⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⡿⣝⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⢱⣽⣆⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡟⣇⡏⠀⠹⡄⠘⣧⡀⠀⣴⣶⣠⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⢳⠻⡆⠀⠀⢹⡄⢹⠻⣿⣿⣿⣿⣷⣦⣄⣀⣠⣤⣶⣿⣿⣷⣿⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⢸⣹⠛⠆⠀⠀⢷⣸⠀⢈⣀⣈⣿⣿⣷⡌⠻⣷⣿⣿⣿⠋⠀⡼⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⠸⡌⠧⣤⡀⣠⠟⢿⠀⠘⠛⣯⣽⣍⢿⣿⠀⣿⣿⣿⣇⢀⣴⢳⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣇⣳⣻⣥⠞⠁⠀⢈⣧⣶⣶⣿⣿⣿⡟⠛⠀⢿⣯⣼⣿⣀⣾⡟⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡶⠿⠟⢱⡚⢛⣦⣶⣿⣿⣯⣿⠈⢻⡯⡿⠀⢀⣾⣿⣿⣿⣿⣿⡦⢤⣤⣤⠴⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣏⡴⠂⣠⠶⣿⣿⠿⠈⢿⡿⢋⡞⠀⣸⡀⡇⠀⡞⣾⣟⡏⣏⢯⡀⠀⠀⠀⠀⣈⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⡋⢀⡞⣱⣻⣿⠀⠀⢰⠊⠉⢻⠤⢴⡏⠉⢷⠀⢿⣿⣿⢣⢿⣌⠻⣆⠀⢀⠎⢁⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⠀⠀⠀⠀⠀⠀ ⠀⣽⠁⠈⢻⠁⠋⣇⠀⢠⠇⠀⠀⢸⡇⣤⣀⠀⢿⣤⣄⣹⣟⣩⠤⡇⠳⣼⠀⡼⠐⠛⠚⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀ ⠀⢻⡀⠀⡏⣠⠖⠺⣶⠋⠀⠀⠀⠀⠳⣿⡿⠀⠈⢻⣿⠿⡋⠀⢠⡇⠀⣿⠞⠁⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡿⣓⠲⣌⢻⣤⣤⣸⣿⠀⠀⠀⠀⠀⠀ ⠀⠈⢳⣶⣿⠁⠀⠀⡌⠳⣤⡀⠀⠀⠀⠈⠛⡏⠓⢻⠴⠚⢁⣤⣿⡀⠀⣾⠀⠀⣀⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠻⣷⡼⠂⣸⣾⠵⣾⡿⠟⢶⡄⠀⠀⠀⠀ ⠀⠀⢸⡁⠹⠦⢦⣀⢻⣄⠹⣟⣿⣶⣤⣄⠀⠙⠒⣪⡴⢚⠋⠀⣿⣧⡼⠃⠀⠀⠀⠀⠈⠓⢛⣲⣄⠀⠀⢀⣀⡼⠦⣤⣠⠤⣤⠀⠀⠀⠉⢷⠀⠀⠀⠀⡿⣄⠀⠀⠀ ⠀⢀⡼⠓⣀⡤⠔⠻⠭⣍⠙⣫⠾⠋⠉⠉⠙⣿⠋⣁⣴⣾⡴⠟⣁⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⡾⠁⠀⠀⣿⣀⠙⠶⢋⡥⠖⢯⣄⠀⣀⠀⠘⣦⣤⣤⡞⠁⢸⠀⠀⠀ ⢀⡟⠀⡴⠁⠀⠀⠀⠀⠘⣶⠋⠀⢀⡀⠀⠸⣷⠞⣩⠝⠛⠉⠉⠉⠉⠉⠑⠢⢤⣠⠴⠋⠀⢸⡇⠀⣀⣼⢃⡼⣣⣤⡻⣄⣀⡤⠟⠋⣹⡇⠀⡼⠀⠀⡇⠀⠸⣦⡀⠀ ⠸⡇⠀⢧⠀⢻⡝⣆⠀⠀⡇⠀⢰⠋⠉⢷⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣸⡅⠙⢋⡞⠁⢀⡷⠈⣡⠖⠛⠙⣯⠐⡞⠁⢀⡼⠃⠀⠀⠈⢷⠀ ⠀⢻⣄⠀⠉⠉⢀⡟⠀⠀⢷⡀⠈⠂⠀⡼⢠⠏⢀⣀⣤⡤⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⢼⢿⡷⠛⢮⠓⢞⡽⠚⢳⢹⣄⣠⠴⠛⢹⡇⠀⢸⠇⠀⢰⠀⠀⢸⡇ ⠀⠀⠈⠛⠒⣾⣋⡄⠀⠀⠀⠙⠓⠒⠛⠁⣾⡞⠋⢻⣭⣇⡞⠓⢮⠙⢲⠦⢤⣤⢤⣴⠞⣹⣿⣶⢮⢳⢖⡫⠶⣼⡇⣀⡼⠀⣩⡴⠛⠛⣿⠁⣀⣞⡀⠀⡎⠀⣠⡞⠀ ⠀⠀⠀⠀⣠⡬⠿⠿⢤⣄⠀⢀⡀⠀⠀⠀⡟⣇⠀⣠⢥⢸⠀⣤⠞⢀⠯⣄⣠⢟⣀⠙⡿⣯⣾⣵⣫⢤⣾⣀⣠⠟⢹⡽⠚⠹⣼⡄⠀⠰⡗⠞⠉⠉⠙⠺⠧⣤⠟⠀⠀ ⠀⠀⣠⢾⡏⠀⠀⢀⠀⠉⠛⠛⠳⢤⣀⠀⣷⠘⢦⢿⣸⢟⣚⠁⢠⠏⣀⡀⠀⠛⠋⢀⡽⢿⣦⢿⣀⣤⣇⢩⠖⠋⡇⣧⠀⢀⡏⠧⠖⠚⢹⠦⢤⡀⠀⠀⠀⢸⡆⠀⠀ ⠀⣰⠃⠘⣧⢖⡿⣏⣠⠆⠀⠀⠀⢀⡇⠀⢹⡗⢮⢳⡀⠘⠛⣰⠟⠋⢯⣩⢙⣒⣚⣿⣿⣄⣿⢧⣰⡋⣹⠜⣦⠤⠇⢘⣺⣭⡀⡴⠒⣺⠋⠀⠀⣹⡄⠀⠀⡾⠁⠀⠀ ⠀⡟⢦⡞⡽⣿⡿⠛⠳⢦⣤⣤⣴⠞⣹⣆⠀⢻⡼⠀⠙⠤⠚⢹⡄⣠⣾⣿⡿⠿⠿⣿⣿⣿⣿⠶⠋⢩⠭⡄⡖⠋⢹⣿⠀⠀⡗⣿⣰⠏⠀⠀⠞⠉⢹⡆⠀⣿⠀⠀⠀ ⠀⠻⣬⣿⡿⠟⠁⠀⣰⣿⣩⠿⠓⠚⠁⠙⡆⢸⡗⠀⠀⠀⢀⣴⠟⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣧⣹⡴⣷⢷⠒⢿⣼⡖⠚⣧⢿⠛⠲⣤⠖⣦⢳⣾⣡⡴⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠋⠉⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢠⠟⠉⠛⡇⣠⣾⣿⡿⣀⣤⣴⣿⡿⠻⣷⣶⣾⢁⣛⣖⠋⣩⣭⣭⡉⣬⣍⣉⣽⠛⢁⣼⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⡏⠀⠀⠀⢳⡙⢿⠃⢾⣿⣿⣿⣋⡑⣶⣾⣿⣟⡾⠷⣿⠾⠓⠲⠯⣾⠓⢲⣻⠏⠀⢻⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣀⡀⠀⠀⠀⠀⣇⠀⠀⠀⣷⠀⠀⠀⠀⠙⢤⣀⠀⣽⣿⢿⣿⣿⣿⠟⠻⡷⠀⠀⠀⠀⠀⠀⠀⠘⠓⠋⠘⠷⠴⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⢞⡯⠉⣉⠍⠉⠛⠓⠶⠤⣿⠀⠀⠀⠈⣷⣄⣀⠀⠀⠀⢨⠟⠉⢿⣿⣿⣦⣷⣶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣏⡏⣰⣋⣀⣠⢴⣶⠶⢶⡶⢣⠖⠀⡄⠸⡷⡶⠋⡹⠋⠛⡾⢧⣀⣤⣾⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⠯⠭⠷⠤⠴⠛⠀⠀⣾⣀⣇⣀⣀⣇⣀⡟⣷⣤⣧⣤⣤⣷⣶⡿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠒⠛⠉⠉⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀