⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡻⡒⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⡚⠉⠉⠀⢠⠀⠀⠈⠁⠌⡣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢮⣶⠞⠁⡠⠄⡊⡄⢸⡆⠀⠀⠈⣆⠀⠹⠭⠗⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⣴⢎⢖⢽⠃⠃⠈⣼⡄⠀⢄⢹⣆⠀⠀⠙⢦⣭⡓⢤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢃⡰⠋⢠⢣⡿⡏⠀⠸⡄⣿⢳⣄⠀⠑⢯⣄⠀⠀⠀⢻⡎⠙⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⡞⠀⠀⢾⣿⠟⡇⡇⠀⠱⣧⠟⠻⡾⡶⣤⣈⣑⡦⠄⡀⢣⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢻⡇⢧⢀⡿⠋⠁⣷⡁⠀⡄⡏⠐⠢⣇⣧⣿⡀⠇⠀⡀⡵⡈⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣼⡖⢸⣸⠁⠀⠀⢻⢣⠀⢰⡇⠀⠀⣷⠈⡾⢰⢸⠀⣧⡇⣧⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠭⣾⢱⠈⡏⠓⢲⣯⣞⠂⢣⣸⣇⣀⣴⣧⣴⡇⠀⣿⢸⠿⡇⢧⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣷⣭⠛⠋⠉⠉⠀⠀⠉⠈⠛⢶⣦⡼⢀⡞⠛⡞⠁⢹⠒⠓⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⡷⣼⡈⠛⠋⠀⢰⡒⠒⡖⠐⠝⢆⢼⠵⣋⡷⡷⠁⣠⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡽⠋⡰⣾⣻⣦⡀⠀⠀⢳⢠⠇⠀⠀⠠⣾⢯⡙⡟⣷⣮⢻⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣔⡚⣥⠔⠚⣇⡿⣿⡟⠈⢳⣦⣬⣭⣤⡤⠒⣎⣘⢆⢧⠳⢫⡛⠧⣽⢻⣛⣛⣛⣥⢆⡓ ⠀⠀⣠⠤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣣⢣⠈⢸⡇⣿⠁⡄⢸⣿⣿⠿⡿⠀⢄⣀⣀⣠⣤⣴⢾⡼⠒⠨⠭⢥⣬⣿⡉⣚⡿ ⢀⠎⢀⣴⣽⠟⠁⠀⠀⠀⠀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⢨⠃⠈⠳⢌⣷⡘⢰⠀⠈⡝⣧⠀⡇⠤⠤⢸⣽⡼⠛⢿⣸⡷⢶⣄⠀⠀⠫⢖⢷⡊⡝ ⢸⣰⣷⣟⢷⣄⡠⠤⠤⠴⢎⣩⡏⢠⢋⣑⣯⣑⣦⡀⠀⠈⠀⠀⠀⠀⣠⠇⡯⠣⡀⢱⡹⡦⡧⠄⣂⢹⡿⠁⠀⠀⢻⡇⠀⠙⠷⠞⠳⣦⡑⣽⡓ ⠸⣽⠏⠉⠉⠉⠉⠉⠙⠓⠭⣓⢣⠊⡜⠁⣖⠋⠁⡹⠦⣀⣀⡀⣠⣾⠃⢰⠁⠇⠈⠓⣻⠃⢃⣀⠠⠼⡇⠀⠀⢀⡀⢿⠀⠀⠀⠀⠀⠘⢷⡘⣃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠢⠤⠬⠲⣯⡇⠀⠈⢻⣋⢿⠣⣀⠈⠂⢸⠀⡼⠁⢠⢻⠤⠤⠚⡇⢀⣰⡍⠀⣾⣦⣤⣄⣀⣀⣀⣘⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⠀⢀⣿⢸⠂⠈⠑⠀⠀⡟⠁⢀⢇⣼⠀⠀⠀⢻⣯⠀⠀⠀⣿⢷⣦⣬⣭⣭⣭⣏⣽⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣞⠎⢾⠀⠀⠀⠀⠀⡇⢀⣼⣿⣿⢀⣠⣴⠟⠉⣤⠄⠒⣿⡈⠉⠉⢉⣿⠟⢻⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠎⣘⠃⠀⠀⠀⠀⠀⠁⠸⡿⣿⡿⠟⠋⢁⣠⠶⡧⠊⣠⣿⣇⣠⡶⠋⣠⣶⢿⠉⣸ ⠀⠀⠀⠀⠀⢰⠛⠛⠛⠟⠛⠛⡀⠀⠀⠀⠀⠀⠸⣿⡿⡙⠸⣃⣀⣀⡀⠀⠀⢠⣾⣿⣷⠼⢦⡄⠾⠋⠁⠀⠙⣯⠞⠉⣷⠁⣴⡿⠋⠁⠸⡇⢸ ⡀⠠⠤⠤⠄⢸⠤⠤⠤⢤⡾⠦⡇⣀⠠⠤⢐⡺⠶⠘⡣⠅⡄⠛⣓⣦⠙⠨⠵⢻⢟⠻⠿⣆⠈⠳⡀⠀⠀⠀⢀⠏⣤⣦⣿⡄⣿⣷⠀⠀⣤⡇⠈ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⣏⣶⡚⠟⢻⣗⣢⠬⠶⢠⣭⣠⣩⠥⣀⠴⠶⠌⢊⠂⠀⠘⢦⡄⡼⢄⢀⣤⣾⣿⣿⣿⣿⣧⣿⡟⠀⠀⣿⠀⣿ ⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⠀⡇⠈⠑⣒⣽⢟⡰⠖⠉⠉⠥⠚⠛⠛⠚⠲⠒⢘⣿⡒⢴⣒⠮⣉⣁⢉⣉⠼⠛⡄⠀⠈⠉⠛⠫⢄⡀⠀⢻⠀⣿ ⠳⣔⠒⣲⣦⡤⣍⣐⠒⠲⠟⠊⠁⠀⡞⠡⢀⢱⢒⣒⡶⠶⠶⠲⠒⠒⠒⠲⢦⣽⣿⣪⠋⠀⠉⠉⠀⠀⠈⠉⠁⠳⣀⠀⣠⡤⠶⠶⠮⣵⣷⣦⡸ ⣧⣿⣧⡙⣿⣿⣿⣧⡹⢷⡤⢄⡀⠀⠈⠲⢤⣌⣉⡓⠒⠒⠒⠒⠒⠒⠒⠛⢒⣹⣿⡆⠀⠀⡼⠋⠓⡤⢀⠄⠀⠀⣿⡿⢋⡝⠣⢀⣀⣀⢈⡗⠙ ⣿⠋⣻⣧⡹⣿⣿⡟⡅⠘⢌⡓⣌⡒⢄⡀⠀⠀⠈⣉⡹⡿⠿⠿⠿⢛⡛⠛⠋⠉⠙⢿⣀⢛⢑⠤⠤⢏⡁⠀⠀⠔⠉⠀⡿⠯⢿⣷⣶⠭⢿⠁⠀