⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢄⣂⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⢧⡇⢃⠎⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠨⠕⠉⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⣁⣤⠖⣠⢶⢸⡇⢸⠸⢡⠈⢄⠀⢳⣄⠀⠀⠀⠀⠀⠀⠒⠤⢀⡀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⡡⠔⣩⠖⣡⡶⠃⢸⣼⠃⠘⡄⢣⠆⠈⢣⠀⢡⡕⠤⡀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠨⠭⠀⠠⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⢞⠔⠉⣠⠞⣡⣼⡗⠀⠀⢸⣽⢸⠀⢧⠀⢻⡀⠀⢧⠀⢛⢦⡨⣒⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡢⠬⠑⠂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⠛⢁⡠⠊⢀⠴⢋⡟⠀⠀⠀⢨⡟⠈⡆⠸⡆⠀⢳⡄⠘⡆⠘⡄⠙⢮⢮⡙⠱⠠⣄⠀⠀⠀⠀⠀⠀⠀⠨⡂⣠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⣯⢾⡾⣛⠃⣮⠃⠀⠀⠀⢸⢇⡇⠹⡄⢻⡄⠀⠙⣄⣸⡄⢺⣶⣶⣷⣿⡒⢖⣤⠤⠀⠀⠀⠀⠀⠀⠀⠘⣾⡢⡀⠀⠀ ⠀⠠⣤⡴⠶⠛⠛⣫⣼⡇⢰⡟⢸⣶⠀⠀⠀⢀⣈⣸⣠⠀⢷⡀⢳⡀⠀⠈⠻⣣⠀⢃⣀⡀⠀⠙⢦⡈⠙⠳⠶⣤⣤⡤⠤⣤⣶⠟⢬⠪⢑⠀ ⠀⠜⠁⠀⣀⠔⣺⡟⢽⠁⢸⡇⡾⣸⣤⣴⣾⠿⠛⢻⡥⢆⠈⢷⣄⢳⡀⠀⢰⠝⣇⠘⡀⠀⢀⣀⠈⠉⠲⢄⠀⢸⠄⠀⠀⢣⠀⠀⠈⠣⡀⠑ ⣸⠀⡠⢊⣠⡾⠋⣇⢸⠀⣸⣷⡿⠟⠋⠁⡠⢔⣒⣒⣱⣙⣦⠀⠻⣦⡻⣆⡁⢴⣯⣿⣷⣚⣿⣿⣿⣿⣶⣦⣍⠺⢄⢤⠀⢶⠇⠀⢳⢄⠘⠆ ⠇⢙⣶⣽⡋⢀⣼⣿⢿⢼⠟⢣⡇⢀⠠⠚⠉⠀⢀⡀⠤⡻⣍⠳⢄⡈⡉⠁⠀⠙⢟⣿⣿⣿⣿⡿⠾⢿⣶⡶⠄⠀⣮⡎⡆⠈⢲⢿⡀⠱⡉⡲ ⣦⣪⠊⠀⠈⣾⣿⠂⢺⡄⠀⢈⣷⡁⢀⣠⣶⡟⣻⣿⣿⠗⠀⠉⠀⠀⠀⠀⠀⠀⠈⡼⠀⡇⠀⠁⠀⠀⠁⠀⠀⢰⠧⡇⣇⢠⡷⢯⣪⣭⡉⠭ ⢣⠏⢂⠀⠀⣿⡅⢰⢟⡇⠀⠀⣡⣾⣿⣁⢴⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡄⡇⠀⠀⠀⠀⠀⠀⠀⢸⢻⣥⢧⣿⢬⣹⠤⣻⠃⠀ ⡇⡀⢸⠀⢸⠀⢻⣿⠀⣿⡀⢸⠟⣯⡿⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⢸⢫⡾⣿⢿⡱⣇⣷⠃⠀⠀ ⠘⣇⠘⡄⠸⣀⣠⣹⢸⢛⢷⡀⠀⠀⣐⣬⢦⠀⠀⠀⠀⠀⠀⠀⠀⢄⡨⠃⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣾⢊⣽⠸⠀⢳⣌⡙⠤⣀⠀ ⠑⠚⢆⠱⡀⢹⣱⣿⠈⡎⡝⣷⠀⠰⣼⠻⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢸⠃⣸⠙⡇⠀⠘⠁⠈⠉⠉⠀ ⠄⠀⠀⠑⠛⠋⠙⢻⣆⠘⢦⣈⠢⣆⠁⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⣞⡇⠀⠀⠀⠀⠀⢠⠇⡀⣿⠴⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡟⠆⠀⡝⠮⣉⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣸⠀⠀⠀⠀⠀⣰⢫⣿⢧⠸⡀⠰⠀⠀⠀⢦⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⢰⡇⣰⣼⡇⠀⢠⠋⠟⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢀⠋⠀⠀⠀⢠⢞⢇⡞⢹⡏⢳⣝⢦⢆⠀⠀⠀⠉⠫⣒ ⠀⠀⠀⠀⠀⢀⣪⢎⠔⡏⠛⣧⠀⡇⠀⠘⡄⢫⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀⡴⢻⠪⠛⠀⠈⢻⡄⢧⠀⠈⢆⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠔⠻⠓⠁⠀⡇⡄⢱⡑⡇⠀⠀⠘⢦⡱⣄⡎⡗⠒⢤⣄⡀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⢸⠀⠀⠀⠀⠀⠈⠈⣆⠀⠈⠢⠄⣀⠀⠀ ⠀⢀⠔⠁⠀⠀⠀⠀⠀⠱⣇⠀⠑⠾⣤⡀⠀⠀⠈⠑⣇⠇⠀⢸⠀⠈⠉⠐⠒⠒⠒⠉⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀ ⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡸⠀⠀⠀⠀⠀⠀⠒⢒⠖⠒⠒⠒⠚⠁⢀⢻⠀⠀⠀⠀⠀⠀⠣⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⡈⠸⡀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀ ⠐⠈⠉⠉⠁⠀⠤⢀⠀⠉⠉⠐⠒⠒⠒⠒⠒⠒⠒⠂⢹⠁⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⢀⠃⠀⠑⡤⣀⣀⠀⠀⠀⠀⠀⠀⠉⠢ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠲⠤⠤⢐⣠⡄⡀⠀⠀⢐⠗⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠱⠀⠈⠉⠁⠒⢒⣒⣒⡒⠒