⠀⠀⠀⠀⠀⠀⠀⠀⠞⢉⠏⣀⣴⡠⢞⣝⡭⡡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢏⣴⣿⣭⣮⣎⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠱⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣱⠀⠀⠀⠀⠀⠀⠹⠁⠪⢊⣴⠟⣿⠟⠁⣠⠔⠂⠉⠉⠉⠫⢝⡃⢄⣶⠾⠥⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡼⠃⡴⡫⠔⠒⠂⡊⠉⠑⠂⣠⠛⢦⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠜⠀⠀⠀⠀⠀⠀⠀⣤⡠⠀⠀⠈⠀⡼⠀⠀⢠⣰⣾⢷⡜⣦⣿⣿⡆⢈⠃⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣦⢀⣷⠀⠀⠀⠀⠀⠀⢸⣻⡿⣼⡆⡀⠀⣧⢠⢠⣿⣟⠁⠀⠘⡧⠙⡏⠀⠀⡆⠀⢑⢄⣠⢂⢀⢱⣣⢶⣀⠀⡤⠀⡀⠀⠀⠀⠀⠀ ⡟⠸⠛⡄⠀⠀⠀⠀⠀⠟⠟⢿⣿⣷⣧⣀⣹⡌⣼⡟⢻⣦⠠⢾⣛⠛⣶⣰⠀⣇⣄⠀⠑⣥⣼⣾⡧⢟⣇⠩⣷⢿⣇⢣⠘⠸⠀⠀⠀ ⣷⣆⠂⡇⡀⠀⠀⠀⢸⢸⠀⢻⡞⣏⠙⠋⠁⠳⣼⣟⠒⢁⠀⠈⣑⢻⣻⡟⢠⡧⢉⢆⣀⢹⡧⠊⠀⠀⡀⠀⡿⣾⠀⠈⠉⢢⠀⠀⠀ ⣿⣿⡄⠃⠀⠀⢶⠀⢸⡸⢠⢸⢧⠟⡄⠀⠀⢠⣴⢹⡇⢸⣶⢶⡾⠇⢉⡧⡧⢷⠁⠘⠙⢽⠏⠀⢀⡜⠀⢰⢧⡿⢤⠀⠀⠀⢳⡀⠀ ⣿⣿⣿⣆⠀⠀⠸⡀⠀⢙⠾⢸⡀⢀⣸⣦⣼⣄⡇⠸⡏⠺⡏⠁⠀⡴⢛⡵⣇⣜⠀⠀⣧⡿⠀⢀⠎⠀⢀⣾⡿⠃⠀⠱⡄⠀⠀⠣⡀ ⢻⢛⢸⣿⣆⠀⠀⢳⠇⡎⠰⠟⣷⣟⣽⡯⠉⠿⢹⣦⠇⢢⢧⡤⠴⠋⠁⢸⠁⡸⠀⣠⣿⠃⠀⡖⠀⠀⠈⠉⠁⠀⠀⠀⠈⢆⠀⠀⠑ ⠊⠸⠘⡇⡸⣆⠀⢡⠘⠸⡄⡘⠛⢯⡱⠀⠀⠀⢺⢻⡶⢄⣫⣇⢤⡴⢁⠇⠈⠀⢩⣿⠏⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀ ⠀⠀⢟⢷⠀⠫⡢⡀⢣⠀⠱⠁⠀⠈⢢⡀⠀⠀⡇⢸⣻⣀⣀⡘⣠⢣⣃⣀⣀⣰⣿⠏⠀⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀ ⠀⠀⠈⠰⠃⠀⢝⢜⠌⢢⠀⠅⠀⠠⡀⠙⢄⠀⡆⠘⠿⠟⠛⠛⠿⠟⠛⠛⠻⢵⠏⠀⠀⢠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡇ ⠘⠀⠀⠀⠀⠘⢦⠃⠹⢆⠁⡀⡀⠄⠈⠢⣀⠑⠷⢄⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣠⠊⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃ ⠜⠃⠀⠀⠀⠀⠘⡔⢌⠢⡡⡈⠪⡻⠈⠢⠈⠳⣄⠄⠈⠏⠀⠉⠉⠁⠀⠀⠐⠒⠒⠈⠁⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂ ⠀⠀⠀⠀⠀⠀⠀⡽⡢⣀⢰⣌⠂⠉⠀⠀⠀⠀⠀⠁⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢄⠄⠀⠀⢨⢈⣪⠦⡛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⡮⡪⣢⠁⠈⠁⠌⠊⠂⠀⠀⠀⠀⠀⠀⠀⡴⠁⠘⣦⣄⠀⠀⣀⡀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢆⠀⠀⠈⠫⡀⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣢⠱⣄⡪⣻⡮⡊⠊⠂⠀⠀⠀⠀⠀⠀⠀⠀⣜⢷⣦⣄⣀⡀⠀⠀⠀⠀⢀⣀⣠⣤⠾⣛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣌⠻⣦⡊⠛⢮⡻⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⡿⠶⣯⣭⣽⣛⣛⣛⣫⣭⣭⣶⠞⠛⠉⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⢠⠳⣌⠻⣷⣤⠙⢶⣝⢦⡀⠀⠀⠓⠠⣠⠊⣠⠎⠀⠀⠀⡎⠉⠉⠉⡍⠉⠁⠀⠀⡇⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠨⡉⠚⢗⣌⡛⢿⣦⣙⠻⣮⢆⡀⢀⡔⢡⡞⠁⠀⠀⠀⢰⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠂⠀⠈⠫⠢⢍⣻⢕⡪⣆⠈⢸⣰⠋⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠘⢌⢢⠀⠀⠀⠀⠀⠀⠀⠀