⣠⠞⠁⠀⠀⠀⣠⣿ ⠀⠀⠀⠀⢸⠁⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⠀⠀⠀⠀⣠⠎⠀⠙⠲⠤⢤⠤⠴⢊⡴⠊⠁⠀⠀⠀⢀⣾⣿⣿ ⠀⠀⣠⡾⢻⡄⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠋⠁⠀⠀⠀⠀⠀⣀⡤⠞⠉⠀⠀⠀⠀⢀⣴⣿⣿⣿⠿ ⢀⡴⠋⠀⣿⣷⡄⠀⠀⠀⠀⠈⠑⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠁⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠉⠀⠀ ⠋⠀⠀⢀⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⡏⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠔⠚⠉⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣴⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⣿⠁⠀⠙⢦⡀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠌⠳⢄⠀⠀⠀⢠⠤⣤⣖⠋⠉⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⢸⣷⣄⣠⣶⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⠙⢄⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠱⡄⢀⡿⠀⠀⠈⠓⢦⡀⠀⠀⠀⢿⣿⣷⣤⣤⣀⣸⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢠⣴⣶⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⠻⠛⢿⣿⡟⠁⣀⣀⡈⠹⣿⣄⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀⠀⣴⣿⠿⢿⣦⢀⠀⠀ ⠀⢀⣤⣶⣿⡏⠉⠛⣿⣶⣶⣿⠿⣿⣧⠀⠀⠀⠀⠀⣼⡿⠁⠀⢀⣴⣦⡿⠃⢸⣿⣿⡗⣠⣿⠿⣿⣿⣿⣶⣶⣦⠄⠀⠀⠀⢠⣿⠟⠻⣿⣶⣿⠇⣠⣾⡿⠿⣿⣆ ⢰⣿⡟⠙⠻⣷⣶⡄⠈⢻⡟⠁⣰⣿⠃⠀⠀⠀⢠⣤⣿⣷⡀⠀⠻⣿⣿⣷⣾⣿⣿⣿⣿⡿⠋⠀⠀⠀⠙⠛⠿⢿⣷⣄⠀⠀⠈⢿⣦⡀⠛⢿⣇⠸⣿⡃⢀⣴⣿⡏ ⠘⢿⣿⣦⣄⠿⠋⠀⣰⡿⠃⠀⢿⣷⡀⠀⢀⣴⣿⠿⠏⠻⢿⣶⣦⣶⣿⣿⠋⠀⠈⠻⣿⣿⡄⠀⠀⠀⠀⢶⣶⣤⣿⣿⡄⠀⠀⢀⣿⡇⠀⢸⡿⠀⠀⢿⠟⠉⣻⣿ ⣰⣿⠿⢿⠟⠀⠀⠀⠙⠁⠀⠀⢸⣿⣇⣴⡾⠟⢃⣀⠀⠀⠀⠀⠈⢹⣿⠇⠀⠀⠀⠀⢸⣿⡧⠀⠀⠀⠀⣠⣾⡿⣱⣿⡃⠀⣠⣿⠏⠀⠀⠟⠀⠀⢀⣴⣶⡾⠿⠋ ⢿⣿⣦⣤⣤⣦⡀⠀⠀⠀⠀⠀⠘⠿⣿⣿⡷⣰⣿⣋⣀⠀⠀⠀⠀⠸⣿⣧⡀⠀⠀⣠⣾⣿⠇⠀⣤⣤⣿⠟⠋⣀⣿⣿⢇⣾⡿⠃⠀⢴⣶⣤⣤⣶⡿⠟⠁⠀⠀⠀ ⠈⠙⠛⠛⠛⠻⢿⣿⡾⢿⣿⣿⡇⠀⢸⣿⡁⠻⠿⢿⣿⣶⣶⣦⣀⣄⣙⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⡟⠁⠀⢠⣿⡏⣡⣿⠟⠁⠀⠀⣴⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣄⡸⢿⣿⣷⡆⠀⠈⠉⠻⣿⣟⠛⠿⠿⠿⠿⠿⠛⠉⠛⠉⣿⡟⠀⠀⠀⣾⣿⣿⠟⠁⠀⠀⣠⣤⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⣀⠀⣿⣷⣶⣆⠀⠀⠘⢿⣷⣄⣀⠀⠀⠀⠀⠀⣠⣾⡟⠀⠀⣠⣾⣿⠋⠉⠀⢀⣠⣴⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣷⣮⡍⠙⠿⣿⣷⣤⣄⠉⠛⠿⠿⣶⣶⡿⠿⠟⠉⢀⣶⣾⡿⠛⠁⠀⣠⣴⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣷⣦⡈⠙⠻⣿⣷⣤⣦⣀⣤⣤⣠⣤⣶⣶⡿⠟⢁⠀⣠⣴⣾⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣷⣦⣌⣉⠉⠙⠻⠿⠟⠛⠛⠋⠁⠀⠀⠻⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣶⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⡀⠀⠀⠙⢿⣿⣦⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠻⠷⣶⣶⣦⣀⣠⣀⣀⣨⣿⣿⣦⠀⠀⠀⠹⣿⣧⣴⡿⠿⢿⣿⣷⣶⣦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡅⠀⠀⣼⣿⡿⠛⠛⠟⠛⠿⠟⠛⠙⣿⣷⡄⠀⠀⣨⣿⠏⠀⠀⢀⣿⡿⠉⢹⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⡀⢰⣿⠃⠀⠀⢴⣿⠟⠁⣠⣾⡿⢿⣶⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣸⣿⠀⠀⠀⠀⠈⠀⠀⠙⠋⠀⢸⣿⡗⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⢾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣿⣷⣄⠀⠀⠀⠙⠻⣷⣦⡀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡿⠛⠉⠉⠻⣿⣷⣴⠄⠀⠀⠈⢻⣿⡄⠀⠀⠀⠀⠀⠀⣿⣷⣀⢀⠀⠀⢀⣀⣠⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⣴⡾⠇⣠⡄⠀⠉⠁⠀⠀⠀⠀⣰⣿⡇⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⣷⣶⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠋⢀⣾⠟⠋⠀⠀⠀⠀⠀⣠⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣾⣿⡀⠀⢀⣀⣠⣶⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⠀⠀⠀⠀ ⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⠜⣦⠘⢿⣿⡄⠈⣿⡇⢠⡀⠀ ⠀⠀⠸⠀⢀⢀⠀⠀⢀⢀⢀⠾⠀⠀⠹⡇⠀⣿⠇⣾⡗⠀ ⠀⠀⣀⠀⢺⠃⠀⠀⠁⢿⠀⠁⠀⠀⠀⡇⢀⠟⣼⠏⣠⡇ ⠀⠀⠘⢷⣦⣤⣤⣥⣤⣴⣾⠇⠀⠀⠀⠀⠀⠈⠤⠞⣫⡄ ⠀⠀⠀⠀⢈⠉⠉⠉⣭⣭⣤⠀⣀⡀⠀⠀⠀⠀⠒⠛⠛⠁ ⠀⠀⢠⣾⣿⣷⣀⠀⠘⠿⠟⠀⠻⠿⡇⢰⣶⡔⠾⠟⠁⠀ ⠀⣀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀ ⢸⣿⣿⣶⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠛⠛⠛⠋⣁⣼⣿⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠻⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢸⡇⠀⠘⢿⣿⣷⡄⠀⠀⠀⠀⢸⣿⡿⠛⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⡆⠀⠀⢸⡇⠀⠀⠈⢻⣿⣿⣦⠀⠀⠀⣼⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢸⡇⢀⣤⣤⣀⢻⣿⣿⣧⠀⠀⣿⣿⡀⠤⡇⠀⢠⣴⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠋⠉⠀⠀⠀⠉⠻⣿⣿⡄⠀⡇⡼⠁⠀⠀⢙⣿⣿⣿⣷⣤⣿⣿⠀⠀⣇⣰⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⣴⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣄⠸⡇⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣦⠀⣿⣿⣿⣿⣿⣧⠀ ⠀⠀⠀⢀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⠛⠻⣿⣆⢳⣄⣴⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣧⣿⣿⣿⠉⠹⣿⠀ ⠀⠀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠘⢿⣎⢿⣿⣿⣿⣿⣿⡏⠘⠃⠘⣱⣿⣿⣿⣿⠇⠀⠀⣿⠀ ⠀⠀⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⠀⡀⠀⢀⢹⣿⣿⣿⡿⠀⠀⠀⣿⡆ ⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⢀⣠⣴⣶⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣤⣿⣾⡿⣿⣿⠇⠀⠀⠀⣿⠁ ⠀⣼⣿⠇⠀⠀⠀⠀⠀⠀⣴⠏⠀⢀⣠⣶⣿⡿⠛⢉⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣿⣿⠀⠀⠀⠀⣿⠀ ⠀⣿⡟⠀⠀⠀⠀⠀⢀⣼⠏⣠⣴⣿⡿⠛⠁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢀⣿⡇⠀⠀⠀⢰⣿⠀ ⢠⣿⠃⠀⣀⣠⣤⣤⣾⣿⣾⡿⠋⠁⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢧⡀⣼⣿⠀⠀⠀⠀⣸⡏⠀ ⢸⣿⣠⣾⣿⠿⠿⠿⢿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢻⣿⡏⠀⠀⠀⢀⣿⠇⠀ ⢸⡿⠛⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠛⠿⢿⣿⣿⡿⠋⠁⠀⠀⠀⢸⣿⣷⣦⠀⠀⣼⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠋⠀⠀⠀⢠⣿⡿⠋⠀⠀⠀⠀⠀⠀⠋⠉⠉⢿⡇⣸⡟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⣰⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠤⠼⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⣿⣿⡿⠿⣛⣩⣭⣶⣶⣶⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣤⣶⣆⡀ ⠀⠀⠀⠀⠀⠀⠘⢛⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⠹⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⠛⠛⢻⣿⣿⣃ ⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣿⣿⠋⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⣶⣾⣿⣿⣿⡟⠀⠀⠀⠀⢹⣿⣟ ⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠒⠚⠿⣿⢫⣥⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⣀⣾⡿⠋ ⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⣶⣶⣿⣿⣿⠟⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀ ⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⢸⣿⡿⢟⣩⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⢴⣿⣿⣿⣿⠇⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡟⣡⣾⣿⣷⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣿⣿⣿⣿⣿⣿⣿⣾⣌⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⣠⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠉⠛⠿⠿⠿⠟⠛⠉⠁⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⢀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⢋⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣁⣨⣴⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣫⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⣿⠿⠿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⡿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⢸⡏⢹⡇⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃⠘⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⣿⡏⠀⠀⢹⣿⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣦⣤⣤⣀⣀⣤⣤⣴⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⡾⢻⡇⠰⢿⡏⠉⠉⢹⡿⠆⢸⣿⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠟⠀⣿⣧⣤⣄⣤⡄⠀⣤⣴⣶⣾⣿⠈⢿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⡏⠀⠀⠉⠉⠘⠛⣹⡇⠀⣿⡛⠃⠈⠉⠀⠈⢿⣄⠀⠀⠀⠀ ⠀⠀⢀⣾⡟⠀⠀⠀⠀⢀⣴⠿⢻⣿⢸⣿⠛⢷⣄⠀⠀⠀⠸⣿⣷⡀⠀⠀ ⠀⢀⣿⣿⡇⠀⠀⠀⠀⣾⣯⡾⠛⣿⣼⡟⠻⣶⣿⡆⠀⠀⠀⣿⠙⣿⡀⠀ ⢀⣾⠃⣿⡇⠀⠀⠀⠀⠈⠉⠀⠀⢹⣿⡇⠀⠈⠉⠀⠀⠀⠀⣿⠀⠘⣷⡀ ⢸⡟⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⢻⡇ ⠘⠁⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠈⠃

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠿⣿⣦⠀⠀⣿⣿ ⣿⣿⠀⠀⣿⣿⣿⠀⠀⣿⣿⣿⣿⠀⠘⣿⣧⣀⣼⣿⠃⠀⣿⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⣿⣿ ⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⠿⣿⠀⠀⠀⣿⣿ ⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢂⠄⠄⠠⠀⡑⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⡀⠀⠀⡀⠀⣆⡐⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⡅⠀⠀⠀⠀⠀⡇⣀⢃⠠⡀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠒⠓⠄⢄⣀⠀⠀⠀⠱⡈⠂⠁⢀⡴⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⡥⠬⠁⡈⠆⠀⠀⠀⠀⢠⠑⠒⢂⡠⠃⠉⠂⢄⠀⠀⠀⠀⠀⠀ ⠀⠉⠒⠓⠢⠄⠒⠂⢸⠀⠸⠀⠘⠀⠀⣀⠀⠀⠀⠡⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡄⠀⠀⣿⡏⡔⢀⣼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡐⠂⠀⠡⠠⠼⠿⣬⣶⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠠⠤⠤⠤⣤⣴⡄⠨⡱⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⠟⠈⠻⠿⣿⣿⣿⣿⣧⣤⣤⣀⠀⠀⠀⠀ ⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣦⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀ ⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇ ⠸⣿⣿⣿⣿⣿⣿⣿⣯⠈⠉⢻⣿⣿⣿⣿⣶⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡏ ⠀⢻⣿⣿⣿⣿⣿⣿⣿⣶⣾⠋⢀⣤⣄⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣉⣁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀ ⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇ ⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀ ⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣶⣿⠿⠿⣿⡷⣦⡀⠀⠀⠀ ⠀⠀⠀⢘⣿⡿⠑⠢⠀⠈⠀⠌⢿⣦⠀⠀ ⠀⠀⠀⢸⡏⠀⠈⠉⠀⠀⠈⠁⠘⢿⠀⠀ ⠀⠀⢰⣾⡇⣀⡀⠀⠒⢄⡠⠀⣀⣸⠀⠀ ⠀⠀⢸⣿⣷⣿⣷⠀⠀⠀⠀⢠⣿⣿⡇⠀ ⠀⠀⢸⣿⣿⣿⣿⣆⠀⠀⠀⢻⣿⣿⣿⠀ ⠀⢀⣨⣿⣿⣿⣿⣿⣷⠀⣠⣿⣿⣿⣿⡄ ⢰⡿⠋⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟ ⢸⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀ ⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀